{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":52709,"title":"Easy Sequences 19: Length of Prime-sided Rectangle with Maximum Area","description":"A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\r\n                                       \r\nGiven an area limit 'n', find the length (i.e. the longer side if sides are unequal) of the prime-sided rectangle, with the largest area less than or equal to 'n'. \r\nIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u003c 100. No other combination of prime sides will produce an area greater than 95 for area \u003c= 100.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 492px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 318px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                       \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"390\" height=\"312\" style=\"vertical-align: baseline;width: 390px;height: 312px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; text-decoration: underline; text-decoration-line: underline; \"\u003earea limit\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e 'n', find the length\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e (i.e. the longer side if sides are unequal) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eof the prime-sided rectangle, with the largest area less than or equal to 'n'. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u0026lt; 100. No other combination of prime sides will produce an area greater than 95 for area \u0026lt;= 100.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function length = maxPrimeRec(n)\r\n    l \u003e= w; % l is the larger side\r\n    isprime(l) == 1; isprime(w) == 1; % both sides are primes\r\n    l*w \u003c= n; % area should be less than or equal to n\r\n    length = 'l such that l*w is the largest area possible';\r\nend","test_suite":"%%\r\nn = 25;\r\nl_correct = 5;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = 100;\r\nl_correct = 19;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nns = 1000:10000;\r\nls = arrayfun(@(n) maxPrimeRec(n),ns);\r\nys = [sum(ls) ls(7500:7529)];\r\nys_correct = [10870381 2833 2833 2833 2833 773 773 773 4253 181 181 127 127 2837 2837 ... \r\n    2837 2837 2837 2837 2837 4259 1217 1217 1217 4261 4261 4261 4261 4261 4261 4261];\r\nassert(isequal(ys,ys_correct))\r\n%%\r\nn = 1000000;\r\nl_correct = 1321;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = 100000000;\r\nl_correct = 77101;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax);\r\nl_correct = 715827881;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax)*109 - 1000000009;\r\nl_correct = 7574033;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax)*109 + 1000000009;\r\nl_correct = 2156657959;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax-1)*1111;\r\nl_correct = 9920021;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nfiletext = fileread('maxPrimeRec.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2021-09-15T07:53:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-14T21:01:26.000Z","updated_at":"2026-02-24T12:09:19.000Z","published_at":"2021-09-15T07:53:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"312\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"390\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003earea limit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 'n', find the length\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e. the longer side if sides are unequal) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eof the prime-sided rectangle, with the largest area less than or equal to 'n'. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u0026lt; 100. No other combination of prime sides will produce an area greater than 95 for area \u0026lt;= 100.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3098,"title":"Scrabble Scores - 13","description":"This problem integrates components of \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11 Scrabble Scores - 11\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Scrabble Scores - 12\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\r\n\r\nRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\r\n\r\nYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\r\n\r\n * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\r\n\r\nThe center multiplier square will be left blank, since it's already covered by a tile.\r\n\r\nRelated problems:\r\n\r\nPrevious problem: 12 - \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Word score optimization (first word)\u003e.","description_html":"\u003cp\u003eThis problem integrates components of \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11\"\u003eScrabble Scores - 11\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eScrabble Scores - 12\u003c/a\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\u003c/p\u003e\u003cp\u003eRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/p\u003e\u003cp\u003eYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\u003c/p\u003e\u003cpre\u003e * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\u003c/pre\u003e\u003cp\u003eThe center multiplier square will be left blank, since it's already covered by a tile.\u003c/p\u003e\u003cp\u003eRelated problems:\u003c/p\u003e\u003cp\u003ePrevious problem: 12 - \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eWord score optimization (first word)\u003c/a\u003e.\u003c/p\u003e","function_template":"function [score,max_word] = scrabble_scores_13(words,mult,first_word)\r\n\r\nscore = 0;\r\nmax_word = {''};\r\n\r\nend","test_suite":"%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 39;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T'];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 30;\r\nmax_word_corr = {'maltha'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = [' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T '];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 45;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'thinning'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'eodnirl'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'diner','doter','droit','drone','elint','eloin','enrol','ident','idler','indol','inert','inlet','inter','intro','irone','lento','lined','liner','lirot','liter','litre','loden','loner','nerol','niter','nitre','nitro','noted','noter','oiled','oiler','olden','older','oldie','olein','oriel','redon','relit','reoil','riled','ronde','teind','teloi','tenor','tilde','tiled','tiler','tined','tired','toile','toled','tondi','toned','toner','trend','tried','trine','triol','trode','trone','dentil','dinero','dotier','editor','entoil','indole','ironed','linted','linter','loiter','neroli','norite','orient','retold','rident','rioted','rodent','roiled','rondel','tinder','tirled','toiled','toiler','tonier','trined','triode','lentoid','retinol','tendril','trindle'};\r\nwords{2} = {'dhole','diner','drone','eloin','enrol','helio','heron','hider','hired','holed','honed','honer','horde','idler','indol','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','rhino','riled','ronde','dehorn','dinero','heroin','hinder','hoiden','holden','holder','holier','hondle','honied','horned','indole','ironed','neroli','roiled','rondel','hordein','inholder'};\r\nwords{3} = {'diner','drone','eloin','enrol','idler','indie','indol','indri','iodin','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','riled','ronde','dinero','indole','inlier','iodine','ironed','linier','neroli','oilier','roiled','rondel'};\r\nwords{4} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{5} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{6} = {'diner','drone','eloin','enrol','idler','indie','indol','indri','iodin','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','riled','ronde','dinero','indole','inlier','iodine','ironed','linier','neroli','oilier','roiled','rondel'};\r\nwords{7} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{8} = {'deign','diner','dinge','dingo','dirge','dogie','doing','drone','eloin','enrol','gelid','genro','geoid','giron','glide','goner','gored','gride','grind','groin','idler','indol','ingle','irone','liger','lined','liner','lingo','loden','lodge','login','loner','longe','nerol','ogled','ogler','oiled','oiler','olden','older','oldie','olein','oriel','redon','reign','renig','reoil','ridge','riled','ronde','dinero','dinger','dingle','doling','dongle','eloign','engild','engird','eringo','gilder','girdle','girned','glider','golden','golder','ignore','indole','ironed','legion','linger','lodger','logier','longed','longer','neroli','reding','regild','region','ridgel','ringed','roiled','rondel','eroding','glenoid','gloried','godlier','groined','ignored','lording','negroid','redoing'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';'   D       D   ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n\t\tmax_score_corr = 33;\r\n\t\tmax_word_corr = {'godlier'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   '];\r\n\t\tmax_score_corr = 16;\r\n\t\tmax_word_corr = {'indole','iodine','ironed','endrin','linden'};\r\n\tcase 3\r\n\t\tmult = ['T   d     d   T';' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T '];\r\n\t\tmax_score_corr = 45;\r\n\t\tmax_word_corr = {'hordein'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'novels'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'dmvxeao'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'ad','ae','am','an','ax','da','de','do','ed','em','en','ex','ma','me','mo','na','ne','no','od','oe','om','on','ox','ado','and','ane','ave','avo','axe','dam','dan','den','dev','dex','doe','dom','don','emo','end','eon','mad','mae','man','max','med','men','moa','mod','mon','nae','nam','nav','nod','nom','oda','ode','oma','one','ova','van','vex','voe','vox','aeon','amen','axed','axon','dame','damn','dean','demo','deva','dome','dona','done','dove','exam','exon','made','mane','mano','mead','mean','mend','meno','moan','mode','move','moxa','name','nave','nema','node','noma','nome','nova','odea','omen','oven','oxen','vane','vena','vend','admen','amend','anode','axmen','axone','daven','demon','devon','doven','maned','maven','maxed','menad','monad','monde','moved','named','nomad','novae','vaned','venom','daemon','moaned'};\r\nwords{2} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dev','dex','doe','dom','emo','mad','mae','max','med','moa','mod','moo','oda','ode','oma','ova','oxo','vex','voe','vox','axed','dame','demo','deva','dome','doom','dove','exam','made','mead','mode','mood','move','moxa','odea','maxed','mooed','moved'};\r\nwords{3} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dev','dex','doe','dom','emo','mad','mae','max','med','moa','mod','oda','ode','oma','ova','vav','vex','voe','vox','axed','dame','demo','deva','dome','dove','exam','made','mead','mode','move','moxa','odea','maxed','moved'};\r\nwords{4} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dee','dev','dex','doe','dom','eme','emo','eve','mad','mae','max','med','moa','mod','oda','ode','oma','ova','vee','vex','voe','vox','axed','dame','deem','deme','demo','deva','dome','dove','eave','exam','exed','made','mead','meed','mode','move','moxa','odea','adeem','deave','eaved','edema','evade','maxed','moved','vexed','oedema'};\r\nwords{5} = {'ad','ae','al','am','ax','da','de','do','ed','el','em','ex','la','lo','ma','me','mo','od','oe','om','ox','ado','ale','ave','avo','axe','dal','dam','del','dev','dex','doe','dol','dom','eld','elm','emo','lad','lam','lav','lax','lea','led','lev','lex','lox','mad','mae','max','med','mel','moa','mod','mol','oda','ode','old','ole','oma','ova','vex','voe','vox','alme','aloe','axed','axel','axle','dale','dame','deal','demo','deva','dole','dome','dove','exam','lade','lame','lave','lead','leva','levo','load','loam','lode','love','made','male','mead','meal','meld','mode','mola','mold','mole','move','moxa','odea','olde','olea','oval','vale','veal','vela','veld','vole','amole','axled','dolma','domal','laevo','lamed','laved','loved','loxed','maxed','medal','modal','model','moved','voled','voxel','loamed'};\r\nwords{6} = {'ad','ae','am','as','ax','da','de','do','ed','em','es','ex','ma','me','mo','od','oe','om','os','ox','so','ado','ads','ave','avo','axe','dam','das','dev','dex','doe','dom','dos','eds','emo','ems','mad','mae','mas','max','med','moa','mod','mos','oda','ode','ods','oes','oma','oms','ose','ova','sad','sae','sax','sea','sev','sex','sod','som','sox','vas','vex','voe','vox','ados','aves','avos','axed','axes','dame','dams','demo','deva','devs','does','dome','doms','dosa','dose','dove','emos','exam','made','mads','maes','mead','meds','mesa','moas','mode','mods','move','moxa','odas','odea','odes','omas','oxes','sade','same','save','seam','soda','soma','some','vase','voes','dames','demos','devas','domes','doves','exams','maxed','maxes','meads','modes','moved','moves','moxas','oaves','saved','soave','vadose','vamose','vamosed'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';'   D       D   ';' D   t   t   D '];\r\n\t\tmax_score_corr = 37;\r\n\t\tmax_word_corr = {'vox'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  '];\r\n\t\tmax_score_corr = 25;\r\n\t\tmax_word_corr = {'vox'};\r\n\tcase 3\r\n\t\tmult = [' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D'];\r\n\t\tmax_score_corr = 35;\r\n\t\tmax_word_corr = {'voxel'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'zoologist'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aehcmdi'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aced','ache','acid','acme','adze','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cazh','cedi','chad','chai','cham','chem','chez','chia','chid','dace','dame','daze','dice','dime','each','emic','hade','haed','haem','hame','haze','head','hide','hied','iced','idea','idem','mace','mach','made','maid','maze','mead','mech','mica','mice','zeda','ached','aimed','amice','amide','azide','chide','chime','demic','hazed','hemic','maced','mache','maize','mazed','media','medic','miche','chimed','haemic','miched','zaideh'};\r\nwords{2} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{3} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{4} = {'aced','ache','acid','acme','ahed','ahem','aide','alec','alme','amid','amie','cade','cadi','caid','calm','came','cami','cedi','ceil','chad','chai','cham','chem','chia','chid','clad','clam','dace','dahl','dale','dame','deal','deil','deli','dhal','dial','dice','diel','dime','each','elhi','emic','hade','haed','haem','hail','hale','halm','hame','head','heal','heil','held','helm','hide','hied','hila','iced','idea','idem','idle','ilea','lace','lade','laic','laid','lame','lead','lech','lice','lich','lied','lima','lime','mace','mach','made','maid','mail','male','mead','meal','mech','meld','mica','mice','mild','mile','ached','ailed','aimed','alcid','almeh','amice','amide','camel','chela','chide','chiel','child','chile','chime','clade','claim','clime','decal','demic','email','haled','halid','hemal','hemic','ideal','ileac','laced','laich','lamed','leach','limed','maced','mache','macle','maile','malic','medal','media','medic','melic','miche','milch','calmed','chield','childe','chimed','chimla','haemic','hailed','halide','heliac','hiemal','lamedh','macled','mailed','malice','medial','miched','camelid','claimed','decimal','declaim','medical'};\r\nwords{5} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{6} = {'aced','ache','acid','acme','aged','ahed','ahem','aide','amid','amie','cade','cadi','cage','caid','came','cami','cedi','chad','chai','cham','chem','chia','chid','dace','dame','dice','dime','each','egad','emic','gach','gadi','gaed','game','gied','hade','haed','haem','hame','head','hide','hied','iced','idea','idem','mace','mach','made','mage','magi','maid','mead','mech','mega','mica','mice','ached','aimed','amice','amide','cadge','caged','chide','chime','demic','gamed','gamic','hemic','image','maced','mache','magic','media','medic','miche','midge','chimed','degami','gached','haemic','imaged','miched'};\r\nwords{7} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cedi','chad','chai','cham','chem','chia','chid','dace','dame','dice','dime','each','emic','hade','haed','haem','hame','head','hide','hied','iced','idea','idem','imid','mace','mach','made','maid','mead','mech','mica','mice','midi','ached','aimed','amice','amici','amide','chide','chime','demic','hemic','imide','maced','mache','media','medic','medii','miche','amidic','chimed','haemic','miched'};\r\nwords{8} = {'aced','aces','ache','acid','acme','ahed','ahem','ahis','aide','aids','aims','amid','amie','amis','asci','cade','cadi','cads','caid','came','cami','cams','case','cash','cedi','chad','chai','cham','chem','chia','chid','chis','dace','dahs','dais','dame','dams','dash','desi','dice','dies','dime','dims','disc','dish','each','edhs','emic','hade','haed','haem','haes','hame','hams','head','hems','hide','hied','hies','hims','iced','ices','ichs','idea','idem','ides','mace','mach','macs','made','mads','maes','maid','mash','mead','mech','meds','mesa','mesh','mica','mice','mics','mids','mise','sade','sadi','said','same','scad','scam','seam','semi','shad','sham','shea','shed','shim','sice','side','sidh','sima','ached','aches','acids','acmes','aides','aimed','amice','amide','amids','amies','asdic','ashed','aside','cades','cadis','caids','cames','camis','cased','cedis','chads','chais','chams','chase','chasm','chems','chias','chide','chime','daces','dames','dashi','deash','deism','demic','deshi','dices','dimes','disme','emics','hades','haems','hames','heads','hemic','hides','ideas','maced','maces','mache','machs','maids','meads','mechs','media','medic','mesic','micas','miche','sadhe','saice','shade','shame','shied','sidhe','amices','amides','camise','cashed','chaise','chased','chiasm','chides','chimed','chimes','emdash','haemic','maches','mashed','mashie','medias','medics','miched','miches','sachem','samech','schema','shamed','simcha','chamise','chasmed'};\r\nwords{9} = {'aced','ache','acid','acme','adit','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cate','cedi','chad','chai','cham','chat','chem','chia','chid','chit','cite','dace','dame','date','dice','diet','dime','dita','dite','each','eath','echt','edit','emic','emit','etch','etic','hade','haed','haem','haet','hame','hate','head','heat','hide','hied','iced','idea','idem','itch','item','mace','mach','made','maid','mate','math','mead','meat','mech','meta','meth','mica','mice','mite','tace','tach','tame','team','tech','thae','them','tide','tied','time','ached','acted','admit','aimed','aitch','amice','amide','cadet','cheat','chide','chime','cited','death','demic','demit','dicta','ditch','edict','ethic','hated','hemic','maced','mache','match','mated','media','medic','miche','tache','tamed','teach','theca','timed','chimed','dacite','detach','haemic','itched','miched','hematic','matched'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';' d   T   T   d ';'   D       D   ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n\t\tmax_score_corr = 117;\r\n\t\tmax_word_corr = {'haemoid'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T'];\r\n\t\tmax_score_corr = 28;\r\n\t\tmax_word_corr = {'medico'};\r\n\tcase 3\r\n\t\tmult = ['T   d     d   T';' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T ';'T   d     d   T'];\r\n\t\tmax_score_corr = 63;\r\n\t\tmax_word_corr = {'decimal'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2015-03-20T18:02:10.000Z","rescore_all_solutions":false,"group_id":40,"created_at":"2015-03-20T01:53:26.000Z","updated_at":"2026-04-02T20:22:25.000Z","published_at":"2015-03-20T01:53:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem integrates components of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eScrabble Scores - 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eScrabble Scores - 12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ * D: double word\\n * T: triple word\\n * Q: quadruple word\\n * d: double letter\\n * t: triple letter\\n * q: quadruple letter]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe center multiplier square will be left blank, since it's already covered by a tile.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 12 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWord score optimization (first word)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42580,"title":"Conic equation","description":"A conic of revolution (around the |z| axis) can be defined by the equation\r\n\r\n   s^2 – 2*R*z + (k+1)*z^2 = 0\r\n\r\nwhere |s^2=x^2+y^2|, |R| is the vertex radius of curvature, and |k| is the conic constant: |k\u003c-1| for a hyperbola, |k=-1| for a parabola, |-1\u003ck\u003c0| for a tall ellipse, |k=0| for a sphere, and |k\u003e0| for a short ellipse.\r\n\r\nWrite a function |z=conic(s,R,k)| to calculate height |z| as a function of radius |s| for given |R| and |k|.  Choose the branch of the solution that gives |z=s^2/(2*R)+...| for small values of |s|.  This defines a concave surface for |R\u003e0| and a convex surface for |R\u003c0|.  \r\n\r\nThe trick is to get full machine precision for all values of |s| and |R|.  The test suite will require a relative error less than |4*eps|, where |eps| is the machine precision.\r\n\r\nHint (added 2015/09/03): the straightforward solution is \r\n\r\n   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \r\n\r\nbut this does not work if |k=-1|, gives the wrong branch of the solution if |R\u003c0|, and is subject to severe roundoff error if |s^2| is small compared to |R^2|.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\r\n","description_html":"\u003cp\u003eA conic of revolution (around the \u003ctt\u003ez\u003c/tt\u003e axis) can be defined by the equation\u003c/p\u003e\u003cpre\u003e   s^2 – 2*R*z + (k+1)*z^2 = 0\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003es^2=x^2+y^2\u003c/tt\u003e, \u003ctt\u003eR\u003c/tt\u003e is the vertex radius of curvature, and \u003ctt\u003ek\u003c/tt\u003e is the conic constant: \u003ctt\u003ek\u0026lt;-1\u003c/tt\u003e for a hyperbola, \u003ctt\u003ek=-1\u003c/tt\u003e for a parabola, \u003ctt\u003e-1\u0026lt;k\u0026lt;0\u003c/tt\u003e for a tall ellipse, \u003ctt\u003ek=0\u003c/tt\u003e for a sphere, and \u003ctt\u003ek\u0026gt;0\u003c/tt\u003e for a short ellipse.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003ez=conic(s,R,k)\u003c/tt\u003e to calculate height \u003ctt\u003ez\u003c/tt\u003e as a function of radius \u003ctt\u003es\u003c/tt\u003e for given \u003ctt\u003eR\u003c/tt\u003e and \u003ctt\u003ek\u003c/tt\u003e.  Choose the branch of the solution that gives \u003ctt\u003ez=s^2/(2*R)+...\u003c/tt\u003e for small values of \u003ctt\u003es\u003c/tt\u003e.  This defines a concave surface for \u003ctt\u003eR\u0026gt;0\u003c/tt\u003e and a convex surface for \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eThe trick is to get full machine precision for all values of \u003ctt\u003es\u003c/tt\u003e and \u003ctt\u003eR\u003c/tt\u003e.  The test suite will require a relative error less than \u003ctt\u003e4*eps\u003c/tt\u003e, where \u003ctt\u003eeps\u003c/tt\u003e is the machine precision.\u003c/p\u003e\u003cp\u003eHint (added 2015/09/03): the straightforward solution is\u003c/p\u003e\u003cpre\u003e   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \u003c/pre\u003e\u003cp\u003ebut this does not work if \u003ctt\u003ek=-1\u003c/tt\u003e, gives the wrong branch of the solution if \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e, and is subject to severe roundoff error if \u003ctt\u003es^2\u003c/tt\u003e is small compared to \u003ctt\u003eR^2\u003c/tt\u003e.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/p\u003e","function_template":"function z=conic(s,R,k)\r\nz=0;\r\nend","test_suite":"%%\r\nR=5;\r\nk=-1;\r\ns=-5:5;\r\nz=[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=-5;\r\nk=-1;\r\ns=-5:5;\r\nz=-[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6;\r\nk=0;\r\ns=0:0.125:2;\r\nz=[0 0.001302224649086391 0.005210595859100573 ...\r\n   0.01173021649825800 0.02086962844930099 ...\r\n   0.03264086885999461 0.04705955010467117 ...\r\n   0.06414496470811713 0.08392021690038396 ...\r\n   0.1064123829368584 0.1316527028472488 ...\r\n   0.1596768068881667 0.1905249806888747 ...\r\n   0.2242424739260392 0.2608798583755018 ...\r\n   0.3004934424110011 0.3431457505076198];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6800;\r\nk=-2;\r\ns=10.^(-9:9);\r\nz=[7.352941176470588e-23 7.352941176470588e-21 ...\r\n   7.352941176470588e-19 7.352941176470588e-17 ...\r\n   7.352941176470588e-15 7.352941176470588e-13 ...\r\n   7.352941176470548e-11 7.352941176466613e-9 ...\r\n   7.352941176073046e-7 0.00007352941136716365 ...\r\n   0.007352937201052538 0.7352543677216725 ...\r\n   73.13611097583313 5292.973166264779 93430.93334894173 ...\r\n   993223.1197327390 9.993202311999733e6 9.99932002312e7 ...\r\n   9.9999320002312e8];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=exp(1);\r\nk=pi;\r\ns=10.^(-7:0);\r\nz=[1.839397205857214e-15 1.839397205857469e-13 ...\r\n   1.839397205882986e-11 1.839397208434684e-09 ...\r\n   1.839397463604480e-07 0.00001839422981299153 ...\r\n   0.001841981926630790 0.2212216213343403];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nt=fileread('conic.m');\r\nassert(isempty(findstr(t,'roots')))\r\nassert(isempty(findstr(t,'fzero')))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":245,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":37,"created_at":"2015-08-26T21:39:35.000Z","updated_at":"2026-04-08T11:17:23.000Z","published_at":"2015-08-26T22:21:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA conic of revolution (around the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e axis) can be defined by the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   s^2 – 2*R*z + (k+1)*z^2 = 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2=x^2+y^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the vertex radius of curvature, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the conic constant:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026lt;-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a hyperbola,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a parabola,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1\u0026lt;k\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a tall ellipse,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a sphere, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a short ellipse.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=conic(s,R,k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to calculate height\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of radius\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Choose the branch of the solution that gives\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=s^2/(2*R)+...\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for small values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This defines a concave surface for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a convex surface for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe trick is to get full machine precision for all values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The test suite will require a relative error less than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4*eps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the machine precision.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint (added 2015/09/03): the straightforward solution is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1),]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut this does not work if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, gives the wrong branch of the solution if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and is subject to severe roundoff error if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is small compared to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44779,"title":"Don't be mean.  Be nice!","description":"For this problem, you will be given a range of single digits R, and a separate number K.  You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\r\n\r\nFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4.  The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\r\n\r\nIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\r\n\r\n* 120\r\n* 210\r\n* 201\r\n* 102\r\n\r\nbut not 012 or 021 for the purposes of this calculation.\r\n\r\nYou can assume that R will always have at least K digits, and there will be no repeating digits in R.","description_html":"\u003cp\u003eFor this problem, you will be given a range of single digits R, and a separate number K.  You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\u003c/p\u003e\u003cp\u003eFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4.  The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\u003c/p\u003e\u003cp\u003eIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\u003c/p\u003e\u003cul\u003e\u003cli\u003e120\u003c/li\u003e\u003cli\u003e210\u003c/li\u003e\u003cli\u003e201\u003c/li\u003e\u003cli\u003e102\u003c/li\u003e\u003c/ul\u003e\u003cp\u003ebut not 012 or 021 for the purposes of this calculation.\u003c/p\u003e\u003cp\u003eYou can assume that R will always have at least K digits, and there will be no repeating digits in R.\u003c/p\u003e","function_template":"function y = dont_be_mean(R,k)\r\n  y = k.^R;\r\nend","test_suite":"%%\r\nR=1:4;k=2;y_correct = 27.5;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=0:8;k=3;y_correct = 493.3125;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=[1 2 4 6 8];k=4;y_correct = 4666.2;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=[2 8 6 7 4 5];k=1;y_correct = 5.33333333333333;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=0:9;\r\ny=0;\r\nfor k=1:8\r\n    y=y+dont_be_mean(R,k);\r\nend\r\ny_correct=61042519.44444444;\r\nassert(abs(y-y_correct)\u003c1e-3)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":68,"created_at":"2018-11-07T18:32:08.000Z","updated_at":"2026-04-09T15:34:44.000Z","published_at":"2018-11-07T18:32:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, you will be given a range of single digits R, and a separate number K. You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4. The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e201\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e102\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut not 012 or 021 for the purposes of this calculation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can assume that R will always have at least K digits, and there will be no repeating digits in R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1187,"title":"Knave in the middle attack","description":"This is a Matlab adaptation of the \u003chttp://en.wikipedia.org/wiki/Knights_and_Knaves Knights and Knaves\u003e logical puzzles, mixed with the famous \u003chttp://en.wikipedia.org/wiki/Man-in-the-middle_attack man-in-the-middle attack\u003e in computer security. \r\n\r\nYou are in an island where all inhabitants are either _Knights_, who always tell the truth, or _Knaves_, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.  \r\n\r\n*Details:*\r\n\r\nYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function _function answer=F(question)_ takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question; _true_ means 'yes' and _false_ means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\r\n\r\n* *A*: Islander's type. A is a logical variable: true for a Knight, false for a Knave\r\n* *X*: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g. _x\u003e1_).\r\n* *F*: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\r\n\r\nThe function handles associated with a Knight and a Knave look, respectively, something like:\r\n\r\n  function answer = Knight(question)\r\n    A = true;\r\n    X = @(x)x\u003e10;\r\n    F = @Knight;\r\n    answer = eval(question);\r\n  end\r\n\r\n  function answer = Knave(question)\r\n    A = false;\r\n    X = @(x)x\u003e10;\r\n    F = @Knave;\r\n    answer = ~eval(question);\r\n  end\r\n\r\nOf course the values of X will be different and unknown to you.\r\n\r\nA few examples:\r\n\r\n Knight('A==true') == true\r\n\r\nThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question. \r\n\r\n Knave('A|X(1)') == true\r\n\r\nThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\r\n\r\n Knave('F(''A'')') == false\r\n\r\nThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\r\n\r\nYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\r\n\r\n your_function(@Knight,str) should return Knave(str)\r\n your_function(@Knave,str) should return Knight(str)\r\n\r\nYour function might query the function handle of the islander with whatever questions it sees fit before responding.\r\n\r\n*Examples:*\r\n\r\n your_function(@Knight,'A==true') == true;\r\n\r\n your_function(@Knave,'A==true') == true; \r\n\r\nThis question asks whether the islander is a Knight; both Knights and Knaves would respond _true_ to this question.\r\n\r\n your_function(@Knight,'F(''A==true'')==true') == false; \r\n\r\n your_function (@Knave,'F(''A==true'')==true') == true; \r\n\r\nThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\r\n\r\n your_function(@Knight,'X(3)~=X(2)') == true\r\n\r\n your_function(@Knave,'X(3)~=X(2)') == false \r\n\r\n(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 914.5px; vertical-align: baseline; perspective-origin: 332px 914.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis is a Matlab adaptation of the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Knights_and_Knaves\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKnights and Knaves\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e logical puzzles, mixed with the famous\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Man-in-the-middle_attack\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eman-in-the-middle attack\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in computer security.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 94.5px; white-space: pre-wrap; perspective-origin: 309px 94.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are in an island where all inhabitants are either\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eKnights\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, who always tell the truth, or\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eKnaves\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eDetails:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 52.5px; white-space: pre-wrap; perspective-origin: 309px 52.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efunction answer=F(question)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e means 'yes' and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efalse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 50px; perspective-origin: 316px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: Islander's type. A is a logical variable: true for a Knight, false for a Knave\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u0026gt;1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function handles associated with a Knight and a Knave look, respectively, something like:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 130px; perspective-origin: 329px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003eanswer = Knight(question)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  A = true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  X = @(x)x\u0026gt;10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  F = @Knight;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  answer = eval(question);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003eanswer = Knave(question)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  A = false;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  X = @(x)x\u0026gt;10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  F = @Knave;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  answer = ~eval(question);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eOf course the values of X will be different and unknown to you.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA few examples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knight(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knave(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A|X(1)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knave(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A'')'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,str) should \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn Knave(str)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,str) should \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn Knight(str)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour function might query the function handle of the islander with whatever questions it sees fit before responding.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight; both Knights and Knaves would respond\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e to this question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A==true'')==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function (@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A==true'')==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; perspective-origin: 309px 31.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'X(3)~=X(2)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'X(3)~=X(2)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 52.5px; white-space: pre-wrap; perspective-origin: 309px 52.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function answer = AnswerGenerator(F,str)\r\n  answer=F(str);\r\nend","test_suite":"%%\r\n% Ask a Knight whether 4 is prime\r\n% (he will respond false; your function should respond true)\r\nA=true; X=@isprime; str='X(4)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knave whether 4 is prime \r\n% (he will respond true; your function should respond false)\r\nA=false; X=@isprime; str='X(4)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% Ask a Knight whether he is a Knight \r\n% (both Knights and Knaves would respond true and so should your function)\r\nA=true; X=@isprime; str='A==true';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knave whether he is a Knight \r\n% (both Knights and Knaves would respond true and so should your function)\r\nA=false; X=@isprime; str='A==true';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knight whether he would respond affirmatively to the question of whether he is a Knight\r\n% (a Knave would respond false to this same question, and so should your function)\r\n% A=true; X=@isprime; str='F(''A==true'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% Ask a Knave whether he would respond affirmatively to the question of whether he is a Knight\r\n% (a Knight would respond true to this same question, and so should your function)\r\n% A=false; X=@isprime; str='F(''A==true'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=true; X=@isprime; str='diff(X(2:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=false; X=@isprime; str='diff(X(2:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=true; X=@isprime; str='A==X(6)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=false; X=@isprime; str='A==X(6)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=true; X=@isprime; str='A\u0026any(X(1:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=false; X=@isprime; str='A\u0026any(X(1:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% A=true; X=@(x)rem(x,2); str='F(''F(''''X(3)'''')'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% A=false; X=@(x)rem(x,2); str='F(''F(''''X(3)'''')'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),true))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":14,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2020-09-29T00:03:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-07T22:12:02.000Z","updated_at":"2026-04-15T04:00:57.000Z","published_at":"2013-01-08T03:23:02.000Z","restored_at":"2017-11-13T15:02:29.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a Matlab adaptation of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Knights_and_Knaves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKnights and Knaves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e logical puzzles, mixed with the famous\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Man-in-the-middle_attack\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eman-in-the-middle attack\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in computer security.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are in an island where all inhabitants are either\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKnights\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, who always tell the truth, or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKnaves\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction answer=F(question)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means 'yes' and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Islander's type. A is a logical variable: true for a Knight, false for a Knave\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function handles associated with a Knight and a Knave look, respectively, something like:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function answer = Knight(question)\\n  A = true;\\n  X = @(x)x\u003e10;\\n  F = @Knight;\\n  answer = eval(question);\\nend\\n\\nfunction answer = Knave(question)\\n  A = false;\\n  X = @(x)x\u003e10;\\n  F = @Knave;\\n  answer = ~eval(question);\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOf course the values of X will be different and unknown to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knight('A==true') == true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knave('A|X(1)') == true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knave('F(''A'')') == false]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,str) should return Knave(str)\\n your_function(@Knave,str) should return Knight(str)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function might query the function handle of the islander with whatever questions it sees fit before responding.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'A==true') == true;\\n\\n your_function(@Knave,'A==true') == true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight; both Knights and Knaves would respond\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to this question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'F(''A==true'')==true') == false; \\n\\n your_function (@Knave,'F(''A==true'')==true') == true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'X(3)~=X(2)') == true\\n\\n your_function(@Knave,'X(3)~=X(2)') == false]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1092,"title":"Decimation","description":"When dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\r\n\r\nThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\r\n\r\nFirst iteration: 1 2 3 4 5 6 7 8 9 10\r\n\r\n1-2-3 4-5-6 7-8-9 10\r\n\r\nPrisoners 3, 6 and 9 will be killed.\r\n\r\nSecond iteration: 1 2 4 5 7 8 10\r\n\r\nBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\r\n\r\nThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\r\n\r\nFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\r\n\r\nFifth iteration:  10-4 10\r\nPrisoner 10 is executed\r\n\r\nSince the sole survivor is prisoner 4, he is released.\r\n\r\nYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\r\n\r\nGood luck!","description_html":"\u003cp\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/p\u003e\u003cp\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\u003c/p\u003e\u003cp\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/p\u003e\u003cp\u003e1-2-3 4-5-6 7-8-9 10\u003c/p\u003e\u003cp\u003ePrisoners 3, 6 and 9 will be killed.\u003c/p\u003e\u003cp\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/p\u003e\u003cp\u003eBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/p\u003e\u003cp\u003eThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/p\u003e\u003cp\u003eFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\u003c/p\u003e\u003cp\u003eFifth iteration:  10-4 10\r\nPrisoner 10 is executed\u003c/p\u003e\u003cp\u003eSince the sole survivor is prisoner 4, he is released.\u003c/p\u003e\u003cp\u003eYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\u003c/p\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function survivor=decimate(num_prisoners,kill_every)\r\nsurvivor=4;\r\nend","test_suite":"%%\r\nassert(isequal(decimate(10,3),4))\r\n%%\r\nassert(isequal(decimate(1024,3),676))\r\n%%\r\nassert(isequal(decimate(2012,50),543))\r\n%%\r\nassert(isequal(decimate(30,5),3))\r\n%%\r\nassert(isequal(decimate(10,10),8))\r\n%%\r\nassert(isequal(decimate(2048,2),1))","published":true,"deleted":false,"likes_count":20,"comments_count":12,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":314,"test_suite_updated_at":"2012-12-04T21:28:04.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2012-12-04T19:47:49.000Z","updated_at":"2026-04-08T14:49:07.000Z","published_at":"2012-12-04T19:53:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn. The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences. Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others. Instead of killing every tenth prisoner, he chooses a number (kill_every). If kill_every=3, he kills every third prisoner. If kill_every=5, he kills every fifth prisoner. He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left. For example, if there are 10 prisoners, and kill_every=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-2-3 4-5-6 7-8-9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrisoners 3, 6 and 9 will be killed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBecause Prisoner 10 was counted during the first iteration, the executions will proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThird iteration: 1 4 5 8 10 8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFourth Iteration: 10-4-5 10 Prisoner 5 is executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFifth iteration: 10-4 10 Prisoner 10 is executed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince the sole survivor is prisoner 4, he is released.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are an unlucky prisoner caught by Carnage Maximum. Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day. Your job is to figure out which prisoner you need to be in order to survive. Write a MATLAB script that takes the values of num_prisoners and kill_every. The output will be survivor, which is the position of the person who survives. If you write your script quickly enough, that person will be you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44345,"title":"MATLAB Counter","description":"Write a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b. \r\n\r\nE.g.,\r\n\r\n  \u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n  \u003e\u003e f()\r\n  ans =\r\n       0\r\n  \u003e\u003e f()\r\n  ans =\r\n       1\r\n  \u003e\u003e f()\r\n  ans =\r\n       2\r\n\r\n\r\n","description_html":"\u003cp\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/p\u003e\u003cp\u003eE.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     0\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     2\r\n\u003c/pre\u003e","function_template":"function y = counter(x,b)\r\n  y = x;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','counter.m')\r\n\r\n%%\r\nf = counter(0,1);\r\nassert(isequal(f(),0))\r\nassert(isequal(f(),1))\r\nassert(isequal(2,f()))\r\nassert(isequal(3,f()))\r\n\r\n%%\r\nf = counter(1,0);\r\nassert(isequal(f(),1))\r\nassert(isequal(f(),1))\r\nassert(isequal(1,f()))\r\nassert(isequal(1,f()))\r\n\r\n%%\r\nf = counter(10,2);\r\nassert(isequal(f(),10))\r\nassert(isequal(f(),12))\r\nassert(isequal(14,f()))\r\nassert(isequal(16,f()))\r\n\r\n%%\r\nf = counter(0,5);\r\ny_correct = [0, 5, 10, 15, 20, 55];\r\nassert(isequal([f() f() f() f() f() f()+f()],y_correct))\r\n\r\n%%\r\nx0 = randi(10);\r\nb = randi(10);\r\nf = counter(x0,b);\r\ny_correct = x0 + (0:1000)*b;\r\nassert(isequal(arrayfun(@(n)f(),0:1000),y_correct))","published":true,"deleted":false,"likes_count":23,"comments_count":9,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":301,"test_suite_updated_at":"2017-10-17T00:19:49.000Z","rescore_all_solutions":false,"group_id":34,"created_at":"2017-09-24T01:58:21.000Z","updated_at":"2026-04-13T19:23:03.000Z","published_at":"2017-10-16T01:45:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\\n\u003e\u003e f()\\nans =\\n     0\\n\u003e\u003e f()\\nans =\\n     1\\n\u003e\u003e f()\\nans =\\n     2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42503,"title":"Generating random matrix with given probability mass function","description":"Inspired by \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities Problem 2356. Simulating the selection of a state with given probabilities\u003e, let's consider a similar yet more useful problem. Write a function\r\n\r\n                             x = rndsampling(m,n,prob)\r\n\r\nto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u003e0) == 1 and sum(prob) == 1.","description_html":"\u003cp\u003eInspired by \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities\"\u003eProblem 2356. Simulating the selection of a state with given probabilities\u003c/a\u003e, let's consider a similar yet more useful problem. Write a function\u003c/p\u003e\u003cpre\u003e                             x = rndsampling(m,n,prob)\u003c/pre\u003e\u003cp\u003eto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u0026gt;0) == 1 and sum(prob) == 1.\u003c/p\u003e","function_template":"function x = rndsampling(m,n,prob);\r\n  x = rand(m,n)\r\nend","test_suite":"%%\r\nrnd = sort(rand(randi([10,20]),1));\r\nprob = vertcat(rnd(1,:),diff(rnd,1,1),1-rnd(end,:));\r\nsz = [1 1e5;1e5 1;1e3 1e2;randi([100 200], 100, 2)];\r\nsz = sz(randi(size(sz,1)),:);\r\nx = rndsampling(sz(1),sz(2),prob);\r\nprob_est = histcounts(x,1:numel(prob)+1,'Normalization','probability').';\r\nerr = mean(abs(prob_est - prob))\r\nassert(err \u003c 0.005 \u0026\u0026 isequal(size(x),sz) \u0026\u0026 all(~isnan(x(:))));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":108,"test_suite_updated_at":"2015-08-13T18:44:59.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-11T19:26:49.000Z","updated_at":"2026-04-16T11:26:02.000Z","published_at":"2015-08-11T19:26:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2356. Simulating the selection of a state with given probabilities\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, let's consider a similar yet more useful problem. Write a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                             x = rndsampling(m,n,prob)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u0026gt;0) == 1 and sum(prob) == 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1288,"title":"Balanced Ternary Numbers: Easy as |, |-, |o","description":"This problem concerns the so-called \u003chttp://en.wikipedia.org/wiki/Balanced_ternary balanced ternary\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1. \r\n\r\nIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \"|\" for one, \"o\" for zero (that's a lower-case O), and \"-\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \"|o-\". Thus\r\n \r\n dec 8  =\u003e bt \"|o-\"\r\n\r\nHere are some more examples.\r\n\r\n dec 3  =\u003e bt \"|o\"\r\n dec 15 =\u003e bt \"|--o\"\r\n dec 52 =\u003e bt \"|-o-|\"\r\n \r\nGiven an integer d, return the string bt. Leading zeros should always be suppressed.","description_html":"\u003cp\u003eThis problem concerns the so-called \u003ca href = \"http://en.wikipedia.org/wiki/Balanced_ternary\"\u003ebalanced ternary\u003c/a\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1.\u003c/p\u003e\u003cp\u003eIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \"|\" for one, \"o\" for zero (that's a lower-case O), and \"-\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \"|o-\". Thus\u003c/p\u003e\u003cpre\u003e dec 8  =\u003e bt \"|o-\"\u003c/pre\u003e\u003cp\u003eHere are some more examples.\u003c/p\u003e\u003cpre\u003e dec 3  =\u003e bt \"|o\"\r\n dec 15 =\u003e bt \"|--o\"\r\n dec 52 =\u003e bt \"|-o-|\"\u003c/pre\u003e\u003cp\u003eGiven an integer d, return the string bt. Leading zeros should always be suppressed.\u003c/p\u003e","function_template":"function bt = balanced_ternary(d)\r\n  bt = 'o';\r\nend","test_suite":"%%\r\nd = 3;\r\nbt_correct = '|o';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 52;\r\nbt_correct = '|-o-|';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 182;\r\nbt_correct = '|-|-|-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 26;\r\nbt_correct = '|oo-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = -5;\r\nbt_correct = '-||';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = -164;\r\nbt_correct = '-|oo-|';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 512;\r\nbt_correct = '|-o|oo-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":74,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-02-21T23:26:14.000Z","updated_at":"2026-04-03T19:20:00.000Z","published_at":"2013-02-21T23:36:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem concerns the so-called\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Balanced_ternary\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ebalanced ternary\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \\\"|\\\" for one, \\\"o\\\" for zero (that's a lower-case O), and \\\"-\\\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \\\"|o-\\\". Thus\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ dec 8  =\u003e bt \\\"|o-\\\"]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere are some more examples.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ dec 3  =\u003e bt \\\"|o\\\"\\n dec 15 =\u003e bt \\\"|--o\\\"\\n dec 52 =\u003e bt \\\"|-o-|\\\"]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer d, return the string bt. Leading zeros should always be suppressed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":81,"title":"Mandelbrot Numbers","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nFor any complex c, we can continue this iteration until either\r\nabs(z(n+1)) \u003e 2 or n == lim, then return the iteration count n.\r\n\r\n* If c = 0   and lim = 3, then z = [0 0 0] and n = 3.\r\n* If c = 1   and lim = 5, then z = [1 2], and n = length(z) or 2.\r\n* If c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\r\n\r\nFor a matrix of complex numbers C, return a corresponding matrix N such\r\nthat each element of N is the iteration count n for each complex number c\r\nin the matrix C, subject to the iteration count limit of lim.\r\n\r\nIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments\r\nwith MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf \r\nChapter 10, Mandelbrot Set (PDF)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 296.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 148.083px; transform-origin: 407px 148.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot Set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is built around a simple iterative equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(1)   = c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(n+1) = z(n)^2 + c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 142.5px 8px; transform-origin: 142.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.5px 8px; transform-origin: 226.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 149.5px 8px; transform-origin: 149.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCleve Moler has a whole chapter on the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in his book \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/moler/exm/chapters.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eExperiments with MATLAB\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = mandelbrot(C,lim)\r\n  N = ones(size(C));\r\nend","test_suite":"%%\r\nC = 0;\r\nlim = 5;\r\nN_correct = 5;\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\nC = [0 0.5; 1 4];\r\nlim = 5;\r\nN_correct = [5 4; 2 1];\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\ni = sqrt(-1);\r\nC = [i 1 -2*i -2];\r\nlim = 10;\r\nN_correct = [10 2 1 10];\r\nassert(isequal(mandelbrot(C,lim),N_correct))","published":true,"deleted":false,"likes_count":17,"comments_count":9,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1778,"test_suite_updated_at":"2012-01-26T03:21:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:28.000Z","updated_at":"2026-04-13T19:34:30.000Z","published_at":"2012-01-18T01:00:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in his book \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/moler/exm/chapters.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExperiments with MATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59516,"title":"Determine aquifer properties: slug test","description":"An important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems 59152, 49473,  and 59147, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity  of the aquifer are determined. \r\nInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement  of water in the well is given as a function of time  by\r\n\r\nwhere  is the initial displacement,  is the radius of the well casing,  is the radius of the well screen,  is the length of the well screen, and  is the effective distance over which the water table returns to its undisturbed level. If the distance  from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness , then \r\n\r\nIf ,\r\n\r\nBouwer and Rice provided the coefficients , , and  in a figure, and Yang and Yeh (2004) fit the curves as functions of :\r\n\r\n\r\n\r\nWrite a function that computes the distance  and determines the hydraulic conductivity  by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1075.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 537.75px; transform-origin: 407px 537.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.358px 8px; transform-origin: 382.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59152\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59152\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/49743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e49473\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59147\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.4667px 8px; transform-origin: 89.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.56667px 8px; transform-origin: 9.56667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer are determined. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.933px 8px; transform-origin: 383.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.075px 8px; transform-origin: 152.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of water in the well is given as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"181\" height=\"42\" alt=\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\" style=\"width: 181px; height: 42px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"H0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.6333px 8px; transform-origin: 83.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the initial displacement, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" alt=\"rc\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1833px 8px; transform-origin: 99.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well casing, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well screen, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"20\" alt=\"Le\" style=\"width: 16px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the length of the well screen, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAoCAYAAABw65OnAAACXElEQVRYR+1XOy8FQRi9t1cIFYVIKEgkKuEHCJXoPGqJV6Ik4QeQUGm8Eo0KhUQjIRKVxKNSUZCgoKKh5xyZ7+a7Y3Z29tpNrmQ3Odm5O+ObM9/jfKNYqIKnWAUcCjkJiULuiX/liU2wHQAaPFX0ibkjYBs4qaTaQnKiDobflHFuNA08AH3AKtBm5jnXn5RICAna/FKGRzDeU79J8gmoMd8W8F5KQiSERBcMXimj9Ri/W5uQ1JD5dod3e9oklmFw1hi9xLvHsYFe84r5xrRJXMBgtzG6gvecYwPtiSiikbxCwqHzgUlnV4CdE1NYs5GmJ4ZhbNcYpJs7rHwggXNAqmMfY5Kwc8bLKc4T1IlxRz4wWXuBGUA0ZAvj+aQEaDuOxK06pes0jP8hcApcJwmBXusj0YKF92pxK8YUqA9ANMGVI4m5+EhMwtq6sahrX4eoIoW0WfpI6LJjvCfMH9viFRfSWM/4DLyopLOlWudKYpkO9UScVLMKFh1VE3tq14IoT8RtYndWSdpUSRzDGts0nyipDlkTRCrKE77WLYZtNfU1LZY7u2wz0AlQ5Eq64iKhQ8EN7aTUp9OaEdUz2GE5x07MnsKG2ASUSGsSdP+YYaw34vWNekF9oFjpR2sGv7OUuamskzIXgiKA7DH05M/z5xq3SOmfInbS2llxO8AzMAqUmlyWJERnqKqPQC1wBvxq81mRELez/Q8C3uaWFQnmF0vYddVjWMpIZUWCuSGVo5NyDd9vgLIrYpYkeGLeNeTSw4o4APS/C5lXh6dwyqey9EROItgDsjAPR1V54htUynUpQju3qgAAAABJRU5ErkJggg==\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.475px 8px; transform-origin: 302.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"Lw\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.0416667px 8px; transform-origin: 0.0416667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"305.5\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\" style=\"width: 305.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"20\" alt=\"Lw = h\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.9px; text-align: left; transform-origin: 384px 21.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\" style=\"width: 203px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.525px 8px; transform-origin: 132.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBouwer and Rice provided the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.15px 8px; transform-origin: 206.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"101\" height=\"20\" alt=\"x = log10(Le/R)\" style=\"width: 101px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"332.5\" height=\"19.5\" alt=\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\" style=\"width: 332.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"342\" height=\"19.5\" alt=\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\" style=\"width: 342px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"351\" height=\"19.5\" alt=\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\" style=\"width: 351px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136px 8px; transform-origin: 136px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.258px 8px; transform-origin: 132.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and determines the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.625px 8px; transform-origin: 83.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 412.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 206.35px; text-align: left; transform-origin: 384px 206.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"455\" height=\"407\" style=\"vertical-align: baseline;width: 455px;height: 407px\" src=\"data:image/png;base64,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\" alt=\"Schematic of the Bouwer-Rice slug test\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h)\r\n%  t = measurement time\r\n%  H = displacement\r\n%  rc = casing radius\r\n%  R = screen radius\r\n%  Le = screen length\r\n%  Lw = distance from undisturbed water table to bottom of well\r\n%  h = initial saturated thickness\r\n  Re = ln(Re/R) = [1.1/ln(Lw/R) + [A+B*ln((h-Lw)/R)]/(Le/R)]^{-1}\r\n  K = rc^2*log(Re/R)*log(H(1)/H)/(2*Le*t);\r\nend","test_suite":"%%\r\nt = 0:2:16;             %  Measurement times (sec)                                                 \r\nrc = 0.05;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 3;                 %  Screen length (m)\r\nLw = 5;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.5 0.645 0.372 0.195 0.13 0.067 0.044 0.023 0.015];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 2.82e-4;\r\nRe_correct = 1.11;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:5:40;             %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 3.5;               %  Screen length (m)\r\nLw = 15;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [0.8 0.404 0.204 0.103 5.21e-2 2.63e-2 1.33e-2 6.72e-3 3.4e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 9.4e-5;\r\nRe_correct = 4.065;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 14;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 0.978 0.562 0.323 0.186 0.107 6.15e-2 3.53e-2 2.03e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 2.179;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 28;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 1.11 0.719 0.467 0.304 0.197 0.128 8.35e-2 5.43e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 5.592;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:60:480;           %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 5;                 %  Screen length (m)\r\nLw = 30;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 30;                 %  Undisturbed saturated thickness (m)\r\nH = [1.3 0.651 0.326 0.163 8.16e-2 4.09e-2 2.05e-2 1.02e-2 5.13e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 7.43e-6;\r\nRe_correct = 5.608;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nfiletext = fileread('BouwerRice.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-30T14:18:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-30T13:54:14.000Z","updated_at":"2026-02-12T15:36:49.000Z","published_at":"2023-12-30T14:04:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59152\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e59152\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/49743\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e49473\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e59147\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer are determined. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of water in the well is given as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH = H_0 \\\\exp\\\\left(-\\\\frac{2 K L_e t}{r_c^2 \\\\ln(R_e/R)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the initial displacement, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well casing, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well screen, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Le\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the length of the well screen, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{A+B\\\\ln((h-L_w)/R)}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw = h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w = h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{C}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBouwer and Rice provided the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = log10(Le/R)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = \\\\log_{10}(L_e/R)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and determines the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"407\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"455\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Schematic of the Bouwer-Rice slug test\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59217,"title":"List lunar triangular numbers without duplication","description":"Triangular numbers—which are the subject of Cody Problems 5, 291, 44289, 44732, 45833, 55680, 55695, and 55705—are the sums of consecutive integers. For example, the 10th triangular number is the sum of the numbers 1 to 10, or 55. \r\nLunar addition, which is the subject of Cody Problem 44785, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\r\nWrite a function to compute the th lunar triangular number without duplicating any terms. For example, the 10th lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11th lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.683px 8px; transform-origin: 192.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangular numbers—which are the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/5\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44289\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44289\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44732\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44732\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45833\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45833\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55680\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55680\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55695\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55695\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55705\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55705\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.2px 8px; transform-origin: 18.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—are the sums of consecutive integers. For example, the 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 186.3px 8px; transform-origin: 186.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangular number is the sum of the numbers 1 to 10, or 55. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118.642px 8px; transform-origin: 118.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLunar addition, which is the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44785\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 44785\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.608px 8px; transform-origin: 199.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.6583px 8px; transform-origin: 98.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 238.45px 8px; transform-origin: 238.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth lunar triangular number without duplicating any terms. For example, the 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.45px 8px; transform-origin: 19.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.042px 8px; transform-origin: 168.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = lunarTriNum(n)\r\n  y = num2str(n);\r\nend","test_suite":"%%\r\ns = char(48:57);\r\nfor n = 0:9\r\n    assert(strcmp(lunarTriNum(n),s(n+1)));\r\nend\r\n\r\n%%\r\nassert(strcmp(lunarTriNum(10),'19'))\r\n\r\n%%\r\nfor k = 1:1000\r\n    n = randi(10000);\r\n    assert(isequal(sum(lunarTriNum(n)-'0'),n))\r\nend\r\n\r\n%%\r\nn = 77;\r\np_correct = 215233605;\r\nassert(isequal(prod(lunarTriNum(n)-'0'),p_correct))\r\n\r\n%%\r\nn = 134;\r\np_correct = 183014339639688;\r\nassert(isequal(prod(lunarTriNum(n)-'0'),p_correct))\r\n\r\n%%\r\nn = 6259;\r\nlen_correct = 696;\r\nassert(isequal(length(lunarTriNum(n)),len_correct))\r\n\r\n%%\r\nn = 5*(10.^(1:7));\r\np = primes(1e8);\r\nx_correct = [267 4103 256889 33082235 4266286911 523279276675 61893416706717];\r\nfor k = 1:length(n)\r\n    a = str2num(reshape(lunarTriNum(n(k)),[],2));\r\n    x(k) = sum(a+p(1:size(a,1))');\r\nend\r\nassert(isequal(x,x_correct))\r\n\r\n%%\r\nfiletext = fileread('lunarTriNum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-11-25T14:58:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-11-25T14:57:46.000Z","updated_at":"2023-11-25T14:58:06.000Z","published_at":"2023-11-25T14:58:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangular numbers—which are the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/291\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44289\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44289\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44732\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44732\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45833\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45833\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55680\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55680\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55695\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55695\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55705\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55705\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—are the sums of consecutive integers. For example, the 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangular number is the sum of the numbers 1 to 10, or 55. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLunar addition, which is the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44785\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 44785\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth lunar triangular number without duplicating any terms. For example, the 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44374,"title":"Tautology","description":"Check if the given expression is always true. For example, the sentence\r\n\r\n  '~(A \u0026 B) == (~A | ~B)'\r\n\r\nis always true.\r\n\r\nCharacters in the input sequences may include *~ \u0026 | == ( )*, whitespace, 0 for false, 1 for true and letters for variables.","description_html":"\u003cp\u003eCheck if the given expression is always true. For example, the sentence\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e'~(A \u0026 B) == (~A | ~B)'\r\n\u003c/pre\u003e\u003cp\u003eis always true.\u003c/p\u003e\u003cp\u003eCharacters in the input sequences may include \u003cb\u003e~ \u0026 | == ( )\u003c/b\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/p\u003e","function_template":"function y = tautology(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = '0';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1\u0026A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A\u0026B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|~A';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '0==0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(A \u0026 B) == (~A | ~B)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(Z \u0026 Y) == (~Y | ~Z)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|~A|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nassert(isequal(tautology('(A|B)|C'),false));\r\n%%\r\nassert(isequal(tautology('(A|B)|(C == C)'),true));\r\n%%\r\nassert(isequal(tautology('(A == B)|(B == C)|(C == A)'),true));\r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(0))))))'),false)); \r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(~0))))))'),true));\r\n% provided by Alfonso:\r\nassert(isequal(tautology('((0\u00261)|~B)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((0\u0026~B)\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)\u0026~A)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((0|~B)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((1\u00260)|B)'),false)); \r\n%%\r\nassert(isequal(tautology('((1\u00261)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('((1|0)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|A)|0)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|~A)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u00261)|~A)|A'),true)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~A)\u0026~B)|~A'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~B)\u00261)|B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|0)\u00261)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|A)\u0026A)|~A'),true)); \r\n%%\r\nassert(isequal(tautology('((B|0)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((B|1)\u0026B)\u0026A'),false)); \r\n%%\r\nassert(isequal(tautology('((B|A)|~A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)\u00260)\u0026B'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|0)'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|~A)|1'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|A)|~B)\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|B)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~B)\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('((~B\u00260)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('(0\u00261)|1\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('(0|~A\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(1|A\u00260)'),true)); \r\n%%\r\nassert(isequal(tautology('(A\u0026A\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('(A\u0026~A|1)'),true)); \r\n%%\r\nassert(isequal(tautology('(A|1)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(A|A)|A|1'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u00261)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u0026~B)\u0026~B\u00260'),false)); \r\n%%\r\nassert(isequal(tautology('(B|~B)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A\u0026B\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|0)|~B\u0026~A'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|1)|1'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|B\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|B)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|~A)|0'),false)); \r\n%%\r\nassert(isequal(tautology('(~B\u00260)\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('1\u0026B|~B|0'),true)); \r\n%%\r\nassert(isequal(tautology('B\u00261\u0026A\u00261'),false)); \r\n%%\r\nassert(isequal(tautology('~A\u00260\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('~B\u00260\u0026~A|B'),false)); \r\n%%\r\nassert(isequal(tautology('~B|1|1|~B'),true)); \r\n%%\r\nassert(isequal(tautology('~B|~B\u00261|1'),true));\r\n%%\r\nassert(isequal(tautology('A==~A'),false));\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":30,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2017-10-31T07:45:16.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-10T23:20:08.000Z","updated_at":"2026-02-03T08:59:32.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck if the given expression is always true. For example, the sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA['~(A \u0026 B) == (~A | ~B)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis always true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCharacters in the input sequences may include\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~ \u0026amp; | == ( )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56423,"title":"French Conundrum","description":"The French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\r\nThe battle-ground is in a form of a 2-D rectangular lattice spanning from (0,0) to (m,n). In order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position (although relative, consider it to be 0,0) to the end point (m,n).\r\nHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\r\n\r\nThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\r\n\r\nGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 285px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 142.5px; transform-origin: 407px 142.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357px 8px; transform-origin: 357px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 228.5px 8px; transform-origin: 228.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe battle-ground is in a form of a 2-D rectangular lattice spanning from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15px 8px; transform-origin: 15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(0,0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(m,n). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(although relative, consider it to be 0,0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the end point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5px 8px; transform-origin: 19.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(m,n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 291px 8px; transform-origin: 291px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357px 8px; transform-origin: 357px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = henridnum(m,n)\r\n  y = f(m,n);\r\nend","test_suite":"%%\r\nfiletext = fileread('henridnum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || ...\r\n          contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nassert(isequal(henridnum(1,1),3))\r\n\r\n%%\r\nassert(isequal(henridnum(1,3),7))\r\n\r\n%%\r\nassert(isequal(henridnum(3,2),(3+2)^2))\r\n\r\n%%\r\nassert(isequal(henridnum(2,8),145))\r\n\r\n%%\r\nassert(isequal(henridnum(5,5),1683))\r\n\r\n%%\r\nfor i=0:9\r\n    assert(isequal(henridnum(i,1),2*i+1))\r\nend\r\n\r\n%%\r\nassert(isequal(henridnum(6,4),1289))\r\n\r\n%%\r\nassert(isequal(henridnum(7,6),19825))\r\n\r\n%%\r\nassert(isequal(henridnum(3,3),(3+3+1)*3*3))\r\n\r\n%%\r\nassert(isequal(henridnum(8,6),40081))\r\n\r\n%%\r\nassert(isequal(henridnum(10,10),8097453))\r\n\r\n%%\r\nassert(isequal(henridnum(5,3),(5*3)^2+3+3))\r\n\r\n%%\r\nassert(isequal(henridnum(3,7),575))\r\n\r\n%%\r\nassert(isequal(henridnum(11,9),7059735))\r\n\r\n%%\r\nassert(isequal(henridnum(4,2),4*2*5+1))\r\n\r\n%%\r\nassert(isequal(henridnum(8,7),108545))\r\n\r\n%%\r\nassert(isequal(henridnum(11,13),224298231))\r\n\r\n%%\r\nassert(isequal(henridnum(12,12),251595969))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2022-10-27T11:34:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-26T17:38:03.000Z","updated_at":"2025-09-19T20:55:15.000Z","published_at":"2022-10-27T11:34:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe battle-ground is in a form of a 2-D rectangular lattice spanning from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(m,n). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eIn order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(although relative, consider it to be 0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e to the end point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(m,n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58019,"title":"Factor a number into Fermi-Dirac primes","description":"Cody Problem 58018 asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, . \r\nWrite a function analogous to factor(n) that factors the number  into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58018\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 58018\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"18\" alt=\"2250 = 2x5x9x25\" style=\"width: 122px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function analogous to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efactor(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that factors the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = factorFD(n)\r\n  y = factor(n).^n;\r\nend","test_suite":"%%\r\nassert(isequal(factorFD(1),1))\r\n\r\n%%\r\np = primes(1000);\r\nfor q = p\r\n    assert(isequal(factorFD(q),q))\r\nend\r\n\r\n%%\r\nassert(isequal(factorFD(56),[2 4 7]))\r\n\r\n%%\r\nassert(isequal(factorFD(64),[4 16]))\r\n\r\n%%\r\nassert(isequal(factorFD(644),[4 7 23]))\r\n\r\n%%\r\nassert(isequal(factorFD(2250),[2 5 9 25]))\r\n\r\n%%\r\nassert(isequal(factorFD(6444),[4 9 179]))\r\n\r\n%%\r\nassert(isequal(factorFD(64444),[4 16111]))\r\n\r\n%%\r\nassert(isequal(factorFD(644444),[4 73 2207]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(5784354),[2 9 211 1523]))\r\n\r\n%%\r\nassert(isequal(factorFD(11739420),[4 5 9 11 49 121]))\r\n\r\n%%\r\nassert(isequal(factorFD(28437991),[17 103 109 149]))\r\n\r\n%%\r\nassert(isequal(factorFD(1106427169),[841 961 1369]))\r\n\r\n%%\r\nassert(isequal(factorFD(753345263125),[13 73 529 625 2401]))\r\n\r\n%%\r\nassert(isequal(factorFD(159360553668481),[14641 83521 130321]))\r\n\r\n%%\r\nassert(isequal(factorFD(2760834326158300),[4 7 25 49 10201 7890481]))\r\n\r\n%%\r\nfiletext = fileread('factorFD.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-28T23:50:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-25T01:29:47.000Z","updated_at":"2025-03-02T18:40:23.000Z","published_at":"2023-04-25T01:29:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58018\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 58018\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2250 = 2x5x9x25\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2250 = 2 \\\\cdot5\\\\cdot9\\\\cdot25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function analogous to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efactor(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that factors the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60406,"title":"Alert a city about a spill","description":"Problem statement\r\nCody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s maximum contaminant level (MCL). As in CP 54750, the spill of mass  will be assumed instantaneous at position  and time  and mixed over the cross section (with area ). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with  \r\n\r\nwhere  is the mean velocity of the river,  is the discharge or volumetric flow rate, and  is a dispersion coefficient, which describes spreading by several mechanisms. \r\nWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position  downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return 'The MCL is not exceeded.' Please note that the MCL is given in mg/L, whereas other variables are given in SI units. \r\nDetails\r\nMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of Seo and Cheong (1998):\r\n\r\nwhere  is the width of the channel (assumed rectangular here),  is the water depth, and  is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\r\n\r\nwhere  is the gravitational acceleration,  is the longitudinal slope of the channel,  is the hydraulic radius, and  is the wetted perimeter. For a rectangular channel, . \r\nIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 690.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345.017px; transform-origin: 407px 345.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 7.79167px; transform-origin: 63.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/54750\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 54750\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 307.167px 7.79167px; transform-origin: 307.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.9px 7.79167px; transform-origin: 129.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (MCL). As in CP 54750, the spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3417px 7.79167px; transform-origin: 23.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assumed instantaneous at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2333px 7.79167px; transform-origin: 34.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and mixed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.79167px; transform-origin: 104.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6083px 7.79167px; transform-origin: 62.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20px; text-align: left; transform-origin: 384px 20px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"204.5\" height=\"40\" alt=\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\" style=\"width: 204.5px; height: 40px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61.5\" height=\"18.5\" alt=\"U = Q/A\" style=\"width: 61.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.892px 7.79167px; transform-origin: 101.892px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.858px 7.79167px; transform-origin: 138.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the discharge or volumetric flow rate, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.625px 7.79167px; transform-origin: 48.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.758px 7.79167px; transform-origin: 376.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 218.967px 7.79167px; transform-origin: 218.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.95px 7.79167px; transform-origin: 103.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 103.95px 8.25px; transform-origin: 103.95px 8.25px; \"\u003e'The MCL is not exceeded.' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.242px 7.79167px; transform-origin: 132.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDetails\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 322.725px 7.79167px; transform-origin: 322.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eSeo and Cheong (1998)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.1333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.0667px; text-align: left; transform-origin: 384px 22.0667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"44\" alt=\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\" style=\"width: 190.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.9083px; text-align: left; transform-origin: 384px 31.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.65px 7.79167px; transform-origin: 174.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the channel (assumed rectangular here), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 7.79167px; transform-origin: 74.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"u*\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.6083px 7.79167px; transform-origin: 86.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"21\" alt=\"u* = sqrt(gRS0)\" style=\"width: 90px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"19.5\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 7.79167px; transform-origin: 101.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gravitational acceleration, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.483px 7.79167px; transform-origin: 124.483px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18.5\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 7.79167px; transform-origin: 50.5667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 159.858px 7.79167px; transform-origin: 159.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter. For a rectangular channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"78\" height=\"18\" alt=\"P = B + 2H\" style=\"width: 78px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.00833px 7.79167px; transform-origin: 1.00833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = spillAlert(x,t0,M,Q,B,H,S0,MCL)\r\n% See the tests for the definitions of the variables and note that the MCL is given in mg/L.\r\n  t = datetime(x*B*H/Q);\r\nend","test_suite":"%% Benzene\r\nx = 80000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 26000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.005;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 08 05; 2018 05 28 05 06 05])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Chlorobenzene\r\nx = 79500;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 34000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.1;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 43 39; 2018 05 28 03 41 07])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Atrazine\r\nx = 14300;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2020,7,3,16,35,0);    %  Datetime for spill\r\nM = 5600;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 32;                             %  Width of channel (m)\r\nH = 0.4;                            %  Depth of channel (m)\r\nS0 = 6e-4;                          %  Longitudinal slope of channel\r\nMCL = 0.003;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2020 07 04 00 51 03; 2020 07 04 14 00 39])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Dalapon\r\nx = 4200;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2019,6,13,14,23,0);   %  Datetime for spill\r\nM = 3000;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 15;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.2;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2019 06 13 15 47 17; 2019 06 13 19 39 06])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 2\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 80;                             %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 3\r\nx = 94000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 37;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Nitrate \r\nx = 1600;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2024,4,30,15,20,00);  %  Datetime for spill\r\nM = 140;                            %  Mass of spill (kg)\r\nQ = 14;                             %  Discharge (m3/s)\r\nB = 14;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 5e-4;                          %  Longitudinal slope of channel\r\nMCL = 10;                           %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2024 4 30 15 32 22; 2024 4 30 15 38 03])';\r\nassert(isequal(t,t_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-28T15:13:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-27T17:17:23.000Z","updated_at":"2026-01-25T17:02:57.000Z","published_at":"2024-05-27T17:22:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/54750\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 54750\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MCL). As in CP 54750, the spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will be assumed instantaneous at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and mixed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the discharge or volumetric flow rate, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'The MCL is not exceeded.' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSeo and Cheong (1998)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = 5.915u_*H\\\\left(\\\\frac{B}{H}\\\\right)^{\\\\!\\\\!0.62}\\\\left(\\\\frac{U}{u_*}\\\\right)^{\\\\!\\\\!1.428}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the channel (assumed rectangular here), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u*\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u* = sqrt(gRS0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_* = (g R S_0)^{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\,\\\\rm{m/s^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gravitational acceleration, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter. For a rectangular channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P = B + 2H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = B + 2H\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46636,"title":"Montgomery Multiplication","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMultiply all elements of an input matrix (A) modulo N, given all elements are less than R (2^number of bits). Where gcd(R,N)=1 and N\u0026lt;R. Output the final result, P (in normal form) and all intermediate products (p) in Montgomery form \u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; \"\u003e(\u003c/span\u003e\u003cspan style=\"\"\u003efirst product is just first element of matrix (A)*R modulo N\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; \"\u003e)\u003c/span\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [P,p] = montgomeryMult(a,R,N)\r\n  P=N-1;\r\n  p=mod(a,N);\r\nend","test_suite":"%%\r\nR=2^16;\r\nN=3329;\r\nY=2050;\r\ny =[    1263         470        2922         960         982         369        2562        2142        1318         744];\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44576       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51731       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22389\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n%%\r\nN=3347;\r\nR=2^16;\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44596       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51771       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22389\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\nY=1870;\r\ny=[130,1496,2440,2533,1292,1876,783,751,107,3006];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n%%\r\nR=2^16;\r\nN=3967;\r\nY=3799;\r\ny=[788,2020,2960,1688,2874,3752,1280,2265,1542,1371];\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44596       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51771       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22999\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-30T21:17:47.000Z","updated_at":"2025-10-12T15:14:20.000Z","published_at":"2020-09-30T21:17:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMultiply all elements of an input matrix (A) modulo N, given all elements are less than R (2^number of bits). Where gcd(R,N)=1 and N\u0026lt;R. Output the final result, P (in normal form) and all intermediate products (p) in Montgomery form (first product is just first element of matrix (A)*R modulo N).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44793,"title":"Project Euler 249: Prime Subset Sums","description":"Inspired by Problem 249 of Project Euler.\r\n\u003chttps://projecteuler.net/problem=249\u003e\r\n\r\nLet S = {2, 3, 5, ...} be the set of prime numbers less than N.\r\n\r\nFind the number of subsets of S, the sum of whose elements is a prime number.\r\nEnter the rightmost 16 digits as your answer.\r\nThe answer must be a uint64 integer.","description_html":"\u003cp\u003eInspired by Problem 249 of Project Euler. \u003ca href = \"https://projecteuler.net/problem=249\"\u003ehttps://projecteuler.net/problem=249\u003c/a\u003e\u003c/p\u003e\u003cp\u003eLet S = {2, 3, 5, ...} be the set of prime numbers less than N.\u003c/p\u003e\u003cp\u003eFind the number of subsets of S, the sum of whose elements is a prime number.\r\nEnter the rightmost 16 digits as your answer.\r\nThe answer must be a uint64 integer.\u003c/p\u003e","function_template":"function num = euler249(N)\r\n  num = uint64(7) % answer for N = 10\r\nend","test_suite":"%%\r\ntic;\r\nSUM = euler249(10)\r\ntoc;\r\nassert(isequal(SUM, uint64(7)))\r\n\r\n%%\r\ntic;\r\nSUM = euler249(100)\r\ntoc;\r\nassert(isequal(SUM, uint64(5253640)))\r\n\r\n%%\r\ntic;\r\nSUM = euler249(1000)\r\ntoc;\r\nassert(isequal(SUM, uint64(5725053962252706)))\r\n%%\r\ntic;\r\nSUM = euler249(2000)\r\ntoc;\r\nassert(isequal(SUM, uint64(9536598422264105)))\r\n%%\r\ntic;\r\nSUM = euler249(4900)\r\ntoc;\r\nassert(isequal(SUM, uint64(2455225028344813)))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":8269,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-11-22T00:50:24.000Z","updated_at":"2025-12-15T21:24:15.000Z","published_at":"2018-11-22T00:50:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by Problem 249 of Project Euler.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://projecteuler.net/problem=249\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://projecteuler.net/problem=249\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S = {2, 3, 5, ...} be the set of prime numbers less than N.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of subsets of S, the sum of whose elements is a prime number. Enter the rightmost 16 digits as your answer. The answer must be a uint64 integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2266,"title":"2048 tile game","description":"The popular 2048 game has been implemented here:\r\n\r\nhttp://gabrielecirulli.github.io/2048/\r\n\r\nGiven the board like this:\r\n\r\n  [2 4 8 0\r\n   4 0 0 0\r\n   2 0 0 0\r\n   2 0 4 0]\r\n\r\nYou give the direction\r\n\r\n1 (left)\r\n2 (up)\r\n3 (right)\r\n4 (down)\r\n\r\nThe system here will keep calling your solver.  Score for each board is the biggest tile achieved.  The Cody score is the maximum board score plus the average score across all 200 boards.","description_html":"\u003cp\u003eThe popular 2048 game has been implemented here:\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://gabrielecirulli.github.io/2048/\"\u003ehttp://gabrielecirulli.github.io/2048/\u003c/a\u003e\u003c/p\u003e\u003cp\u003eGiven the board like this:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[2 4 8 0\r\n 4 0 0 0\r\n 2 0 0 0\r\n 2 0 4 0]\r\n\u003c/pre\u003e\u003cp\u003eYou give the direction\u003c/p\u003e\u003cp\u003e1 (left)\r\n2 (up)\r\n3 (right)\r\n4 (down)\u003c/p\u003e\u003cp\u003eThe system here will keep calling your solver.  Score for each board is the biggest tile achieved.  The Cody score is the maximum board score plus the average score across all 200 boards.\u003c/p\u003e","function_template":"function direction = getMove(board)\r\n  direction = 1;\r\nend","test_suite":"%%\r\nfh=fopen('main.m','wt');\r\nfprintf(fh, '%s \\n', 'function out = main(n)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'result = 0;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'for i = 1:n    ');\r\nfprintf(fh, '%s \\n', '    board = zeros(4);');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', '    %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    direction = 1;');\r\nfprintf(fh, '%s \\n', '    while (direction ~= 0)');\r\nfprintf(fh, '%s \\n', '        %pause(0.1)');\r\nfprintf(fh, '%s \\n', '        %clc');\r\nfprintf(fh, '%s \\n', '        direction = getMove(board);');\r\nfprintf(fh, '%s \\n', '        board = updateBoard(board, direction);');\r\nfprintf(fh, '%s \\n', '        %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    end');\r\nfprintf(fh, '%s \\n', '    %figure(1)');\r\nfprintf(fh, '%s \\n', '    %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    %figure(2)');\r\nfprintf(fh, '%s \\n', '    %hist(result,[2 4 8 16 32 64 128 256 512 1024,2048])');\r\nfprintf(fh, '%s \\n', '    %drawnow');\r\nfprintf(fh, '%s \\n', '    result(i) = max(board(:));');\r\nfprintf(fh, '%s \\n', '    %disp([i result(i) max(result)])');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = max(result) + mean(result)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = collapse(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'in = squish(in);');\r\nfprintf(fh, '%s \\n', 'for i = 1:3');\r\nfprintf(fh, '%s \\n', '    result = miniCollapse(in(i:i+1));');\r\nfprintf(fh, '%s \\n', '    out(i:i+1) = result;');\r\nfprintf(fh, '%s \\n', '     in(i:i+1) = result;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = squish(in);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = squish(in);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = in(in ~= 0);');\r\nfprintf(fh, '%s \\n', 'if numel(out) ~= 4');\r\nfprintf(fh, '%s \\n', '    out(4) = 0;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = miniCollapse(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if in(1) == in(2)');\r\nfprintf(fh, '%s \\n', '    out(1) = in(1) * 2;');\r\nfprintf(fh, '%s \\n', '    out(2)  = 0;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    out = in;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = saltBoard(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if nnz(in) == 16');\r\nfprintf(fh, '%s \\n', '    out = nan;');\r\nfprintf(fh, '%s \\n', '    return;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'vi = find(in == 0);');\r\nfprintf(fh, '%s \\n', 'selected = randi(numel(vi));');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'thresh = 0.1;');\r\nfprintf(fh, '%s \\n', 'if (rand \u003c thresh)');\r\nfprintf(fh, '%s \\n', '    salt = 4;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    salt = 2;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = in;');\r\nfprintf(fh, '%s \\n', 'out(vi(selected)) = salt;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function board = updateBoard(board, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'boardOriginal = board;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'board = collapseBoard(board,direction);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if ~isequal(boardOriginal, board)');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function dispBoard(board)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'clf');\r\nfprintf(fh, '%s \\n', 'r = 1;');\r\nfprintf(fh, '%s \\n', 'c = 1;');\r\nfprintf(fh, '%s \\n', 'v = 2;');\r\nfprintf(fh, '%s \\n', 'for r = 1:4');\r\nfprintf(fh, '%s \\n', '    for c = 1:4');\r\nfprintf(fh, '%s \\n', '        v = board(r,c);');\r\nfprintf(fh, '%s \\n', '        dispSquare(r,c,v)');\r\nfprintf(fh, '%s \\n', '    end');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function dispSquare(r,c,v)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'cmap = autumn(12);');\r\nfprintf(fh, '%s \\n', 'absIndex = (r-1)*4 + c;');\r\nfprintf(fh, '%s \\n', 'if v == 0 ');\r\nfprintf(fh, '%s \\n', '    cMapIndex = 1;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    cMapIndex = log2(v) + 1;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'h = subplot(4,4,absIndex);');\r\nfprintf(fh, '%s \\n', 'set(h,''xtick'',[])');\r\nfprintf(fh, '%s \\n', 'set(h,''ytick'',[])');\r\nfprintf(fh, '%s \\n', 'set(h,''color'',cmap(cMapIndex,:))');\r\nfprintf(fh, '%s \\n', '%axis off');\r\nfprintf(fh, '%s \\n', 'text(0.5,0.5,num2str(v), ''fontsize'', 20)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function flag = isMoveDirection(board, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'originalBoard = board;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'board = updateBoard(board, direction);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'flag = ~isequal(board, originalBoard);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = collapseBoard(in, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'rotDirection = direction-1;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'in = rot90(in,rotDirection);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'for r = 1:4');\r\nfprintf(fh, '%s \\n', '    out(r,:) = collapse(in(r,:));');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = rot90(out,-rotDirection);');\r\n\r\nfclose(fh);\r\n\r\nrehash path\r\n%%\r\nn = 200;\r\nscore = main(n)\r\nscore = 4056 - score;\r\n\r\nassert(score \u003c (4056 - 256))\r\nassignin('caller','score',score)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":240,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2014-04-02T17:36:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-04-01T20:01:55.000Z","updated_at":"2026-02-03T10:02:13.000Z","published_at":"2014-04-02T14:29:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe popular 2048 game has been implemented here:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://gabrielecirulli.github.io/2048/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://gabrielecirulli.github.io/2048/\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the board like this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[2 4 8 0\\n 4 0 0 0\\n 2 0 0 0\\n 2 0 4 0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou give the direction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 (left) 2 (up) 3 (right) 4 (down)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe system here will keep calling your solver. Score for each board is the biggest tile achieved. The Cody score is the maximum board score plus the average score across all 200 boards.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60834,"title":"Bell 202 Decoder","description":"Decode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \r\nWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\r\nDuration of each bit is based on the baud-rate.\r\nDigitized audio stream is produced at the sample rate and is smooth between bits.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 66px; transform-origin: 408px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDecode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDuration of each bit is based on the baud-rate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDigitized audio stream is produced at the sample rate and is smooth between bits.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function decodedStream = decodeBell202(audioSignal, sampleRate, bitRate)\r\n decodedStream=audioSignal/bitRate;\r\nend","test_suite":"%%\r\nrng(2718);\r\nbS=num2str(randi(2,1,1e4)-1);\r\nbS(bS==' ')=[];\r\nt = 1/1e5:1/1e5:1/9.2e2;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1e5,920),bS))\r\n%%\r\nrng(2718);\r\nbS=num2str(randi(2,1,1e4)-1);\r\nbS(bS==' ')=[];\r\nt = 1/1e5:1/1e5:1/1e3;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1e5,1e3),bS))\r\n%%\r\nbS='1011110001100110011001110001110101011010101010111000111000111000111100011100110101011001';\r\nt = 1/1.2e5:1/1.2e5:1/600;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1.2e5,600),bS))\r\n%%","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-03-27T15:12:44.000Z","updated_at":"2025-12-07T15:19:32.000Z","published_at":"2025-03-27T15:12:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDecode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDuration of each bit is based on the baud-rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDigitized audio stream is produced at the sample rate and is smooth between bits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60749,"title":"Compute the dispersion coefficient","description":"A contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\r\nG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \r\n\r\nwhere  is the width of the stream,  is the transverse mixing coefficient, and  is the deviation of the velocity profile from the cross-sectional average velocity\r\n\r\nWrite a function that takes a (normalized) velocity profile  specified at several points and computes the quantity \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 187.5px; transform-origin: 407px 187.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"240\" height=\"44\" alt=\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 240px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the stream, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the transverse mixing coefficient, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64\" height=\"19\" alt=\"u' = u - bar(u)\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103\" height=\"44\" alt=\"ubar = (1/h) integral(u(y),0\u003c=y\u003c=h)\" style=\"width: 103px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a (normalized) velocity profile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30\" height=\"18\" alt=\"u(y)\" style=\"width: 30px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e specified at several points and computes the quantity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"215\" height=\"44\" alt=\"I = -integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 215px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = computeK(y,u)\r\n  I = -integral(u'*integral(integral(u',0,y1),0,y),0,h);\r\nend","test_suite":"%%\r\nny = 1000;\r\ny = linspace(0,1,ny);\r\nu = y.*(1-y);\r\nI = computeK(y,u);\r\nI_correct = 1/7560;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = 2*y;\r\nu(y\u003e1/2) = 2*(1-y(y\u003e1/2));\r\nI = computeK(y,u);\r\nI_correct = 1/480;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 2.5;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.00788915;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 3;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01168232;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 3.2; \r\nb = 3.2;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01192484;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-10-16T01:19:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-16T01:18:30.000Z","updated_at":"2024-10-27T15:58:26.000Z","published_at":"2024-10-16T01:19:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = -\\\\frac{1}{hD}\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the stream, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the transverse mixing coefficient, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u' = u - bar(u)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu^\\\\prime = u-{\\\\bar u}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ubar = (1/h) integral(u(y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\bar u} = \\\\frac{1}{h} \\\\int_0^h u(y) dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a (normalized) velocity profile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u(y)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu(y)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e specified at several points and computes the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = -integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = -\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1949,"title":"Get top 5 Cody Player Emails Automatically","description":"Yes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\r\n\r\nLooking at the list of the players \u003chttp://www.mathworks.com/matlabcentral/cody/players\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \"View Profile Information\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand. \r\n\r\nFor this program, let's say we want the top 5 profiles that give a \"real\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it. \r\n\r\nIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \"mailto:\" and if it is there, the email address is immediately following it. If the string \"mailto:\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\r\n\r\nAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\r\n\r\n*I am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.*\r\n\r\n*If this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \"My Community Profile\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.* ","description_html":"\u003cp\u003eYes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\u003c/p\u003e\u003cp\u003eLooking at the list of the players \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/players\"\u003ehttp://www.mathworks.com/matlabcentral/cody/players\u003c/a\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \"View Profile Information\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand.\u003c/p\u003e\u003cp\u003eFor this program, let's say we want the top 5 profiles that give a \"real\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it.\u003c/p\u003e\u003cp\u003eIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \"mailto:\" and if it is there, the email address is immediately following it. If the string \"mailto:\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\u003c/p\u003e\u003cp\u003eAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\u003c/p\u003e\u003cp\u003e\u003cb\u003eI am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eIf this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \"My Community Profile\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.\u003c/b\u003e\u003c/p\u003e","function_template":"function emails = getCodyEmails()\r\n  emails = {};\r\nend","test_suite":"%%\r\n% My code is below, it's used to generate the expected result.\r\n\r\n%Read in the player page\r\nplayerPage=urlread('http://www.mathworks.com/matlabcentral/cody/players');\r\n\r\n%Find where the web address for each profile starts\r\nstartIdx=strfind(playerPage,'\u003cdiv class=\"grid_53 push_3\"\u003e')+104; \r\n\r\n%Initialize output array\r\nemails={};\r\n\r\n%Get top 5 only\r\nfor i=1:5\r\n    % Get the profile page link\r\n   tempStr=playerPage(startIdx(i):startIdx(i)+100);\r\n   quoteIdx=strfind(tempStr,'\"')-1;\r\n   profilePageLink=['http://www.mathworks.com' tempStr(1:quoteIdx(1))];\r\n   \r\n   profilePage=urlread(profilePageLink);\r\n   % Try and find mailto link\r\n   tStartIdx=strfind(profilePage,'mailto');\r\n   \r\n   %If you could find it\r\n   if ~isempty(tStartIdx)\r\n       % Get the email\r\n       tEndIdx=strfind(profilePage(tStartIdx:tStartIdx+100),'\"')+tStartIdx;\r\n       \r\n       % Add it to our cell array\r\n       emails{length(emails)+1}=profilePage(tStartIdx+7:tEndIdx-2);\r\n   end\r\n    \r\nend\r\n\r\n\r\ntic\r\nyourResponse=getCodyEmails()\r\ntimeElapsed=toc\r\n\r\n\r\nassert(isequal(yourResponse,emails))\r\nassert(isequal(1,timeElapsed\u003e3))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":3743,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-20T05:40:10.000Z","updated_at":"2025-07-31T17:14:24.000Z","published_at":"2013-10-20T05:40:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLooking at the list of the players\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/players\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.mathworks.com/matlabcentral/cody/players\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \\\"View Profile Information\\\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this program, let's say we want the top 5 profiles that give a \\\"real\\\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \\\"mailto:\\\" and if it is there, the email address is immediately following it. If the string \\\"mailto:\\\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \\\"My Community Profile\\\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":53990,"title":"Classify product/digit-sum sequences","description":"Cody Problem 53120 involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\r\nWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved Cody Problem 53120, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \r\nWrite a function to classify the product/digit-sum sequences given the first two terms  and . To encourage solvers to find the pattern, loops are banned, and to allow for large inputs,  and  are specified as strings. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 93px; transform-origin: 407.5px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 309.642px 7.66667px; transform-origin: 309.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.883px 7.66667px; transform-origin: 383.883px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.075px 7.66667px; transform-origin: 103.075px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.017px 7.66667px; transform-origin: 262.017px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.35px 7.66667px; transform-origin: 93.35px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 7.66667px; transform-origin: 77.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are specified as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = PDSseq(a,b)\r\n  c = [1 9 26 62 163];\r\n  y = c(a+b);\r\nend","test_suite":"%%\r\na = '1';\r\nb = '2';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7';\r\nb = '31';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '17';\r\nb = '28';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '51';\r\nb = '77';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '82';\r\nb = '262';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7021';\r\nb = '8878';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264';\r\nb = '412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8675308';\r\nb = '2941300';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '9142534264';\r\nb = '8424812653';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164';\r\nb = '8424812753';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '1352408463575';\r\nb = '9898989898985';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264534264534264534264';\r\nb = '412578412578412578412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '86753088675308867530886753088675308';\r\nb = '28413002941300294130029413002941300';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '914253426491425342649142534264914253463';\r\nb = '842481265384248126538424812653842481265324';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164842481275380314231648424812753';\r\nb = '84248127538031423164842481275380314231648424812756';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '43524084635758031423164842481275380314231648424812753';\r\nb = '98989898989858031423164842481275380614231648424812753';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = num2str(randi(835042)*57);\r\nb = char(randi(9,20,1)+48);\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = repelem('1',1,23);\r\na(randi(23)) = '4';\r\nb = num2str(10^randi(14));\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\nfiletext = fileread('PDSseq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'system') || contains(filetext,'regexp') || contains(filetext,'java') || contains(filetext,'for') || contains(filetext,'while') || contains(filetext,'numpy'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2022-02-05T01:46:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-02-04T04:01:11.000Z","updated_at":"2026-01-15T18:05:52.000Z","published_at":"2022-02-04T04:04:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are specified as strings. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55315,"title":"Chain multiplication - 04","description":"Following up on the problem in 55305, you found the optimal way to multiply a chain of matrices.\r\nHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\r\nFor example, \r\nd= [1, 2, 3, 2] and s = \"A(BC)\".\r\nhere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\r\nFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\r\n\r\nn.b. only valid parenthesization are given in this problem for simplicity.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 273px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 136.5px; transform-origin: 407px 136.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFollowing up on the problem in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55305-chain-multiplication-02\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e55305\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, you found the optimal way to multiply a chain of matrices.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ed= [1, 2, 3, 2] and s = \"A(BC)\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ehere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en.b. only valid parenthesization are given in this problem for simplicity.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = chain_mul_04(s,d)\r\n  y = x;\r\nend","test_suite":"%%\r\nd= [1, 2, 3, 2];\r\ns = \"A(BC)\";\r\ny_correct = 16;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [1, 2, 3, 2];\r\ns = \"(AB)C\";\r\ny_correct = 12;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [40, 20, 30, 10, 30];\r\ns = \"A(B(CD))\";\r\ny_correct = 51000;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [40, 20, 30, 10, 30];\r\ns = \"(AB)(CD)\";\r\ny_correct = 69000;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n\r\n%%\r\nd= [81,213,78,96,2,1,98,102, 1200,4];\r\ns = \"(((AB)C)(DE))((FG)(HI))\";\r\ny_correct = 2460558;\r\nassert(isequal(chain_mul_04(s,d),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":363598,"edited_at":"2022-08-16T22:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-16T21:31:49.000Z","updated_at":"2022-08-16T22:04:11.000Z","published_at":"2022-08-16T22:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollowing up on the problem in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55305-chain-multiplication-02\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e55305\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, you found the optimal way to multiply a chain of matrices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ed= [1, 2, 3, 2] and s = \\\"A(BC)\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en.b. only valid parenthesization are given in this problem for simplicity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54720,"title":"Hyperperfect Numbers","description":"A k-hyperperfect number is a natural number n for which the equality n = 1 + k(σ(n)  − n  − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n).\r\n%Example\r\nsigma(6) = 1 + 2 + 3 + 6 = 12\r\n%for k=1\r\n1 + 1*(12-6-1) = 1 + 5 = 6\r\n\r\n%Example\r\nsigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\r\n%for k=3\r\n1 + 3*(434-325-1) = 1 + 3*108 = 324  \r\n\r\nGiven a number x, return the xth Hyperperfect number (serial/order wise) and corresponding k value.\r\n\r\n\r\nP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 386.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 193.45px; transform-origin: 408px 193.45px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.60833px 8px; transform-origin: 6.60833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Hyperperfect_number\"\u003e\u003cspan style=\"perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 72.3417px 8px; transform-origin: 72.3417px 8px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-hyperperfect number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7917px 8px; transform-origin: 63.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a natural number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.625px 8px; transform-origin: 69.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for which the equality \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.8417px 8px; transform-origin: 19.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e = 1 + \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.64167px 8px; transform-origin: 4.64167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eσ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.25px 8px; transform-origin: 12.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e)  − \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.1417px 8px; transform-origin: 16.1417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e  − 1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5667px 8px; transform-origin: 43.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e holds, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.225px 8px; transform-origin: 4.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eσ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Divisor_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003edivisor function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120.175px 8px; transform-origin: 120.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., the sum of all positive divisors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.9px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 91.95px; transform-origin: 405px 91.95px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 111.65px 8.5px; tab-size: 4; transform-origin: 111.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esigma(6) = 1 + 2 + 3 + 6 = 12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%for k=1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.5px; tab-size: 4; transform-origin: 100.1px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 + 1*(12-6-1) = 1 + 5 = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 8.5px; tab-size: 4; transform-origin: 173.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%for k=3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.5px; tab-size: 4; transform-origin: 142.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 + 3*(434-325-1) = 1 + 3*108 = 324  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.7333px 8px; transform-origin: 51.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8333px 8px; transform-origin: 33.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.4417px 8px; transform-origin: 12.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003exth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.175px 8px; transform-origin: 185.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHyperperfect number (serial/order wise) and corresponding \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.675px 8px; transform-origin: 18.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.442px 8px; transform-origin: 360.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = hyper(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('hyper.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'interp1') || contains(filetext, 'find') || ...\r\n          contains(filetext, 'str2num') || contains(filetext, 'switch') || ...\r\n          contains(filetext, '26977') || contains(filetext, '1403221')|| ...\r\n          contains(filetext, '1570153') || contains(filetext, '4304341'); \r\nassert(~illegal)\r\n\r\n\r\n%%\r\nx = 1;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,6)\u0026isequal(k,1))\r\n\r\n%%\r\nx = 2;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,21)\u0026isequal(k,2))\r\n\r\n%%\r\nx = 4;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,6)\u0026isequal(n,301))\r\n\r\n%%\r\nx = 7;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,697)\u0026isequal(k,12))\r\n\r\n%%\r\nx = 11;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,2)\u0026isequal(n,2133))\r\n\r\n%%\r\nx = 17;\r\n[n,k]=hyper(x);\r\nassert(isequal(60,k)\u0026isequal(24601,n))\r\n\r\n%%\r\nx = 18;\r\n[n,k]=hyper(x);\r\nassert(isequal(26977,n)\u0026isequal(48,k))\r\n\r\n%%\r\nx = 20;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,132)\u0026isequal(96361,n))\r\n\r\n%%\r\nx = 21;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,130153)\u0026isequal(k,132))\r\n\r\n%%\r\nx = 25;\r\n[n,k]=hyper(x);\r\nassert(isequal(214273,n)\u0026isequal(k,31))\r\n\r\n%%\r\nx = 31;\r\n[n,k]=hyper(x);\r\nassert(isequal(78,k)\u0026isequal(n,486877))\r\n\r\n%%\r\nx = 37;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,1055833)\u0026isequal(k,348))\r\n\r\n%%\r\nx = 39;\r\n[n,k]=hyper(x);\r\nassert(isequal(1232053,n)\u0026isequal(498,k))\r\n\r\n%%\r\nx = 43;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,12)\u0026isequal(1570153,n))\r\n\r\n%%\r\nx = 45;\r\n[n,k]=hyper(x);\r\nassert(isequal(1787917,n)\u0026isequal(438,k))\r\n\r\n%%\r\nx = 48;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,336)\u0026isequal(2462881,n))\r\n\r\n%%\r\nx = 52;\r\n[n,k]=hyper(x);\r\nassert(isequal(798,k)\u0026isequal(n,2708413))\r\n\r\n%%\r\nx = 53;\r\n[n,k]=hyper(x);\r\nassert(isequal(810,k)\u0026isequal(2768581,n))\r\n\r\n%%\r\nx = 54;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,2856481)\u0026isequal(k,528))\r\n\r\n%%\r\nx = 60;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,162)\u0026isequal(n,4304341))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-13T06:25:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2025-09-13T06:25:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-07T10:09:14.000Z","updated_at":"2025-12-15T21:31:12.000Z","published_at":"2022-06-08T17:42:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Hyperperfect_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-hyperperfect number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a natural number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for which the equality \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e = 1 + \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eσ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e)  − \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e  − 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e holds, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eσ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Divisor_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edivisor function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., the sum of all positive divisors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Example\\nsigma(6) = 1 + 2 + 3 + 6 = 12\\n%for k=1\\n1 + 1*(12-6-1) = 1 + 5 = 6\\n\\n%Example\\nsigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\\n%for k=3\\n1 + 3*(434-325-1) = 1 + 3*108 = 324  ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eHyperperfect number (serial/order wise) and corresponding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54750,"title":"Find the length of stream affected by a spill","description":"When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration  is often computed as a function of time  and distance  from the spill using the advection-dispersion equation:\r\n\r\nwhere  is the mean velocity of the river and  is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass  mixed over the cross section (with area ) at , the concentration can be shown—using some of the math needed for Cody Problem 51625—to be\r\n\r\nWrite a function to compute the length of stream affected by the spill. In other words, find the position  (say) beyond which the concentration never exceeds a threshold . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 282.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 141.35px; transform-origin: 407px 141.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.317px 8px; transform-origin: 378.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.675px 8px; transform-origin: 123.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is often computed as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.833px 8px; transform-origin: 168.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the spill using the advection-dispersion equation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dC/dt + U dC/dx = K d^2C/dx^2\" style=\"width: 126.5px; height: 36.5px;\" width=\"126.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.158px 8px; transform-origin: 202.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.242px 8px; transform-origin: 125.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e mixed over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 8px; transform-origin: 12.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration can be shown—using some of the math needed for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51625\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51625\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5583px 8px; transform-origin: 22.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—to be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.05px; text-align: left; transform-origin: 384px 20.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\" style=\"width: 204.5px; height: 40px;\" width=\"204.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.617px 8px; transform-origin: 313.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFUAAAAoCAYAAACPSbZFAAADXElEQVRoQ+1YO89NQRT9vh8g4lGJyqNQESESoVEgNAoJeolHoRKCQuGREBqJV6LQCIJGQlBoKAgFiUThUao8gh/AWjL7Zptz3D0zZ853cfdJVs69d2bvmbtmP2dywp/qDExW1+gKJ5zUHozASXVSe2CgB5VuqU5qZwZWGRo+YPx911XGzVJJ6krgRETcfXw/CrwGPjmpZQzcg9i6IPoc7+Vlatqlxs1ShYXP+DAjfNmG9zUntRsD8yD+TqmYXyOO6i2No6XuAAEXAgkkd0G3M2pKjyOpdPUtgYrjeB8aFal0mTl/yI7MqN+Bl7U315M+HU83Yo27tdcZZqmLsRhdZS3AuMNHnyzHb4WxL3gvS4hNszBnUYU/UVpPcs8v1Pq9eOowpbTOrwDrtreBPMagFcB0gKXIeYCuNDPA4otW/cialDC+E3MuJsyLp+zDD1KjsjZdX6DDFEk9Kb0ZWu114DSQW4rQUuLC29xky4Qz+K3EbXV9uh86TpYsbsmkkqotjBb6AKge4K3Ndhxn6PmodKzG58cddbaKp5JK4R9BA+Mn3f1fezZgw3em4j/kkCquU72tm6LTOYZ1Doa1GL629rVuDqlS39FSFwIlFw+jzP7PsGdWKHxKE13SOaSSqrsQKi6t70aV/UtaUxrAFSC7QkghVWo7Zn3pmUs7kVFlf7r61WBmqa0pK56lJWHCIpWn9RTYA7CEaYur5/D7KaDz5W6Sb5VN4h53BVHW1rsNNWJIRTdYbaTS1fk8AS4BNwCp5+J6dS/GGGP/9vJKt6aWlzFE3QZ4NRjfYEmXqc+EXnAAGDQjMalxzIuzZNzm9ZpFy4yyIRXnA1Yvh4Fv0cy5+L4JkMuWuOOSEKLziRzWb+THpNLdjwAM7A+Vher1aa1rhoxX4qKzGv6HzWGvJcp01yaExlbO2r1RYloxtWQz/5sMDe0NQKvkvYeUkuK1jXDipNomIE1DfFcgya9RXjqpNqnSNCzBVLkz1rlltrLeX9qcVJtUufOQZMRwcDYkNMbT7cA0YHA546TapEptTvd/BbBmvwywmWCFQJLZdQ3adifVJpVVBOtxqYhuBhHGVDY8jcbHSbVJzZ7hpGZTZgs4qTZH2TOc1GzKbAEn1eYoe4aTmk2ZLeCk2hxlz/gJfpacKXO5h08AAAAASUVORK5CYII=\" alt=\"x = L_a\" style=\"width: 42.5px; height: 20px;\" width=\"42.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3417px 8px; transform-origin: 44.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) beyond which the concentration never exceeds a threshold \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = C_t\" style=\"width: 46px; height: 20px;\" width=\"46\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function La = affectedReach(U,K,M,A,Ct)\r\n% La = length of affected reach of stream [L]\r\n% U  = mean velocity [L/T]\r\n% K  = dispersion coefficient [L^2/T]\r\n% M  = mass of contaminant [M]\r\n% A  = cross-sectional area (L^2)\r\n% Ct = threshold concentration (M/L^3)\r\n\r\n  La = M/(Ct*A);\r\nend","test_suite":"%%\r\nM = 100;                    %  Mass (kg)\r\nA = 30;                     %  Cross-sectional area (m2)\r\nU = 0.3;                    %  Mean velocity (m/s)\r\nK = 2;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 50;                     %  Mass (kg)\r\nA = 15;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 8.4;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.001;                 %  Target concentration (kg/m3)\r\nLa_correct = 26332.1;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 0.003;                 %  Target concentration (kg/m3)\r\nLa_correct = 91.59;         %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 3e-4;                  %  Target concentration (kg/m3)\r\nLa_correct = 7256.28;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 70;                     %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.15;                   %  Mean velocity (m/s)\r\nK = 1;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 280;                    %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.54;                   %  Mean velocity (m/s)\r\nK = 3.7;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.007;                 %  Target concentration (kg/m3)\r\nLa_correct = 42140.42;      %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%% Approximately plug flow\r\nM = 5*rand;                 %  Mass (kg)\r\nA = 40;                     %  Cross-sectional area (m2)\r\nU = 0.3*(1+rand);           %  Mean velocity (m/s)\r\nK = rand*1e-3;              %  Dispersion coefficient (m2/s)\r\nCt = 0.02*rand;             %  Target concentration (kg/m3)\r\nLa_approx = (U/(4*pi*K))*(M/(Ct*A))^2;\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_approx)/La_approx\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('affectedReach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'if'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-14T05:04:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-06-14T05:04:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-14T04:57:20.000Z","updated_at":"2022-06-14T05:04:44.000Z","published_at":"2022-06-14T04:59:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is often computed as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the spill using the advection-dispersion equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + U dC/dx = K d^2C/dx^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t} + U \\\\frac{\\\\partial C}{\\\\partial x} = K \\\\frac{\\\\partial^2 C}{\\\\partial x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e mixed over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the concentration can be shown—using some of the math needed for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51625\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51625\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—to be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L_a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L_a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) beyond which the concentration never exceeds a threshold \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = C_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = C_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61010,"title":"q-dimensional Cartesian product","description":"Your mission, should you choose to accept it, is to compute a q-dimensional Cartesian product, as follows. Let the input G be an 1×q cell array of vectors of size 1×n_i each (here and in the following, 1≤i≤q). The output V should be a q-dimensional cell array of size n_1×n_2×…×n_q such that for 1≤k_i≤n_i, V{k_1,k_2,…,k_q} is equal to the vector [ G{1}(k_1), G{2}(k_2), …, G{q}(k_q) ]. In other words, the indices into V are the Cartesian product of the indices into the vectors in G, and each element of V is the combination of values from those vectors at those indices.\r\n\r\nAn example: if G = { 1:2, 3:4 }, then V = { [1 3], [1 4] ; [2 3], [2 4] }; if G = { 1:2, 3:4, 5:6 }, then V(:, :, 1) = { [1 3 5], [1 4 5] ; [2 3 5], [2 4 5] } and V(:, :, 2) = { [1 3 6], [1 4 6] ; [2 3 6], [2 4 6] }; and so on.\r\n\r\nNote: due to the way MATLAB handles trailing singleton dimensions, ndims(V) will report a number less than q if n_j = … = n_q = 1 for some j≤q. This is alright since indexing V along q dimensions will still work. \r\n\r\nNote 2: cheating isn't banned by the test suite, but don't do it. It's not sportsmanlike.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 348px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 174px; transform-origin: 408px 174px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.5px; text-align: left; transform-origin: 385px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour mission, should you choose to accept it, is to compute a q-dimensional Cartesian product, as follows. Let the input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eG\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an 1×q cell array of vectors of size 1×n_i each (here and in the following, 1≤i≤q). The output \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should be a q-dimensional cell array of size n_1×n_2×…×n_q such that for 1≤k_i≤n_i, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV{k_1,k_2,…,k_q}\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is equal to the vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[ G{1}(k_1), G{2}(k_2), …, G{q}(k_q) ]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In other words, the indices into \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the Cartesian product of the indices into the vectors in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eG\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and each element of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the combination of values from those vectors at those indices.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn example: if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eG = { 1:2, 3:4 }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV = { [1 3], [1 4] ; [2 3], [2 4] }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eG = { 1:2, 3:4, 5:6 }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV(:, :, 1) = { [1 3 5], [1 4 5] ; [2 3 5], [2 4 5] }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV(:, :, 2) = { [1 3 6], [1 4 6] ; [2 3 6], [2 4 6] }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote: due to the way MATLAB handles trailing singleton dimensions, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003endims(V)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will report a number less than q if n_j = … = n_q = 1 for some j≤q. This is alright since indexing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e along q dimensions will still work. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote 2: cheating isn't banned by the test suite, but don't do it. It's not sportsmanlike.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function V = grid2vectors(G)\r\n    \r\nend\r\n","test_suite":"%%\r\nassert(isequal(grid2vectors({1:10}), num2cell(1:10).'))\r\n\r\n%% \r\nassert(isequal(grid2vectors({1:2, 3:4}), {[1 3], [1 4] ; [2 3], [2 4]}))\r\n\r\n%%\r\nV = grid2vectors({1:2, 3:4, 5:6});\r\nassert(isequal(V(:, :, 1), { [1 3 5], [1 4 5] ; [2 3 5], [2 4 5] }));\r\nassert(isequal(V(:, :, 2), { [1 3 6], [1 4 6] ; [2 3 6], [2 4 6] }));\r\n\r\n%%\r\nassert(isequal(grid2vectors({1, 2, 3, 4, 5}), {[1 2 3 4 5]}))\r\n\r\n%%\r\nV = grid2vectors({1:2 3 4:5 6 7});\r\nassert(isequal(V(:, :, 1), { [1 3 4 6 7] ; [2 3 4 6 7] }));\r\nassert(isequal(V(:, :, 2), { [1 3 5 6 7] ; [2 3 5 6 7] }));\r\n\r\n%%\r\nV(:,:,1,1) = [\r\n    {[-1 2 -1 1]}    {[-1 2.2500 -1 1]}    {[-1 2.5000 -1 1]}    {[-1 2.7500 -1 1]}    {[-1 3 -1 1]};\r\n    {[ 0 2 -1 1]}    {[ 0 2.2500 -1 1]}    {[ 0 2.5000 -1 1]}    {[ 0 2.7500 -1 1]}    {[ 0 3 -1 1]};\r\n    {[ 1 2 -1 1]}    {[ 1 2.2500 -1 1]}    {[ 1 2.5000 -1 1]}    {[ 1 2.7500 -1 1]}    {[ 1 3 -1 1]}\r\n];\r\n\r\nV(:,:,2,1) = [\r\n    {[-1 2 1 1]}    {[-1 2.2500 1 1]}    {[-1 2.5000 1 1]}    {[-1 2.7500 1 1]}    {[-1 3 1 1]};\r\n    {[ 0 2 1 1]}    {[ 0 2.2500 1 1]}    {[ 0 2.5000 1 1]}    {[ 0 2.7500 1 1]}    {[ 0 3 1 1]};\r\n    {[ 1 2 1 1]}    {[ 1 2.2500 1 1]}    {[ 1 2.5000 1 1]}    {[ 1 2.7500 1 1]}    {[ 1 3 1 1]}\r\n];\r\n\r\nV(:,:,1,2) = [\r\n    {[-1 2 -1 1.2500]}    {[-1 2.2500 -1 1.2500]}    {[-1 2.5000 -1 1.2500]}    {[-1 2.7500 -1 1.2500]}    {[-1 3 -1 1.2500]};\r\n    {[ 0 2 -1 1.2500]}    {[ 0 2.2500 -1 1.2500]}    {[ 0 2.5000 -1 1.2500]}    {[ 0 2.7500 -1 1.2500]}    {[ 0 3 -1 1.2500]};\r\n    {[ 1 2 -1 1.2500]}    {[ 1 2.2500 -1 1.2500]}    {[ 1 2.5000 -1 1.2500]}    {[ 1 2.7500 -1 1.2500]}    {[ 1 3 -1 1.2500]}\r\n];\r\n\r\nV(:,:,2,2) = [\r\n    {[-1 2 1 1.2500]}    {[-1 2.2500 1 1.2500]}    {[-1 2.5000 1 1.2500]}    {[-1 2.7500 1 1.2500]}    {[-1 3 1 1.2500]};\r\n    {[ 0 2 1 1.2500]}    {[ 0 2.2500 1 1.2500]}    {[ 0 2.5000 1 1.2500]}    {[ 0 2.7500 1 1.2500]}    {[ 0 3 1 1.2500]};\r\n    {[ 1 2 1 1.2500]}    {[ 1 2.2500 1 1.2500]}    {[ 1 2.5000 1 1.2500]}    {[ 1 2.7500 1 1.2500]}    {[ 1 3 1 1.2500]}\r\n];\r\n\r\nV(:,:,1,3) = [\r\n    {[-1 2 -1 1.5000]}    {[-1 2.2500 -1 1.5000]}    {[-1 2.5000 -1 1.5000]}    {[-1 2.7500 -1 1.5000]}    {[-1 3 -1 1.5000]};\r\n    {[ 0 2 -1 1.5000]}    {[ 0 2.2500 -1 1.5000]}    {[ 0 2.5000 -1 1.5000]}    {[ 0 2.7500 -1 1.5000]}    {[ 0 3 -1 1.5000]};\r\n    {[ 1 2 -1 1.5000]}    {[ 1 2.2500 -1 1.5000]}    {[ 1 2.5000 -1 1.5000]}    {[ 1 2.7500 -1 1.5000]}    {[ 1 3 -1 1.5000]}\r\n];\r\n\r\nV(:,:,2,3) = [\r\n    {[-1 2 1 1.5000]}    {[-1 2.2500 1 1.5000]}    {[-1 2.5000 1 1.5000]}    {[-1 2.7500 1 1.5000]}    {[-1 3 1 1.5000]};\r\n    {[ 0 2 1 1.5000]}    {[ 0 2.2500 1 1.5000]}    {[ 0 2.5000 1 1.5000]}    {[ 0 2.7500 1 1.5000]}    {[ 0 3 1 1.5000]};\r\n    {[ 1 2 1 1.5000]}    {[ 1 2.2500 1 1.5000]}    {[ 1 2.5000 1 1.5000]}    {[ 1 2.7500 1 1.5000]}    {[ 1 3 1 1.5000]}\r\n];\r\n\r\nV(:,:,1,4) = [\r\n    {[-1 2 -1 1.7500]}    {[-1 2.2500 -1 1.7500]}    {[-1 2.5000 -1 1.7500]}    {[-1 2.7500 -1 1.7500]}    {[-1 3 -1 1.7500]};\r\n    {[ 0 2 -1 1.7500]}    {[ 0 2.2500 -1 1.7500]}    {[ 0 2.5000 -1 1.7500]}    {[ 0 2.7500 -1 1.7500]}    {[ 0 3 -1 1.7500]};\r\n    {[ 1 2 -1 1.7500]}    {[ 1 2.2500 -1 1.7500]}    {[ 1 2.5000 -1 1.7500]}    {[ 1 2.7500 -1 1.7500]}    {[ 1 3 -1 1.7500]}\r\n];\r\n\r\nV(:,:,2,4) = [\r\n    {[-1 2 1 1.7500]}    {[-1 2.2500 1 1.7500]}    {[-1 2.5000 1 1.7500]}    {[-1 2.7500 1 1.7500]}    {[-1 3 1 1.7500]};\r\n    {[ 0 2 1 1.7500]}    {[ 0 2.2500 1 1.7500]}    {[ 0 2.5000 1 1.7500]}    {[ 0 2.7500 1 1.7500]}    {[ 0 3 1 1.7500]};\r\n    {[ 1 2 1 1.7500]}    {[ 1 2.2500 1 1.7500]}    {[ 1 2.5000 1 1.7500]}    {[ 1 2.7500 1 1.7500]}    {[ 1 3 1 1.7500]}\r\n];\r\n\r\nV(:,:,1,5) = [\r\n    {[-1 2 -1 2]}    {[-1 2.2500 -1 2]}    {[-1 2.5000 -1 2]}    {[-1 2.7500 -1 2]}    {[-1 3 -1 2]};\r\n    {[ 0 2 -1 2]}    {[ 0 2.2500 -1 2]}    {[ 0 2.5000 -1 2]}    {[ 0 2.7500 -1 2]}    {[ 0 3 -1 2]};\r\n    {[ 1 2 -1 2]}    {[ 1 2.2500 -1 2]}    {[ 1 2.5000 -1 2]}    {[ 1 2.7500 -1 2]}    {[ 1 3 -1 2]}\r\n];\r\n\r\nV(:,:,2,5) = [\r\n    {[-1 2 1 2]}    {[-1 2.2500 1 2]}    {[-1 2.5000 1 2]}    {[-1 2.7500 1 2]}    {[-1 3 1 2]};\r\n    {[ 0 2 1 2]}    {[ 0 2.2500 1 2]}    {[ 0 2.5000 1 2]}    {[ 0 2.7500 1 2]}    {[ 0 3 1 2]};\r\n    {[ 1 2 1 2]}    {[ 1 2.2500 1 2]}    {[ 1 2.5000 1 2]}    {[ 1 2.7500 1 2]}    {[ 1 3 1 2]}\r\n];\r\n\r\nassert(isequal(grid2vectors({[-1 0 1], 2:0.25:3, [-1 1], 1:0.25:2}), V))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":332395,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-02T09:35:39.000Z","updated_at":"2026-03-03T15:00:19.000Z","published_at":"2025-10-02T09:35:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYour mission, should you choose to accept it, is to compute a q-dimensional Cartesian product, as follows. Let the input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e be an 1×q cell array of vectors of size 1×n_i each (here and in the following, 1≤i≤q). The output \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e should be a q-dimensional cell array of size n_1×n_2×…×n_q such that for 1≤k_i≤n_i, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV{k_1,k_2,…,k_q}\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e is equal to the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ G{1}(k_1), G{2}(k_2), …, G{q}(k_q) ]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. In other words, the indices into \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e are the Cartesian product of the indices into the vectors in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, and each element of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e is the combination of values from those vectors at those indices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eAn example: if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG = { 1:2, 3:4 }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV = { [1 3], [1 4] ; [2 3], [2 4] }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e; if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG = { 1:2, 3:4, 5:6 }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV(:, :, 1) = { [1 3 5], [1 4 5] ; [2 3 5], [2 4 5] }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV(:, :, 2) = { [1 3 6], [1 4 6] ; [2 3 6], [2 4 6] }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e; and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eNote: due to the way MATLAB handles trailing singleton dimensions, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003endims(V)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e will report a number less than q if n_j = … = n_q = 1 for some j≤q. This is alright since indexing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e along q dimensions will still work. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eNote 2: cheating isn't banned by the test suite, but don't do it. It's not sportsmanlike.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53125,"title":"Easy Sequences 54: Product of Products of Proper Divisors","description":"A divisor of a number that is less than the number is called a \"proper divisor\". \r\nFor a given positive integer , we are asked to evaluate the following summation:\r\n             \r\nThis is equivalent to finding the product of the products of proper divisors of all integers from  to .\r\nFor example for , we have:\r\n                            \r\nPlease present your output modulo .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 413.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.75px; transform-origin: 407px 206.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA divisor of a number that is less than the number is called a \"proper divisor\". \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eor a given positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we are asked to evaluate the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.75px; text-align: left; transform-origin: 384px 22.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 110px; height: 45.5px;\" width=\"110\" height=\"45.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is equivalent to finding \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233px 8px; transform-origin: 233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethe product of the products of proper divisors of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e2\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 209px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.5px; text-align: left; transform-origin: 384px 104.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-99px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 509px; height: 209px;\" width=\"509\" height=\"209\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.5px 8px; transform-origin: 112.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease present your output modulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 55.5px; height: 18px;\" width=\"55.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = pppd(n)\r\n    s = 2 * (n + 2) ^ 2 * n;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 2880;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 20;\r\ns_correct = 178754;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 651627;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 200;\r\ns_correct = 471492;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 132068;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 2000;\r\ns_correct = 192916;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 700691;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 20000;\r\ns_correct = 135567;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 919193;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 200000;\r\ns_correct = 581218;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 811966;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nns = 2000000:2222222;\r\ns = arrayfun(@(n) pppd(n),ns);\r\nss = mod([sum(s) sum(num2str(s))],1000003);\r\nss_correct = [526924 445038];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('pppd.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-12-04T15:11:17.000Z","updated_at":"2026-03-19T13:19:46.000Z","published_at":"2021-12-06T15:33:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA divisor of a number that is less than the number is called a \\\"proper divisor\\\". \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eor a given positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we are asked to evaluate the following summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\prod_{i=2}^{n}\\\\left (\\\\prod_{\\\\ d|i\\\\ \\\\\u0026amp;\\\\  d\u0026lt;i}^{}d\\\\   \\\\right )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is equivalent to finding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe product of the products of proper divisors of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\prod_{i=2}^{10}\\\\prod_{d|i\\\\ \\\\\u0026amp;\\\\  d\u0026lt;i}^{}d\\\\ = \\\\prod_{d|2\\\\ \\\\\u0026amp;\\\\  d\u0026lt;2}^{}d \\\\ \\\\times\\\\prod_{d|3\\\\ \\\\\u0026amp;\\\\  d\u0026lt;3}^{}d \\\\ \\\\times\\\\prod_{d|4\\\\ \\\\\u0026amp;\\\\  d\u0026lt;4}^{}d  \\\\ \\\\times\\\\prod_{d|5\\\\ \\\\\u0026amp;\\\\  d\u0026lt;5}^{}d\\\\ \\\\times\\\\prod_{d|6\\\\ \\\\\u0026amp;\\\\  d\u0026lt;6}^{}d \\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\times\\\\prod_{d|7\\\\ \\\\\u0026amp;\\\\  d\u0026lt;7}^{}d \\\\ \\\\times\\\\prod_{d|8\\\\ \\\\\u0026amp;\\\\  d\u0026lt;8}^{}d \\\\ \\\\times\\\\prod_{d|9\\\\ \\\\\u0026amp;\\\\  d\u0026lt;9}^{}d \\\\ \\\\times\\\\prod_{d|10\\\\ \\\\\u0026amp;\\\\  d\u0026lt;10}^{}d \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =1\\\\times1\\\\times(1\\\\cdot2)\\\\times1\\\\times(1\\\\cdot2\\\\cdot3)\\\\times1\\\\times(1\\\\cdot2\\\\cdot4)\\\\times(1\\\\cdot3)\\\\times(1\\\\cdot2\\\\cdot5) \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =1\\\\times1\\\\times2\\\\times1\\\\times6\\\\times1\\\\times8\\\\times3\\\\times10 \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =2880\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present your output modulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1000003\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61176,"title":"[Master Regular Expression] Reformat Phone Number","description":"You are given a phone number as a string number. number consists of digits, spaces ' ', and/or dashes '-'.\r\nYou would like to reformat the phone number in a certain manner. Firstly, remove all spaces and dashes. Then, group the digits from left to right into blocks of length 3 until there are 4 or fewer digits. The final digits are then grouped as follows:\r\n2 digits: A single block of length 2.\r\n3 digits: A single block of length 3.\r\n4 digits: Two blocks of length 2 each.\r\nThe blocks are then joined by dashes. Notice that the reformatting process should never produce any blocks of length 1 and produce at most two blocks of length 2.\r\nReturn the phone number after formatting.\r\n \r\nExample 1:\r\nInput: number = \"1-23-45 6\"\r\nOutput: \"123-456\"\r\nExplanation: The digits are \"123456\".\r\nStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \"123\".\r\nStep 2: There are 3 digits remaining, so put them in a single block of length 3. The 2nd block is \"456\".\r\nJoining the blocks gives \"123-456\".\r\nExample 2:\r\nInput: number = \"123 4-567\"\r\nOutput: \"123-45-67\"\r\nExplanation: The digits are \"1234567\".\r\nStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \"123\".\r\nStep 2: There are 4 digits left, so split them into two blocks of length 2. The blocks are \"45\" and \"67\".\r\nJoining the blocks gives \"123-45-67\".\r\nExample 3:\r\nInput: number = \"123 4-5678\"\r\nOutput: \"123-456-78\"\r\nExplanation: The digits are \"12345678\".\r\nStep 1: The 1st block is \"123\".\r\nStep 2: The 2nd block is \"456\".\r\nStep 3: There are 2 digits left, so put them in a single block of length 2. The 3rd block is \"78\".\r\nJoining the blocks gives \"123-456-78\".\r\n \r\nConstraints: \r\n2 \u003c= number.length \u003c= 100\r\nnumber consists of digits and the characters '-' and ' '.\r\nThere are at least two digits in number","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1056.62px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 528.312px; transform-origin: 408px 528.312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a phone number as a string number. number consists of digits, spaces ' ', and/or dashes '-'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou would like to reformat the phone number in a certain manner. Firstly, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eremove\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e all spaces and dashes. Then, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003egroup\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the digits from left to right into blocks of length 3 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003euntil\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e there are 4 or fewer digits. The final digits are then grouped as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2 digits: A single block of length 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3 digits: A single block of length 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4 digits: Two blocks of length 2 each.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe blocks are then joined by dashes. Notice that the reformatting process should \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enever\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e produce any blocks of length 1 and produce \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eat most\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e two blocks of length 2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ethe phone number after formatting.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number = \"1-23-45 6\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"123-456\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The digits are \"123456\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \"123\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: There are 3 digits remaining, so put them in a single block of length 3. The 2nd block is \"456\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eJoining the blocks gives \"123-456\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number = \"123 4-567\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"123-45-67\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe digits are \"1234567\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \"123\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: There are 4 digits left, so split them into two blocks of length 2. The blocks are \"45\" and \"67\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eJoining the blocks gives \"123-45-67\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 3:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number = \"123 4-5678\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"123-456-78\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The digits are \"12345678\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: The 1st block is \"123\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: The 2nd block is \"456\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: There are 2 digits left, so put them in a single block of length 2. The 3rd block is \"78\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eJoining the blocks gives \"123-456-78\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2 \u0026lt;= number.length \u0026lt;= 100\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003enumber consists of digits and the characters '-' and ' '.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are at least \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etwo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits in number\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(number)\r\n\r\nend","test_suite":"%%\r\ncode = fileread('solution.m');\r\nassert(contains(code, 'regexp') || contains(code, 'regexprep'), 'Phải dùng regexp hoặc regexprep');\r\nassert(~contains(code, 'for'), 'Không cho dùng for');\r\nassert(~contains(code, 'while'), 'Không cho dùng while');\r\n%%\r\nnumber = '1-23-45 6';\r\ncorrect_answer = '123-456';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '123 4-567';\r\ncorrect_answer = '123-45-67';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '123 4-5678';\r\ncorrect_answer = '123-456-78';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5048 479  2-57---6-65 323408- 3 0 44 53832506002399320060523835 44 0 3 -804323 56-6---75-2  974 8405';\r\ncorrect_answer = '504-847-925-766-532-340-830-445-383-250-600-239-932-006-052-383-544-038-043-235-667-529-748-405';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '885-2- 703- 33 -307 -2-588';\r\ncorrect_answer = '885-270-333-307-25-88';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '18 61891-7449764808-74-2166  73266237  6612-47-8084679447-19816 81';\r\ncorrect_answer = '186-189-174-497-648-087-421-667-326-623-766-124-780-846-794-471-981-681';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '--4-88- 8056928602564-99-4652068296508 -88-4--';\r\ncorrect_answer = '488-805-692-860-256-499-465-206-829-650-88-84';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '2 950668--55--866059 2';\r\ncorrect_answer = '295-066-855-866-05-92';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '- -99508 9009 80599- -';\r\ncorrect_answer = '995-089-009-805-99';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = ' 7542-528825-2457 ';\r\ncorrect_answer = '754-252-882-524-57';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '85  58';\r\ncorrect_answer = '85-58';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '7817 2 -77- 2 7187';\r\ncorrect_answer = '781-727-727-187';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5--5';\r\ncorrect_answer = '55';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = ' 5486-513315-6845 ';\r\ncorrect_answer = '548-651-331-568-45';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-999841-44-148999-';\r\ncorrect_answer = '999-841-441-489-99';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '7934 -4--- 3--- 7--0 68---5445885445---86 0--7 ---3 ---4- 4397';\r\ncorrect_answer = '793-443-706-854-458-854-458-607-344-397';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-  220985027  --  720589022  -';\r\ncorrect_answer = '220-985-027-720-589-022';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '651831 6 168--55193-5621 -6-92014  2 2 11 2 2  41029-6- 1265-39155--861 6 138156';\r\ncorrect_answer = '651-831-616-855-193-562-169-201-422-112-241-029-612-653-915-586-161-381-56';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-7-4825-5- 07 628--------826 70 -5-5284-7-';\r\ncorrect_answer = '748-255-076-288-267-055-28-47';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-- 2171645---30- 8380624--35  031  130  53--4260838 -03---5461712 --';\r\ncorrect_answer = '217-164-530-838-062-435-031-130-534-260-838-035-461-712';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '4 25-  -494- -  612-08--61724-2 5710-1-5650  0565-1-0175 2-42716--80-216  - -494-  -52 4';\r\ncorrect_answer = '425-494-612-086-172-425-710-156-500-565-101-752-427-168-021-649-45-24';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '9  7-1062-0163-57488475-3610-2601-7  9';\r\ncorrect_answer = '971-062-016-357-488-475-361-026-01-79';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-9-1609  0 45 1368464-9290  0929-4648631 54 0  9061-9-';\r\ncorrect_answer = '916-090-451-368-464-929-009-294-648-631-540-906-19';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5  5';\r\ncorrect_answer = '55';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '628826';\r\ncorrect_answer = '628-826';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5-0 4-45------54-4 0-5';\r\ncorrect_answer = '504-455-44-05';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '15 9-3430 4041180-0726-9-56 - 2443 4--9-499481  184994-9--4 3442 - 65-9-6270-0811404 0343-9 51';\r\ncorrect_answer = '159-343-040-411-800-726-956-244-349-499-481-184-994-943-442-659-627-008-114-040-343-951';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '90-03562-1 941--256 -- 9-5- -61-9 8-2 2198 00 8912 2-8 9-16- -5-9 -- 652--149 1-26530-09';\r\ncorrect_answer = '900-356-219-412-569-561-982-219-800-891-228-916-596-521-491-265-30-09';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '8 2882 8';\r\ncorrect_answer = '828-828';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '90427 -0--7512 8 6 6-19-48-8 88 8-84-91-6 6 8 2157--0- 72409';\r\ncorrect_answer = '904-270-751-286-619-488-888-849-166-821-570-724-09';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '61-67 05 0045 26 -8--9--5--5 42 9834 8443781221873448 4389 24 5--5--9--8- 62 5400 50 76-16';\r\ncorrect_answer = '616-705-004-526-895-542-983-484-437-812-218-734-484-389-245-598-625-400-507-616';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '87126  98-742368-44932070888807023944-863247-89  62178';\r\ncorrect_answer = '871-269-874-236-844-932-070-888-807-023-944-863-247-896-21-78';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5 867768 5';\r\ncorrect_answer = '586-776-85';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '1  89893   20 -804--  --408- 02   39898  1';\r\ncorrect_answer = '189-893-208-044-080-239-89-81';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = ' 186960670076069681 ';\r\ncorrect_answer = '186-960-670-076-069-681';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4945898,"edited_by":4945898,"edited_at":"2026-02-01T15:35:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2026-02-01T15:35:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T12:40:48.000Z","updated_at":"2026-04-01T12:48:58.000Z","published_at":"2026-01-31T12:40:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a phone number as a string number. number consists of digits, spaces ' ', and/or dashes '-'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou would like to reformat the phone number in a certain manner. Firstly, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eremove\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e all spaces and dashes. Then, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egroup\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the digits from left to right into blocks of length 3 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003euntil\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e there are 4 or fewer digits. The final digits are then grouped as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2 digits: A single block of length 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3 digits: A single block of length 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4 digits: Two blocks of length 2 each.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe blocks are then joined by dashes. Notice that the reformatting process should \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enever\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e produce any blocks of length 1 and produce \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eat most\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e two blocks of length 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe phone number after formatting.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number = \\\"1-23-45 6\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"123-456\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The digits are \\\"123456\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \\\"123\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: There are 3 digits remaining, so put them in a single block of length 3. The 2nd block is \\\"456\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJoining the blocks gives \\\"123-456\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number = \\\"123 4-567\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"123-45-67\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe digits are \\\"1234567\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \\\"123\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: There are 4 digits left, so split them into two blocks of length 2. The blocks are \\\"45\\\" and \\\"67\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJoining the blocks gives \\\"123-45-67\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 3:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number = \\\"123 4-5678\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"123-456-78\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The digits are \\\"12345678\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: The 1st block is \\\"123\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: The 2nd block is \\\"456\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: There are 2 digits left, so put them in a single block of length 2. The 3rd block is \\\"78\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJoining the blocks gives \\\"123-456-78\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2 \u0026lt;= number.length \u0026lt;= 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003enumber consists of digits and the characters '-' and ' '.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are at least \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e digits in number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60411,"title":"Compute a sequence with the whyphi sieve","description":"A few problems on Cody involve sieving. For example, Cody Problem 45367 involves the famous Sieve of Eratosthenes. CP 50811 uses the sieve of Flavius Josephus, and CP 50913 uses the golden sieve. \r\nThis problem uses a process that I will call the whyphi sieve: \r\nMake a list x of integers 1, 2, 3,… \r\nRemove the first term. That is, delete x(1).\r\nRenumber the terms. \r\nDelete x(2) and x(2+1)\r\nRenumber the terms. \r\nDelete x(3), x(3+2), and x(3+2+1). \r\nContinue renumbering and deleting terms in this way. \r\nWrite a function to compute the nth term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 266.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 133.017px; transform-origin: 407px 133.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170.375px 7.79167px; transform-origin: 170.375px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA few problems on Cody involve sieving. For example, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45367\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 45367\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.075px 7.79167px; transform-origin: 138.075px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the famous Sieve of Eratosthenes. \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50811\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 50811\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.967px 7.79167px; transform-origin: 127.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uses the sieve of Flavius Josephus, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50913\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 50913\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 7.79167px; transform-origin: 73.5167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uses the golden sieve. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.65px 7.79167px; transform-origin: 188.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem uses a process that I will call the whyphi sieve: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 143.033px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 71.5167px; transform-origin: 391px 71.5167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.775px 7.79167px; transform-origin: 105.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake a list x of integers 1, 2, 3,… \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 130.667px 7.79167px; transform-origin: 130.667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemove the first term. That is, delete x(1).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRenumber the terms. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 69.8333px 7.79167px; transform-origin: 69.8333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDelete x(2) and x(2+1)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRenumber the terms. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 107.567px 7.79167px; transform-origin: 107.567px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDelete x(3), x(3+2), and x(3+2+1). \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 166.758px 7.79167px; transform-origin: 166.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eContinue renumbering and deleting terms in this way. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 181.108px 7.79167px; transform-origin: 181.108px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the nth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = whyphiSieve(n)\r\n  c = 100*[0.000057513128234 0.093378634167431 -2.856145294974328]\r\n  y = polyval(c,n);\r\nend","test_suite":"%%\r\nassert(isequal(whyphiSieve(1),2))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(5),14))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(19),79))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(54),305))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(89),594))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(135),1032))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(336),3443))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(689),8948))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(1000),14685))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(4509),109040))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(whyphiSieve(428)),116991))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(whyphiSieve(620)),225368))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(10000),315192))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(20000),793960))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-04T15:38:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-28T02:46:53.000Z","updated_at":"2026-03-30T07:39:19.000Z","published_at":"2024-05-28T02:47:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few problems on Cody involve sieving. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45367\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45367\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the famous Sieve of Eratosthenes. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50811\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 50811\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e uses the sieve of Flavius Josephus, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50913\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 50913\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e uses the golden sieve. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem uses a process that I will call the whyphi sieve: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a list x of integers 1, 2, 3,… \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemove the first term. That is, delete x(1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRenumber the terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDelete x(2) and x(2+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRenumber the terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDelete x(3), x(3+2), and x(3+2+1). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eContinue renumbering and deleting terms in this way. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the nth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61277,"title":"The Optimal 2D Guillotine Cutting Stock Problem","description":"You are working in a factory that produces rectangular glass sheets. You have a large stock plate of size W x H. Customers have placed order for N differents types of smaller rectangular pieces. Each piece type  has dimensions  and a specific market value .\r\nThe Challenge:\r\nYou need to cut the stock plate to maximize the total value of the pieces obtained. However, you must follow the Guillotine Cut constraint:\r\nEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\r\nYou can rotate the pieces 90 degrees if it helps.\r\nThis is a \"2nd-stage\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). Or, to make it harder, we allow recursive guillotine cuts to any depth.\r\nInput:\r\nStockSize: A 1x2 vector [W, H] ( The dimensions of the large plate ).\r\nItems: An N x 3 matrix. Each row is [width, height, value].\r\nOutput:\r\nmaxValue: The maximum total value you can extract from the stock plate","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 440.367px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 333.5px 220.183px; transform-origin: 333.5px 220.183px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 31.7333px; text-align: left; transform-origin: 309.5px 31.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are working in a factory that produces rectangular glass sheets. You have a large stock plate of size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eH\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Customers have placed order for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e differents types of smaller rectangular pieces. Each piece type \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"20\" style=\"width: 42.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a specific market value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12.5\" height=\"20\" style=\"width: 12.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe Challenge:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou need to cut the stock plate to maximize the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etotal value\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the pieces obtained. However, you must follow the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGuillotine Cut constraint:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 122.6px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 61.3px; transform-origin: 316.5px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou can rotate the pieces 90 degrees if it helps.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 30.65px; text-align: left; transform-origin: 288.5px 30.65px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is a \"2nd-stage\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOr, to make it harder, we allow recursive guillotine cuts to any depth.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eStockSize: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA 1x2 vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[W, H]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ( The dimensions of the large plate ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eItems:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex 3 matrix. Each row is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[width, height, value].\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 10.2167px; transform-origin: 316.5px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emaxValue:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The maximum total value you can extract from the stock plate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function maxValue = solve_guillotine(StockSize,Item)\r\n\r\nend","test_suite":"%% Test Case 1: \r\nassert(isequal(solve_guillotine([10, 10], [5, 5, 100]), 400))\r\n\r\n%% Test Case 2: \r\nItems2 = [3, 3, 10; 4, 2, 8; 1, 10, 12];\r\nassert(isequal(solve_guillotine([10, 10], Items2), 120)) % Giá trị giả định\r\n\r\n%% Test Case 3: \r\nrand_w = randi([15, 20]);\r\nrand_h = randi([15, 20]);\r\nval1 = randi([50, 100]);\r\nval2 = randi([50, 100]);\r\nitems_rand = [rand_w, floor(rand_h/2), val1; rand_w, ceil(rand_h/2), val2];\r\nexpected = val1 + val2;\r\nactual = solve_guillotine([rand_w, rand_h], items_rand);\r\nassert(actual \u003e= expected);\r\n\r\n%% Test Case 4: \r\nassert(isequal(solve_guillotine([5, 5], [10, 10, 100; 6, 2, 50]), 0))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945722,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-17T14:07:03.000Z","updated_at":"2026-04-05T12:47:10.000Z","published_at":"2026-03-17T14:07:03.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are working in a factory that produces rectangular glass sheets. You have a large stock plate of size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e x \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. Customers have placed order for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e differents types of smaller rectangular pieces. Each piece type \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e has dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew_{i} \\\\times h_{i}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and a specific market value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_{i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Challenge:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYou need to cut the stock plate to maximize the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etotal value\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e of the pieces obtained. However, you must follow the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGuillotine Cut constraint:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYou can rotate the pieces 90 degrees if it helps.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eThis is a \\\"2nd-stage\\\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOr, to make it harder, we allow recursive guillotine cuts to any depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStockSize: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eA 1x2 vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[W, H]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e ( The dimensions of the large plate ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eItems:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ex 3 matrix. Each row is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[width, height, value].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaxValue:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e The maximum total value you can extract from the stock plate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55,"title":"Counting Sequence","description":"Given a vector x, find the \"counting sequence\" y.\r\n\r\nA counting sequence is formed by \"counting\" the entries in a given sequence.\r\n\r\nFor example, the sequence\r\n\r\n x = 5, 5, 2, 1, 1, 1, 1, 3\r\n\r\ncan be read as\r\n\r\n Two 5's, one 2, four 1's, one 3\r\n\r\nwhich translates to\r\n\r\n y = 2, 5, 1, 2, 4, 1, 1, 3\r\n\r\nSo y is the counting sequence for x.\r\n\r\nFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\r\n","description_html":"\u003cp\u003eGiven a vector x, find the \"counting sequence\" y.\u003c/p\u003e\u003cp\u003eA counting sequence is formed by \"counting\" the entries in a given sequence.\u003c/p\u003e\u003cp\u003eFor example, the sequence\u003c/p\u003e\u003cpre\u003e x = 5, 5, 2, 1, 1, 1, 1, 3\u003c/pre\u003e\u003cp\u003ecan be read as\u003c/p\u003e\u003cpre\u003e Two 5's, one 2, four 1's, one 3\u003c/pre\u003e\u003cp\u003ewhich translates to\u003c/p\u003e\u003cpre\u003e y = 2, 5, 1, 2, 4, 1, 1, 3\u003c/pre\u003e\u003cp\u003eSo y is the counting sequence for x.\u003c/p\u003e\u003cp\u003eFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\u003c/p\u003e","function_template":"function y = CountSeq(x)\r\ny = x;\r\nend","test_suite":"%%\r\nx = [5 5 2 1 1 1 1 3];\r\ncorrect = [2 5 1 2 4 1 1 3];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = [9];\r\ncorrect = [1 9];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = ones(1,9);\r\ncorrect = [9 1];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = 1:9;\r\ncorrect = [1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n%%\r\nx = [1 2 2 1];\r\ncorrect = [1 1 2 2 1 1];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n","published":true,"deleted":false,"likes_count":30,"comments_count":13,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2181,"test_suite_updated_at":"2013-03-14T15:22:01.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:25.000Z","updated_at":"2026-04-14T15:14:41.000Z","published_at":"2012-01-18T01:00:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector x, find the \\\"counting sequence\\\" y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA counting sequence is formed by \\\"counting\\\" the entries in a given sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = 5, 5, 2, 1, 1, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ecan be read as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Two 5's, one 2, four 1's, one 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich translates to\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = 2, 5, 1, 2, 4, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo y is the counting sequence for x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":803,"title":"Twist 'n' Match","description":"Given n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places. \r\n\r\nThe number of matches m is calculated as follows: \r\n \r\n m = nnz(rot90(a)==a)\r\n\r\nYour answer a is clearly not unique. It must only meet the criteria stated above.\r\n\r\nExamples:\r\n\r\n Input n = 2, m = 1\r\n One possible output: a = [ 1 2 \r\n                            1 3 ]\r\n\r\n Input n = 3, m = 7\r\n One possible output: a = [ 0 1 1\r\n                            1 1 1\r\n                            1 1 1 ]","description_html":"\u003cp\u003eGiven n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places.\u003c/p\u003e\u003cp\u003eThe number of matches m is calculated as follows:\u003c/p\u003e\u003cpre\u003e m = nnz(rot90(a)==a)\u003c/pre\u003e\u003cp\u003eYour answer a is clearly not unique. It must only meet the criteria stated above.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input n = 2, m = 1\r\n One possible output: a = [ 1 2 \r\n                            1 3 ]\u003c/pre\u003e\u003cpre\u003e Input n = 3, m = 7\r\n One possible output: a = [ 0 1 1\r\n                            1 1 1\r\n                            1 1 1 ]\u003c/pre\u003e","function_template":"function a = twist_n_match(n,m)\r\n  a = 0;\r\nend","test_suite":"%%\r\nn = 2; \r\nm = 1;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 3; \r\nm = 7;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 6; \r\nm = 6;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 10; \r\nm = 11;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 10; \r\nm = 14;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 20; \r\nm = 83;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 21; \r\nm = 1;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));","published":true,"deleted":false,"likes_count":9,"comments_count":9,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":85,"test_suite_updated_at":"2012-07-03T15:06:05.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-06-28T15:15:32.000Z","updated_at":"2025-12-16T03:15:00.000Z","published_at":"2012-06-29T19:04:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number of matches m is calculated as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ m = nnz(rot90(a)==a)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour answer a is clearly not unique. It must only meet the criteria stated above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input n = 2, m = 1\\n One possible output: a = [ 1 2 \\n                            1 3 ]\\n\\n Input n = 3, m = 7\\n One possible output: a = [ 0 1 1\\n                            1 1 1\\n                            1 1 1 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1286,"title":"MatCAT - Reconstruct X from Its X-rays","description":"Consider a matrix x\r\n\r\n x = [ 1 2 0\r\n       0 5 0 \r\n       3 0 8 ]\r\n\r\nIf we sum x along the rows we get\r\n\r\n row_sums = [3 5 11]\r\n\r\nSumming along the columns gives \r\n\r\n col_sums = [4 7 8]\r\n\r\nMetaphorically, we might call these sums \"x-rays\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a \u003chttp://en.wikipedia.org/wiki/X-ray_computed_tomography CAT scan\u003e. Can you put all the bones in the right place?\r\n\r\nAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\r\n\r\nBonus question: Under what circumstances does the answer become unique? Discuss.","description_html":"\u003cp\u003eConsider a matrix x\u003c/p\u003e\u003cpre\u003e x = [ 1 2 0\r\n       0 5 0 \r\n       3 0 8 ]\u003c/pre\u003e\u003cp\u003eIf we sum x along the rows we get\u003c/p\u003e\u003cpre\u003e row_sums = [3 5 11]\u003c/pre\u003e\u003cp\u003eSumming along the columns gives\u003c/p\u003e\u003cpre\u003e col_sums = [4 7 8]\u003c/pre\u003e\u003cp\u003eMetaphorically, we might call these sums \"x-rays\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a \u003ca href = \"http://en.wikipedia.org/wiki/X-ray_computed_tomography\"\u003eCAT scan\u003c/a\u003e. Can you put all the bones in the right place?\u003c/p\u003e\u003cp\u003eAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\u003c/p\u003e\u003cp\u003eBonus question: Under what circumstances does the answer become unique? Discuss.\u003c/p\u003e","function_template":"function x = matcat(row_sums,col_sums)\r\n  x = 0;\r\nend","test_suite":"%%\r\nrow_sums = [3 5 11];\r\ncol_sums = [4 7 8];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [2 2 2 2 2 6];\r\ncol_sums = [2 3 3 3 3 2];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [65 65 65 65 65];\r\ncol_sums = [65 65 65 65 65];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [22 34 33];\r\ncol_sums = [15 23 18 21 12];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = 55;\r\ncol_sums = [1 2 3 4 5 6 7 8 9 10];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":4,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":147,"test_suite_updated_at":"2013-02-21T17:46:45.000Z","rescore_all_solutions":false,"group_id":23,"created_at":"2013-02-21T17:25:12.000Z","updated_at":"2026-04-02T21:49:21.000Z","published_at":"2013-02-21T17:46:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a matrix x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 1 2 0\\n       0 5 0 \\n       3 0 8 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf we sum x along the rows we get\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ row_sums = [3 5 11]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSumming along the columns gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ col_sums = [4 7 8]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMetaphorically, we might call these sums \\\"x-rays\\\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/X-ray_computed_tomography\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCAT scan\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Can you put all the bones in the right place?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBonus question: Under what circumstances does the answer become unique? Discuss.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1499,"title":"Kryptos - CIA Cypher Sculpture: Vigenere Encryption","description":"The \u003chttp://en.wikipedia.org/wiki/Kryptos Kryptos Sculpture\u003e contains four encypted messages.\r\n\r\nThis Challenge is to Encrypt two of the original messages for the sculptor.\r\n\r\nThe method employed is \u003chttp://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher Vigenere Encryption\u003e. One clarification is that \"?\" are removed from the coding sequence and then re-inserted in the final encoded message.\r\n\r\nOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\r\n\r\nFor coding purposes spaces and punctuation are removed, except \"?\".\r\n\r\nPhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\r\n\r\n*Input:* Encode Phrase, Vigenere alphabet word, Vigenere shift word\r\n\r\nVigenere alphabet word ='KRYPTOS';\r\n\r\nVigenere shift word ='PALIMPSEST';\r\n\r\n*Output:* EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\r\n\r\nThe encryption matrix for this case:\r\n\r\n  KRYPTOSABCDEFGHIJLMNQUVWXZ\r\n\r\n  PTOSABCDEFGHIJLMNQUVWXZKRY\r\n  ABCDEFGHIJLMNQUVWXZKRYPTOS\r\n  LMNQUVWXZKRYPTOSABCDEFGHIJ\r\n  IJLMNQUVWXZKRYPTOSABCDEFGH\r\n  MNQUVWXZKRYPTOSABCDEFGHIJL\r\n  PTOSABCDEFGHIJLMNQUVWXZKRY\r\n  SABCDEFGHIJLMNQUVWXZKRYPTO\r\n  EFGHIJLMNQUVWXZKRYPTOSABCD\r\n  SABCDEFGHIJLMNQUVWXZKRYPTO\r\n  TOSABCDEFGHIJLMNQUVWXZKRYP\r\n\r\nFollow Up Challenges:\r\n\r\n1) \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption Vigenere Decryption\u003e\r\n\r\n2) Dictionary search\r\n\r\n3) KRYPTOS Part IV\r\n\r\n\u003chttp://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1 KRYPTOS Solutions\u003e\r\n\r\n  \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eThe \u003ca href = \"http://en.wikipedia.org/wiki/Kryptos\"\u003eKryptos Sculpture\u003c/a\u003e contains four encypted messages.\u003c/p\u003e\u003cp\u003eThis Challenge is to Encrypt two of the original messages for the sculptor.\u003c/p\u003e\u003cp\u003eThe method employed is \u003ca href = \"http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher\"\u003eVigenere Encryption\u003c/a\u003e. One clarification is that \"?\" are removed from the coding sequence and then re-inserted in the final encoded message.\u003c/p\u003e\u003cp\u003eOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\u003c/p\u003e\u003cp\u003eFor coding purposes spaces and punctuation are removed, except \"?\".\u003c/p\u003e\u003cp\u003ePhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Encode Phrase, Vigenere alphabet word, Vigenere shift word\u003c/p\u003e\u003cp\u003eVigenere alphabet word ='KRYPTOS';\u003c/p\u003e\u003cp\u003eVigenere shift word ='PALIMPSEST';\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\u003c/p\u003e\u003cp\u003eThe encryption matrix for this case:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eKRYPTOSABCDEFGHIJLMNQUVWXZ\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ePTOSABCDEFGHIJLMNQUVWXZKRY\r\nABCDEFGHIJLMNQUVWXZKRYPTOS\r\nLMNQUVWXZKRYPTOSABCDEFGHIJ\r\nIJLMNQUVWXZKRYPTOSABCDEFGH\r\nMNQUVWXZKRYPTOSABCDEFGHIJL\r\nPTOSABCDEFGHIJLMNQUVWXZKRY\r\nSABCDEFGHIJLMNQUVWXZKRYPTO\r\nEFGHIJLMNQUVWXZKRYPTOSABCD\r\nSABCDEFGHIJLMNQUVWXZKRYPTO\r\nTOSABCDEFGHIJLMNQUVWXZKRYP\r\n\u003c/pre\u003e\u003cp\u003eFollow Up Challenges:\u003c/p\u003e\u003cp\u003e1) \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption\"\u003eVigenere Decryption\u003c/a\u003e\u003c/p\u003e\u003cp\u003e2) Dictionary search\u003c/p\u003e\u003cp\u003e3) KRYPTOS Part IV\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1\"\u003eKRYPTOS Solutions\u003c/a\u003e\u003c/p\u003e","function_template":"function encoded=encode_vigenere(phrase,word1,word2)\r\n encoded=phrase;\r\nend","test_suite":"phrase=upper('Between subtle shading and the absence of light lies the nuance of iqlusion.');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\nencoded_exp='EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD';\r\nword1='KRYPTOS';\r\nword2='PALIMPSEST';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n%%\r\n\r\nphrase=upper('It was totally invisible Hows that possible? They used the Earths magnetic field X The information was gathered and transmitted undergruund to an unknown location X Does Langley know about this? They should Its buried out there somewhere X Who knows the exact location? Only WW This was his last message X Thirty eight degrees fifty seven minutes six point five seconds north Seventy seven degrees eight minutes forty four seconds west ID by rows');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\n\r\nencoded_exp='VFPJUDEEHZWETZYVGWHKKQETGFQJNCEGGWHKK?DQMCPFQZDQMMIAGPFXHQRLGTIMVMZJANQLVKQEDAGDVFRPJUNGEUNAQZGZLECGYUXUEENJTBJLBQCRTBJDFHRRYIZETKZEMVDUFKSJHKFWHKUWQLSZFTIHHDDDUVH?DWKBFUFPWNTDFIYCUQZEREEVLDKFEZMOQQJLTTUGSYQPFEUNLAVIDXFLGGTEZ?FKZBSFDQVGOGIPUFXHHDRKFFHQNTGPUAECNUVPDJMQCLQUMUNEDFQELZZVRRGKFFVOEEXBDMVPNFQXEZLGREDNQFMPNZGLFLPMRJQYALMGNUVPDXVKPDQUMEBEDMHDAFMJGZNUPLGEWJLLAETG';\r\n\r\nword1='KRYPTOS';\r\nword2='ABSCISSA';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n%%\r\nphrase=upper('The fox jumped over the moon');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\nencoded_exp='VUIPFSBYVQMMWPIMEVPZCVK';\r\nword1='KRYPTOS';\r\nword2='MATLAB';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n\r\n%%\r\nphrase=upper('Between the Devil and the deep blue sea');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\n\r\nword1='AWEIGH';\r\nword2='MATLAB';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\nencoded_exp='SENMEDWTZNDDFIBLNNCHVTEDIBBCEZOA';\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":28,"created_at":"2013-05-11T20:36:34.000Z","updated_at":"2026-03-07T04:46:20.000Z","published_at":"2013-05-11T21:19:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Kryptos\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKryptos Sculpture\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contains four encypted messages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to Encrypt two of the original messages for the sculptor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe method employed is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere Encryption\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. One clarification is that \\\"?\\\" are removed from the coding sequence and then re-inserted in the final encoded message.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor coding purposes spaces and punctuation are removed, except \\\"?\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Encode Phrase, Vigenere alphabet word, Vigenere shift word\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere alphabet word ='KRYPTOS';\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere shift word ='PALIMPSEST';\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe encryption matrix for this case:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[KRYPTOSABCDEFGHIJLMNQUVWXZ\\n\\nPTOSABCDEFGHIJLMNQUVWXZKRY\\nABCDEFGHIJLMNQUVWXZKRYPTOS\\nLMNQUVWXZKRYPTOSABCDEFGHIJ\\nIJLMNQUVWXZKRYPTOSABCDEFGH\\nMNQUVWXZKRYPTOSABCDEFGHIJL\\nPTOSABCDEFGHIJLMNQUVWXZKRY\\nSABCDEFGHIJLMNQUVWXZKRYPTO\\nEFGHIJLMNQUVWXZKRYPTOSABCD\\nSABCDEFGHIJLMNQUVWXZKRYPTO\\nTOSABCDEFGHIJLMNQUVWXZKRYP]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow Up Challenges:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere Decryption\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Dictionary search\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) KRYPTOS Part IV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKRYPTOS Solutions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45426,"title":"The Tortoise and the Hare - 02","description":"Previous problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\u003e\r\n\r\nSuppose in an infinitely long line, the tortoise is standing in position 0.\r\n\r\nFrom that place, it can move in both +ve and -ve direction. The condition is that, in i-th jump, it can move i step forward or backward. \r\n\r\nSo one possible scenario can be -\r\n\r\n 0 [i=1] --- 1 step forward\r\n 1 [i=2] --- 2 step forward\r\n 3 [i=3] --- 3 step forward\r\n 6 [i=4] --- 4 step backward\r\n 2 [i=5] --- 5 step forward\r\n 7 [i=6] --- 6 step backward\r\n 1 [i=7] --- 7 step forward\r\n 8\r\n\r\nIf you look carefully, you'll find that -- If the tortoise moves this way, it'll always be able to reach any destination (x). \r\n\r\nThe question is what is the minimum number of moves it'll take to reach destination x.\r\n\r\nFor example -- \r\n\r\n if x=8\r\n  \u003e\u003e in the above example, it takes 7 steps\r\n  \u003e\u003e but if it moves this way  -- [0,-1,1,4,8] -- steps required = 4.\r\n\r\nSo 4 is the optimum way.\r\n","description_html":"\u003cp\u003ePrevious problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSuppose in an infinitely long line, the tortoise is standing in position 0.\u003c/p\u003e\u003cp\u003eFrom that place, it can move in both +ve and -ve direction. The condition is that, in i-th jump, it can move i step forward or backward.\u003c/p\u003e\u003cp\u003eSo one possible scenario can be -\u003c/p\u003e\u003cpre\u003e 0 [i=1] --- 1 step forward\r\n 1 [i=2] --- 2 step forward\r\n 3 [i=3] --- 3 step forward\r\n 6 [i=4] --- 4 step backward\r\n 2 [i=5] --- 5 step forward\r\n 7 [i=6] --- 6 step backward\r\n 1 [i=7] --- 7 step forward\r\n 8\u003c/pre\u003e\u003cp\u003eIf you look carefully, you'll find that -- If the tortoise moves this way, it'll always be able to reach any destination (x).\u003c/p\u003e\u003cp\u003eThe question is what is the minimum number of moves it'll take to reach destination x.\u003c/p\u003e\u003cp\u003eFor example --\u003c/p\u003e\u003cpre\u003e if x=8\r\n  \u0026gt;\u0026gt; in the above example, it takes 7 steps\r\n  \u0026gt;\u0026gt; but if it moves this way  -- [0,-1,1,4,8] -- steps required = 4.\u003c/pre\u003e\u003cp\u003eSo 4 is the optimum way.\u003c/p\u003e","function_template":"function y = rabbit(n)","test_suite":"%%\r\nassert(isequal(rabbit(8),4))\r\n%%\r\nassert(isequal(rabbit(18),7))\r\n%%\r\nassert(isequal(rabbit(-600),35))\r\n%%\r\nassert(isequal(rabbit(6600),115))\r\n%%\r\nassert(isequal(rabbit(99999),449))\r\n%%\r\nassert(isequal(rabbit(-16),7))\r\n%%\r\nassert(isequal(rabbit(45237929),9513))\r\n%%\r\nassert(isequal(rabbit(46),11))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-07T05:20:53.000Z","updated_at":"2026-03-30T18:12:01.000Z","published_at":"2020-04-07T05:20:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose in an infinitely long line, the tortoise is standing in position 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom that place, it can move in both +ve and -ve direction. The condition is that, in i-th jump, it can move i step forward or backward.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo one possible scenario can be -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 0 [i=1] --- 1 step forward\\n 1 [i=2] --- 2 step forward\\n 3 [i=3] --- 3 step forward\\n 6 [i=4] --- 4 step backward\\n 2 [i=5] --- 5 step forward\\n 7 [i=6] --- 6 step backward\\n 1 [i=7] --- 7 step forward\\n 8]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you look carefully, you'll find that -- If the tortoise moves this way, it'll always be able to reach any destination (x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe question is what is the minimum number of moves it'll take to reach destination x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example --\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ if x=8\\n  \u003e\u003e in the above example, it takes 7 steps\\n  \u003e\u003e but if it moves this way  -- [0,-1,1,4,8] -- steps required = 4.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo 4 is the optimum way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":520,"title":"Choose the best fitting dominoes","description":"You will be given a cell array of nx2 matrices. Choose one row from each matrix. These are the ordered pairs that will be placed in a line like this.\r\n{[1 2  [4 5 [0 4\r\n  3 5   2 4  3 2\r\n  1 5]  5 1] 5 3]}\r\nChoices might be: [1 2 3]\r\nyields: [1 2][2 4][5 3]\r\n    or: abs(2-2) + abs(4-5)\r\n    or:        0 + 1\r\n    or: 1\r\nYou are trying to minimize the score, the absolute difference of the sum of the difference at the intersections.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 267.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 133.517px; transform-origin: 407px 133.517px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will be given a cell array of nx2 matrices. Choose one row from each matrix. These are the ordered pairs that will be placed in a line like this.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e{[1 2  [4 5 [0 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  3 5   2 4  3 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 72px 8.5px; tab-size: 4; transform-origin: 72px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  1 5]  5 1] 5 3]}\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5px 8px; transform-origin: 78.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eChoices might be: [1 2 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eyields: [1 2][2 4][5 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    or: abs(2-2) + abs(4-5)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; tab-size: 4; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    or:        0 + 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    or: 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 341px 8px; transform-origin: 341px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are trying to minimize the score, the absolute difference of the sum of the difference at the intersections.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function order = ChooseBestFittingDominoes(list)\r\n  order = 1;\r\nend","test_suite":"%%\r\nlist = {[1 3; 2 4; 5 6],[4 6; 2 5;6 7],[3 4; 6 1; 4 6]}\r\n\r\nselections = [2 1 2];\r\n\r\nassert(isequal(ChooseBestFittingDominoes(list),selections))\r\n\r\n\r\n%%\r\nlist = {[1 5; 2 3; 2 2; 3 4; 0 3], \r\n        [0 4; 1 5; 2 2; 4 5; 4 6],\r\n        [7 7; 3 8; 4 7; 5 9; 0 4]};\r\n    \r\nselections = [4 4 4];\r\n\r\nassert(isequal(ChooseBestFittingDominoes(list),selections))\r\n\r\n%%\r\nlist = {[1 4; 2 2; 1 1; 3 3],[1 2; 2 3],[2 2]};\r\n\r\nselections = [3 1 1];\r\n\r\nassert(isequal(ChooseBestFittingDominoes(list),selections))\r\n\r\n%%\r\nlist = {[3 4; 1 2; 5 6],[5 7; 11 13; 17 19; 29 31; 2 3]};\r\n    \r\nselections = [2 5];\r\n\r\nassert(isequal(ChooseBestFittingDominoes(list),selections))","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":240,"edited_by":223089,"edited_at":"2022-12-28T15:22:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":243,"test_suite_updated_at":"2022-12-28T15:22:04.000Z","rescore_all_solutions":false,"group_id":5,"created_at":"2012-03-22T17:38:21.000Z","updated_at":"2026-02-19T11:48:16.000Z","published_at":"2012-04-03T18:00:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will be given a cell array of nx2 matrices. Choose one row from each matrix. These are the ordered pairs that will be placed in a line like this.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[{[1 2  [4 5 [0 4\\n  3 5   2 4  3 2\\n  1 5]  5 1] 5 3]}]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eChoices might be: [1 2 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[yields: [1 2][2 4][5 3]\\n    or: abs(2-2) + abs(4-5)\\n    or:        0 + 1\\n    or: 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are trying to minimize the score, the absolute difference of the sum of the difference at the intersections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":733,"title":"Extract Built In Functions and Toolbox Functions from String or Function Handle","description":"Find the Built-In functions and Toolbox functions in either a string or a function handle.\r\n\r\nGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\r\n\r\n*Inputs:*\r\n\r\nfh=@(x)log10(x)+log2(x)+abs(x)\r\n\r\nstr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\r\n\r\n*Outputs:*\r\n\r\n'abs log2 log10'\r\n\r\n'abs filter numel sin filter2 smooth3'\r\n\r\nRelated to \r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer Cody_464\u003e","description_html":"\u003cp\u003eFind the Built-In functions and Toolbox functions in either a string or a function handle.\u003c/p\u003e\u003cp\u003eGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003efh=@(x)log10(x)+log2(x)+abs(x)\u003c/p\u003e\u003cp\u003estr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e'abs log2 log10'\u003c/p\u003e\u003cp\u003e'abs filter numel sin filter2 smooth3'\u003c/p\u003e\u003cp\u003eRelated to  \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer\"\u003eCody_464\u003c/a\u003e\u003c/p\u003e","function_template":"function functions = find_functions(fh_str)\r\n  functions = '';\r\nend","test_suite":"%%\r\nfh_str='log2(x)+smooth3(x,y)+abs(2)+log10(5)';\r\nexp_str='abs log10 log2 smooth3';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='for k=log10(x):log2(x)+abs(x)';\r\nexp_str='abs for log10 log2';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str=@(x)x^2+sin(x)-cos(x);\r\nexp_str='cos sin';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='@(x)x^2+sin(x)-cos(x)';\r\nexp_str='cos sin';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='filter2(x,A)+filter(x)-cos(x) expm(z)';\r\nexp_str='cos filter expm filter2';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)';\r\nexp_str='abs filter numel sin filter2 smooth3';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":"2012-07-18T13:18:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-01T23:09:01.000Z","updated_at":"2026-03-31T20:12:36.000Z","published_at":"2012-06-02T00:17:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the Built-In functions and Toolbox functions in either a string or a function handle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efh=@(x)log10(x)+log2(x)+abs(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003estr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'abs log2 log10'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'abs filter numel sin filter2 smooth3'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody_464\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":875,"title":"Return a list sorted by number of consecutive occurrences","description":"Inspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\r\n y = [2 3 7 1 93]\r\nBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\r\n y = [2 1 3 7 1 93]\r\nUpdate - Test case added 22-8-22","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 185.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 92.9333px; transform-origin: 407px 92.9333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365px 8px; transform-origin: 365px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e y = [2 3 7 1 93]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e y = [2 1 3 7 1 93]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUpdate - Test case added 22-8-22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = popularity_bis(x)\r\n  y = unique(x);\r\nend","test_suite":"%%\r\nx = [1 2 2 2 3 3 7 7 93]\r\ny_correct1 = [2 3 7 1 93] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [1 1 2 2 2 3 3 7 7 1 93];\r\ny_correct2 = [2 1 3 7 1 93] ;\r\nassert(isequal(popularity_bis(x),y_correct2))\r\n%%\r\nx = [1 0 0 2 2 -5 9 9 2 1 1 1 0 11];\r\ny_correct1 = [1 0 2 9 -5 0 1 2 11] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [1 0 1 1 0 0];\r\ny_correct0 = [0 1 0 1] ;\r\nassert(isequal(popularity_bis(x),y_correct0))\r\n%%\r\nx = [0 1 0 0 1 1];\r\ny_correct1 = [0 1 0 1] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [-2 -2 3 3 3 -7 -7 0 0 0];\r\ny_correct1 = [0 3 -7 -2] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":5,"created_by":5390,"edited_by":223089,"edited_at":"2022-08-22T17:30:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":432,"test_suite_updated_at":"2022-08-22T17:30:08.000Z","rescore_all_solutions":false,"group_id":12,"created_at":"2012-08-03T00:17:38.000Z","updated_at":"2026-04-16T10:17:24.000Z","published_at":"2012-08-03T00:32:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 3 7 1 93]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 1 3 7 1 93]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUpdate - Test case added 22-8-22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2237,"title":"Mmm! Multi-dimensional Matrix Multiplication ","description":"You have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions.\r\nYou may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar.\r\nIn the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u003e2, or either ndims(A)\u003cn or ndims(B)\u003cn, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\r\n\r\nWrite a function |mtimesm| that does this, and ask Mathworks to include it in the |elmat| toolbox of the Next Release.","description_html":"\u003cp\u003eYou have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions.\r\nYou may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar.\r\nIn the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u0026gt;2, or either ndims(A)\u0026lt;n or ndims(B)\u0026lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003emtimesm\u003c/tt\u003e that does this, and ask Mathworks to include it in the \u003ctt\u003eelmat\u003c/tt\u003e toolbox of the Next Release.\u003c/p\u003e","function_template":"function C = mtimesm(A,B)\r\n  C = A*B;\r\nend","test_suite":"%% case 1\r\nA = 1;\r\nB = 2;\r\nC = mtimesm(A,B);\r\nC_correct = 2;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 2\r\nA = rand(2,3);\r\nB = rand(3,4);\r\nC = mtimesm(A,B);\r\nC_correct = A*B;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 3\r\nA = rand(2,3);\r\nB = 2;\r\nC = mtimesm(A,B);\r\nC_correct = 2*A;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 4\r\nA = rand(2,3,2);\r\nB = rand(3,4,2);\r\nC = mtimesm(A,B);\r\nC_correct = cat(3,A(:,:,1)*B(:,:,1),A(:,:,2)*B(:,:,2));\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 5\r\nA = rand(2,3,3);\r\nB = rand(3,4);\r\nC = mtimesm(A,B);\r\nC_correct = cat(3,A(:,:,1)*B,A(:,:,2)*B,A(:,:,3)*B); \r\nassert(isequal(C,C_correct))\r\n\r\n%% case 6\r\nA = rand(4,3,1,2);\r\nB = rand(3,2,2);\r\nC = mtimesm(A,B);\r\nC_correct(:,:,1,1) = A(:,:,1,1)*B(:,:,1);\r\nC_correct(:,:,1,2) = A(:,:,1,2)*B(:,:,1);\r\nC_correct(:,:,2,1) = A(:,:,1,1)*B(:,:,2);\r\nC_correct(:,:,2,2) = A(:,:,1,2)*B(:,:,2);\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 7\r\nA = rand(4,3,1,2);\r\nB = rand(3,2,1,1,2);\r\nC = mtimesm(A,B);\r\nC_correct(:,:,1,1,1) = A(:,:,1,1)*B(:,:,1,1,1);\r\nC_correct(:,:,1,1,2) = A(:,:,1,1)*B(:,:,1,1,2);\r\nC_correct(:,:,1,2,1) = A(:,:,1,2)*B(:,:,1,1,1);\r\nC_correct(:,:,1,2,2) = A(:,:,1,2)*B(:,:,1,1,2);\r\nassert(isequal(C,C_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":5,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":"2014-03-07T06:22:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-06T11:17:42.000Z","updated_at":"2026-04-03T03:22:22.000Z","published_at":"2014-03-06T11:17:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions. You may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar. In the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u0026gt;2, or either ndims(A)\u0026lt;n or ndims(B)\u0026lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emtimesm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that does this, and ask Mathworks to include it in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eelmat\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e toolbox of the Next Release.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44080,"title":"Construct a \"diagAdiag\" matrix","description":"Construct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\r\n\r\nFor:\r\n\r\n  n = 4\r\n\r\noutput\r\n\r\n  M = \r\n[1   2   6   7;\r\n 3   5   8   13;\r\n 4   9   12  14;\r\n 10  11  15  16]\r\n\r\nNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\r\n","description_html":"\u003cp\u003eConstruct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\u003c/p\u003e\u003cp\u003eFor:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003en = 4\r\n\u003c/pre\u003e\u003cp\u003eoutput\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eM = \r\n[1   2   6   7;\r\n3   5   8   13;\r\n4   9   12  14;\r\n10  11  15  16]\r\n\u003c/pre\u003e\u003cp\u003eNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\u003c/p\u003e","function_template":"function y = diagAdiag(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [1 2 6; 3 5 7;4 8 9];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [1   2   6   7; 3   5   8   13;4   9   12  14;10  11  15  16];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = [1 2 6 7 15;3 5 8 14 16;4 9 13 17 22;10 12 18 21 23;11 19 20 24 25];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = [ 1  2  6  7 15 16;\r\n              3  5  8 14 17 26;\r\n              4  9 13 18 25 27;\r\n             10 12 19 24 28 33;\r\n             11 20 23 29 32 34;\r\n             21 22 30 31 35 36];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [ 1  2  6  7 15 16 28;\r\n              3  5  8 14 17 27 29;\r\n              4  9 13 18 26 30 39;\r\n             10 12 19 25 31 38 40;\r\n             11 20 24 32 37 41 46;\r\n             21 23 33 36 42 45 47;\r\n             22 34 35 43 44 48 49];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":98103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":"2017-04-19T17:09:18.000Z","rescore_all_solutions":false,"group_id":24,"created_at":"2017-03-04T19:12:05.000Z","updated_at":"2026-04-02T22:13:25.000Z","published_at":"2017-03-04T19:15:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConstruct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M = \\n[1   2   6   7;\\n3   5   8   13;\\n4   9   12  14;\\n10  11  15  16]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42829,"title":"Number construction III","description":"Given a positive integer, n, return a, b and c, such that\r\n\r\n1. n = a^1.5+b^2.5+c^3.5\r\n\r\n2. a, b and c are all positive integers greater than 1\r\n\r\nIf a solution does not exist, set all three output variables to zero.\r\n\r\nExample 1:\r\n\r\nn = 168\r\n\r\na = 4\r\n\r\nb = 4\r\n\r\nc = 4\r\n\r\nExample 2:\r\n\r\nn = 100\r\n\r\na = 0\r\n\r\nb = 0\r\n\r\nc = 0","description_html":"\u003cp\u003eGiven a positive integer, n, return a, b and c, such that\u003c/p\u003e\u003cp\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/p\u003e\u003cp\u003e2. a, b and c are all positive integers greater than 1\u003c/p\u003e\u003cp\u003eIf a solution does not exist, set all three output variables to zero.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003en = 168\u003c/p\u003e\u003cp\u003ea = 4\u003c/p\u003e\u003cp\u003eb = 4\u003c/p\u003e\u003cp\u003ec = 4\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003en = 100\u003c/p\u003e\u003cp\u003ea = 0\u003c/p\u003e\u003cp\u003eb = 0\u003c/p\u003e\u003cp\u003ec = 0\u003c/p\u003e","function_template":"function [a b c] = numcons(n)\r\n  a = n;\r\n  b = n;\r\n  c = n;\r\nend","test_suite":"%%\r\nn = 100;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 888;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 19666;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 314159;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 1100;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 116600;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 16999;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 10000040;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 94940;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 9990;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2016-04-28T18:19:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-25T11:29:04.000Z","updated_at":"2026-04-09T07:25:23.000Z","published_at":"2016-04-25T11:29:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, n, return a, b and c, such that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. a, b and c are all positive integers greater than 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a solution does not exist, set all three output variables to zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 168\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":375,"title":"N-Dimensional Array Slice","description":"Given an N-dimensional array, _A_, an index, _I_, and a dimension, _d_, return the _I_ th elements of _A_ in the _d_ dimension.\r\n\r\nFor Example,\r\n\r\n    array_slice( A, 5, 3 )\r\n\r\nis equivalent to\r\n\r\n    A(:,:,5)\r\n\r\nNote: |eval| and |str2func| cannot be used. This is a Cody restriction.","description_html":"\u003cp\u003eGiven an N-dimensional array, \u003ci\u003eA\u003c/i\u003e, an index, \u003ci\u003eI\u003c/i\u003e, and a dimension, \u003ci\u003ed\u003c/i\u003e, return the \u003ci\u003eI\u003c/i\u003e th elements of \u003ci\u003eA\u003c/i\u003e in the \u003ci\u003ed\u003c/i\u003e dimension.\u003c/p\u003e\u003cp\u003eFor Example,\u003c/p\u003e\u003cpre\u003e    array_slice( A, 5, 3 )\u003c/pre\u003e\u003cp\u003eis equivalent to\u003c/p\u003e\u003cpre\u003e    A(:,:,5)\u003c/pre\u003e\u003cp\u003eNote: \u003ctt\u003eeval\u003c/tt\u003e and \u003ctt\u003estr2func\u003c/tt\u003e cannot be used. This is a Cody restriction.\u003c/p\u003e","function_template":"function S = arraySlice(A,I,d)\r\n  S = A(:,I);\r\nend","test_suite":"%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,4,2),A(:,4)))\r\n\r\n%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,4,1),A(4,:)))\r\n\r\n%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,1,10),A))\r\n\r\n%%\r\nA = randn(5,5,5,3);\r\nassert(isequal(arraySlice(A,3,4),A(:,:,:,3)))\r\n\r\n%%\r\nA = randn(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2);\r\nassert(isequal(arraySlice(A,2,18),A(:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,2)))","published":true,"deleted":false,"likes_count":13,"comments_count":7,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":285,"test_suite_updated_at":"2012-02-21T16:23:06.000Z","rescore_all_solutions":false,"group_id":19,"created_at":"2012-02-21T16:23:06.000Z","updated_at":"2026-04-12T19:36:51.000Z","published_at":"2012-02-21T16:23:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an N-dimensional array,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, an index,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and a dimension,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e th elements of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e dimension.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor Example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    array_slice( A, 5, 3 )]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis equivalent to\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    A(:,:,5)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeval\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2func\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cannot be used. This is a Cody restriction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":579,"title":"Spiral In","description":"Create an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\r\nFor example:\r\n\u003e\u003e spiralIn(4,5)\r\nans =\r\n   1    14    13    12    11\r\n   2    15    20    19    10\r\n   3    16    17    18     9\r\n   4     5     6     7     8","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"baseline-shift: 0px; block-size: 190px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 95px; transform-origin: 468.5px 95px; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 434.5px 8px; transform-origin: 434.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8417px 8px; transform-origin: 40.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 108px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 464.5px 54px; transform-origin: 464.5px 54px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; spiralIn(4,5)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1    14    13    12    11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   2    15    20    19    10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   3    16    17    18     9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   4     5     6     7     8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = spiralIn(m,n)\r\n  s = zeros(m,n);\r\nend","test_suite":"%%\r\nm = 3;\r\nn = 5;\r\ns_correct = [1 12 11 10 9; 2 13 14 15 8; 3 4 5 6 7];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 3;\r\ns_correct = [1 12 11; 2 13 10; 3 14 9; 4 15 8; 5 6 7];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n\r\n%%\r\nm = 1;\r\nn = 1;\r\ns_correct = 1;\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 0;\r\ns_correct = zeros(5,0);\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 2;\r\nn = 2;\r\ns_correct = [1 4; 2 3];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n\r\n%%\r\n%Test case added on 4/4/26\r\nm = 2*randi(10)+1;\r\ns_correct = m^2+1-rot90(spiral(m));\r\nassert(isequal(spiralIn(m,m),s_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":3117,"edited_by":223089,"edited_at":"2026-04-04T09:55:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":120,"test_suite_updated_at":"2026-04-04T09:55:47.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-04-13T13:50:35.000Z","updated_at":"2026-04-04T09:56:24.000Z","published_at":"2012-04-13T13:50:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e spiralIn(4,5)\\nans =\\n   1    14    13    12    11\\n   2    15    20    19    10\\n   3    16    17    18     9\\n   4     5     6     7     8]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46938,"title":"Numerical computation of the optimal shooting angle of a catapult","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 879.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 439.833px; transform-origin: 406.5px 439.833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 32.1667px; text-align: left; transform-origin: 383.5px 32.1667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"109\" height=\"21\" style=\"width: 109px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and an initial velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the optimal shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"18.5\" style=\"width: 16px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21.25px; text-align: left; transform-origin: 383.5px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Consider the states \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-position of the projectile, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45\" height=\"22\" style=\"width: 45px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,     \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45.5\" height=\"22\" style=\"width: 45.5px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"22\" style=\"width: 63px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e    \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"22\" style=\"width: 87.5px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.   \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.1667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 31.5833px; text-align: left; transform-origin: 383.5px 31.5833px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"97.5\" height=\"19.5\" style=\"width: 97.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"17.5\" style=\"width: 47.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"231.5\" height=\"20\" style=\"width: 231.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Plotting \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e vs. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 2: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse the following update law, to incrementally update the shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAoCAYAAADpE0oSAAAC8klEQVRYR+3WTagWdRQG8J8UWUS1Ma021UItSUOMPoTIRUptlESpLDUoFQr60EpRzEySKKiUNMSPiErpQyylTVnaIjFaZFBUm9CFSpJkiJqIGAfOXF7mzvveudzh3s2d3cz8/+c5H895zhligJ4hA4RrELjfMj+Y6p5SfTHG4U5cgV+wF6d6ulj+XzfVce4uvI3v8AZuwRYcwAL81RvwOsBx5gG8iS/xYkYYEa/DbDyLtbhQF7wO8D14H38myOEW48vxCj7DE/i3KeCR+ABjEvSLkuECeB9m4VATwJfjdTyJT7OO/7QB/hkP4o8mgKdltGEr6liO9hK8hufQGPBwbMRU7MDjKEd7Gd7KTERLPYIjfY14OrankYUJULZ5Nbbi3mR7ZKXsXFs/qlgdtX0Hj+E3zMSvFRZuwicYi/VYhP/6EnEoU7RHweincLLCYJShqHu7rPQq4qjVh3U9T6dCYL7pxZ1ui0ArUyPK+/F9hcGrsAkzsBtzcLQvwK0GOzH1dnyOa7O2we6Qy2D6lbgZo7MjjlU5VCZXK1M3ZI+eKV28CCsQqlUmXwCHym3G7wh+HK8DHF5+jFvxElZVXLoR23AHlqa6nW85V7A9MrISrf+6jpUj7gk4oo3ptBp7KoZGGJ6MrxBaEOJT+ZSBr8NHmNQm4tuy1cLY3JzNrYbD3rIkXUftLgMPzdQ9nax9BqfT8ghE3e/O2kVJyvO3IGfcid6OTSWIFs9+/IBz8VKlXEVUJ1omzjXpUIhLKNS3bYZ+IT7v5fkg6wuI91C/LkergOPbeCzJvSouXJ/1CqXqtF+F+Lybqf4JD2dpug2POhtIXV0oxGdidkOkOCZc5VbSJPCwnN/3paexPMzrD+AJ2IU1CCeexxR8XUdA6qa16lysuKFoD+V4DAGJrTQ649IUkq60N5XqYhsZlaLyN17FfDyKG7ATBwuPmwIO1sc28iMW42x2QgyPSPvLqXQd26kv6a59t6mIawM2nepB4B4zMGA1/h/Q3qEpP5IZBgAAAABJRU5ErkJggg==\" width=\"15\" height=\"20\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"153.5\" height=\"20\" style=\"width: 153.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21.8333px; text-align: left; transform-origin: 383.5px 21.8333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"20\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"298\" height=\"20\" style=\"width: 298px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis a difference angle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"55.5\" height=\"17.5\" style=\"width: 55.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ean update parameter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample of algorithm's numerical result:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 40px; transform-origin: 403.5px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = catapult(25,3,25)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    0.8431\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 383.5px 132.167px; text-align: left; transform-origin: 383.5px 132.167px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"570\" height=\"259\" style=\"vertical-align: baseline;width: 570px;height: 259px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function theta = catapult(xd,yd,v0) \r\n  \r\n    global g nu;\r\n    \r\n    g   = -9.81;  % grav. acceleration\r\n    nu  = 0.5;    % air friction coeff.\r\n    k   = 0;      % solver increments\r\n    dt  = 1e-2;   % timesteps\r\n    T   = 10;     % simulation time\r\n    TOL = 1e-2;   % absolute tolerance\r\n    \r\n    [~,y] = ode45(@ODECatapult,0:dt:T,[v0,0,0]); \r\n    \r\n    % solver for optimal angle\r\n    while (e \u003e= TOL) \u0026\u0026 (k \u003e 150)        \r\n        \r\n        %theta = theta + beta;\r\n        \r\n        k = k+1;    % add increment\r\n    end\r\n  \r\n    function dx = ODECatapult(t,x)\r\n        global g nu;\r\n        %% fill in ordinary differential equation %%\r\n    end\r\n    \r\n    function e = EuclideanDistance(y,xd,yd)\r\n        %% fill in computation of smallest euclidean distance %%\r\n    end\r\n    \r\n    function beta = UpdateLaw(y,e,lambda)\r\n        %% fill in update law to update the shooting angle %%\r\n    end\r\nend","test_suite":"xd = 8;\r\nyd = 2;\r\nv0 = 35;\r\ny_correct = 1.446;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),3),y_correct))\r\n\r\n%%\r\nxd = 15;\r\nyd = 5;\r\nv0 = 35;\r\ny_correct = 1.33;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),2),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":636373,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-19T12:41:43.000Z","updated_at":"2025-01-02T11:31:42.000Z","published_at":"2020-10-19T13:39:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$z_d = [x_d, y_d] \\\\in \\\\mathbb{R}^2$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and an initial velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, find the optimal shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Consider the states \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-position of the projectile, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x_1} = x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_2 = x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e      \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_3 = -\\\\nu x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_4 = -g - \\\\nu x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.   \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\; (\\\\text{m/s}^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t = 0) = (0,0,v_0 \\\\cos(\\\\theta_k), v_0 \\\\sin(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Plotting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e vs. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 2: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eUse the following update law, to incrementally update the shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{k+1} = \\\\theta_k + \\\\lambda \\\\, \\\\text{sign}(\\\\theta_{e,k})\\\\,e_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee_k \\\\in \\\\mathbb{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{e,k} = \\\\text{atan2}(d_y,d_x) - \\\\text{atan2}(v_0\\\\sin(\\\\theta_k),v_0\\\\cos(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis a difference angle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\lambda = 0.01$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ean update parameter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample of algorithm's numerical result:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[theta = catapult(25,3,25)\\ntheta = \\n    0.8431\\n    ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"570\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57477,"title":"Solve an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAAkCAYAAAAjMNwcAAAAAXNSR0IArs4c6QAABFBJREFUaEPt2HmorWMUBvDfNSXzLInM85QhY4rMJWTOnHkKmSlDMkvGTEUoMpVkDimE8AeJyJQxM5lnPbd17r2dzjn7+/be53C6+63T7bbXu761nne9z3rWO8VgtUJgSivrgbEBYC2LYADYALCWCLQ0H1TYALCWCLQ0H1TYALCWCLQ0n+wVNivmwfct8+7afLICNht2wCk4H490jUDLjZMNsDmwI07D+vga2+Ollnl3bT5ZAJsTu+BUrI0vcSluLtC6BqDtxv87YHNh9wJqVXxeQN2Cb9om2w/7/ytg82KvAmr5AuoSBKhv+5F4tz46AbYItsEySOCr4YIi2Z2xf3HJO7gbN+L3boPBAtinyHxpfIYAdWufgZodG1Vum1du++Lpij24JI6T8Aby29/5rRNg6UYL4+DqRtmzUjl6Ha8WiFchQYRjkmDblW8E/JOxBD4pP7fhu7bOGtgvhiXrWp+LA3BvXf9sTxzrYD0EgzXwaxPAhr69E+7H43gF1+DTGQK7CYdUFaQqp55Gg5XAD6oAA9rHuBi3T6C22gTP4Wcsim0xX1V1dF468y9DuXSqsCG7C6uVh3RTyh8MAyN6KIlmLY4vGoAVkxD5GVXy+f/zOK8O5q+GPno1S2OJPEkn3rO68JmjOW0K2GtYE6fjohGcnYWUdlYCmHYiDbNZC0fjsLJ/pr7zGCYCuAdK34VmNhurupsAthzerURWRAh++Er3OhAvY4OGII1ktjKOwpHFic8WcI+OM3DhrHDvtThmrPibALY37sCT2GoEZyHFD4us8+HLegBsaOuyOBzH1VUJx6SyA9yfffA/3MWuRfqpsNykUVcTwG6oq5KTv24ET5EduTo/YHV81MeE0skOxfGYvzgufJrZsV/ALYg7i+wTeg5rOEdPS6kTYJEKASBEHg325jAw0kUexHY4EZf3EawZXeX7ufKp4HTTFxDgHu4RuOSfIoh+TAVvjd1wX7ekv27JiPexwghyIUmEv+4poffHOAE25Hah0msRlKm+F0tDvdXld6O//kH0Xgb6HMIVOKH8ZW59u42sCAFejeisoQ42FNvGeAIP1bWZsDepup7h1siZdNemzzvRfamqyKNNsUdd94C2BZ4qPl4FmTRSbXk+anwlI1YjWq+vzpWNs9TLQUo5BH8lfuvyhHvdNnc9IAaATitApVpyU9I8AlIG+59qY+bXTBj5N9052iwj0Y9NAQvJ5hklPJYyjeP8LYX3qquMSo6dov+Pfo9e3K8q8pwRXjwyP0a0RkBnzPtqeJxjkf6WJSWiuzI/5kRm+jUWYGcjp5Arl7Y+HuvY0lq9+D6iuLQXH433jgVYWveG9S51V2OP7QxnnEHb7Zxunbf9pqTf7Tc6kn54Kuo9K+NKyHI8VqaE/PWyImUmYt6cGuNoFRYJEYWflU6Up4/BGgGwKOqAFeGWkSErKjjvYKOq35kJyU6j0cyERaNcB4A1gmm60b+d+Mgld6F7bQAAAABJRU5ErkJggg==\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there are no solutions, the function should return three empty vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is adapted from one in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.egmo2012.org.uk/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2012 European Girls’ Math Olympiad\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53064,"title":"Amazing circle of numbers 1 to n","description":"For given natural number n, create amazing circle of numbers 1 to n without a repeat.\r\nThis circle is that the sum of any two adjacent numbers is a perfect square.\r\nFor example, if n = 32,\r\n\r\nSo, output is\r\n                          [1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15]\r\nIf the condition is satisfied, it is the correct answer regardless of the order of the vectors.\r\nIf there is no amazing circle vector, return empty vector [].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 984px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 492px; transform-origin: 407px 492px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor given natural number n, create amazing circle of numbers 1 to n without a repeat.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis circle is that the sum of any two adjacent numbers is a perfect square.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if n = 32,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 774px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 387px; text-align: left; transform-origin: 384px 387px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"768\" height=\"768\" style=\"vertical-align: baseline;width: 768px;height: 768px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSo, output is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                          [1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf the condition is satisfied, it is the correct answer regardless of the order of the vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf there is no amazing circle vector, return empty vector [].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = amazing_circle(n)\r\n  v = n;\r\nend","test_suite":"%%\r\nn=32;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=33;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=34;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=35;\r\nv = amazing_circle(n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=36;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=37;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=38;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":517609,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2021-11-29T05:26:18.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-11-15T02:36:58.000Z","updated_at":"2025-07-07T00:57:09.000Z","published_at":"2021-11-15T04:44:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given natural number n, create amazing circle of numbers 1 to n without a repeat.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis circle is that the sum of any two adjacent numbers is a perfect square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if n = 32,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"768\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"768\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo, output is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                          [1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the condition is satisfied, it is the correct answer regardless of the order of the vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf there is no amazing circle vector, return empty vector [].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57815,"title":"List numbers such that every sum of consecutive positive integers ending in those numbers is not prime","description":"The sequence in question in this problem involves numbers  such that all sums of consecutive positive integers ending with  are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \r\nWrite a function that returns the th number in this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 46.5px; transform-origin: 469px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 31.5px; text-align: left; transform-origin: 445px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sequence in question in this problem involves numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that all sums of consecutive positive integers ending with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth number in this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = lastInCompositeSum(n)\r\n  y = isprime(sum(n:-1:1));\r\nend","test_suite":"%%\r\nfor n = 1:3:51\r\n    y(ceil(n/3)) = lastInCompositeSum(n);\r\nend\r\ny_correct = [1 18 26 33 39 48 58 63 72 78 85 92 95 104 110 118 123];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 104;\r\ny = lastInCompositeSum(n);\r\ny_correct = 226;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 583;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1028;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1117;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1875;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8513;\r\ny = lastInCompositeSum(n);\r\ny_correct = 12567;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 22698;\r\ny = lastInCompositeSum(n);\r\ny_correct = 32092;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 51734;\r\ny = lastInCompositeSum(n);\r\ny_correct = 71082;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 87777;\r\ny = lastInCompositeSum(n);\r\ny_correct = 118638;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 453867;\r\ny = lastInCompositeSum(n);\r\ny_correct = 588425;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1243598;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1579325;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 890;\r\ny = lastInCompositeSum(lastInCompositeSum(lastInCompositeSum(n)));\r\ny_correct = 3949;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nfiletext = fileread('lastInCompositeSum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2026-03-11T00:52:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-20T03:20:55.000Z","updated_at":"2026-03-11T00:52:46.000Z","published_at":"2023-03-20T03:23:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sequence in question in this problem involves numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that all sums of consecutive positive integers ending with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth number in this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60461,"title":"Generate a point cloud on an equilateral triangle 2","description":"The input is the iteration parameter H.\r\nThe output is a point cloud W involving N points.\r\nW is N uniformly distributed points on an equilateral triangle.\r\nThe side length of an equilateral triangle is 2.\r\nThe relationship between H and N is as follows:\r\nH = [1 2 3 4 5 6 7 8 9];\r\nN = [4 10 19 31 46 64 85 109 136];\r\nThe results for cases where H is 1 to 6 are as follows.\r\n\r\n\r\nEx)\r\n[W,N] = lattice2(H=1) -\u003e W = [0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0]; N = 4;\r\n[W,N] = lattice2(H=2) -\u003e W = [0 0; 0.5 sqrt(3)/6; 0.5 sqrt(3)/2; 1 0; 1 sqrt(3)/3; 1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 sqrt(3)/2; 2 0]; N = 10;","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 749.188px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 374.594px; transform-origin: 407px 374.594px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe input is the iteration parameter\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eH\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe output is a point cloud\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003einvolving\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003epoints.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003euniformly distributed points on an equilateral triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe side length of an equilateral triangle is 2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe relationship between H and N is as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2188px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH = [1 2 3 4 5 6 7 8 9];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2188px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eN = [4 10 19 31 46 64 85 109 136];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe results for cases where H is 1 to 6 are as follows.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 197px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 98.5px; text-align: left; transform-origin: 384px 98.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 197px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 98.5px; text-align: left; transform-origin: 384px 98.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEx)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 64.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 32.1562px; transform-origin: 391px 32.1562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.7188px; text-align: left; transform-origin: 363px 10.7188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[W,N] = lattice2(H=1) -\u0026gt; W = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; N = 4;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 21.4375px; text-align: left; transform-origin: 363px 21.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[W,N] = lattice2(H=2) -\u0026gt; W = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e0 0; 0.5 sqrt(3)/6; 0.5 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esqrt(3)/2; 1 0; 1 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003esqrt(3)/3; 1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esqrt(3)/2; 2 0]; N = 10;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [W,N] = lattice2(H)\r\n  W = [0 0; 1 sqrt(3); 2 0];\r\n  N = size(W,1);\r\nend","test_suite":"%%\r\nH = 1;\r\nA = [0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0];\r\n\r\n[W,N] = lattice2(H);\r\nassert(isequal(N,4))\r\nassert(sum(abs(sortrows(W)-sortrows(A)),'all') \u003c 1e-6)\r\n\r\n%%\r\nH = 2;\r\nA = [0 0; 0.5 sqrt(3)/6; 0.5 sqrt(3)/2; 1 0; 1 sqrt(3)/3;\r\n    1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 sqrt(3)/2; 2 0];\r\n\r\n[W,N] = lattice2(H);\r\nassert(isequal(N,10))\r\nassert(sum(abs(sortrows(W)-sortrows(A)),'all') \u003c 1e-6)\r\n\r\n%%\r\nH = 3;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,19))\r\n\r\n%%\r\nH = 4;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,31))\r\n\r\n%%\r\nH = 5;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,46))\r\n\r\n%%\r\nH = 10;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,166))\r\n\r\n%%\r\nH = 100;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,15151))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2217275,"edited_by":2217275,"edited_at":"2024-06-09T21:16:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2024-06-09T21:08:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-09T14:14:29.000Z","updated_at":"2026-03-03T11:47:38.000Z","published_at":"2024-06-09T14:24:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input is the iteration parameter\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output is a point cloud\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003einvolving\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003epoints.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003euniformly distributed points on an equilateral triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe side length of an equilateral triangle is 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe relationship between H and N is as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH = [1 2 3 4 5 6 7 8 9];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eN = [4 10 19 31 46 64 85 109 136];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe results for cases where H is 1 to 6 are as follows.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEx)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[W,N] = lattice2(H=1) -\u0026gt; W = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e; N = 4;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[W,N] = lattice2(H=2) -\u0026gt; W = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0 0; 0.5 sqrt(3)/6; 0.5 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esqrt(3)/2; 1 0; 1 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esqrt(3)/3; 1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esqrt(3)/2; 2 0]; N = 10;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image2.png\",\"relationshipId\":\"rId2\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image3.png\",\"relationshipId\":\"rId3\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image4.png\",\"relationshipId\":\"rId4\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image5.png\",\"relationshipId\":\"rId5\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image6.png\",\"relationshipId\":\"rId6\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAwMAAAL9CAIAAAD4ry2pAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6AYJFDgY21emZAAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAxMC1KdW4tMjAyNCAwNTo1NjoyNDd0e8EAACAASURBVHic7N1/cFTV/f/xt0igiTQoyWgRUhZHEuwUxX4tHVLtbEqtjAN12hGtSNndMjpqaz8WbItMyu7Saj+WwowdgWbE7rX+pIq1DTodR8zNgGESfwDlY2tShOsEUSSLiBgiuJvvH2dZQ35usvfu/fV8/BV3k5PjL/LKOed1z1nd3d0CAADgS6PsngAAAIBtRts9gYyqqiq7pwAAAHyktbVVnJOE5PSELFJVVWXp+HAU/nX7Cv+6fYV/3b5i6b/u7BIMu2MAAMC/SEIAAMC/SEIAAMC/SEIAAMC/SEIAAMC/SEIAAMC/znLIM6YpRgIAgILJBg/WhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+NNnGsdDq9e/fuTz755NJLLy0tLTVxZAAAACuYloTq6urq6uo++eQT9ZezZs36zW9+EwgEzBofAADAdObsjq1atWrt2rXjx48PBoPl5eUi0tLSsmDBgtbWVlPGBwAAsIIJSWjnzp3//Oc/N27c2NDQUFdX98orr0SjURE5duzY8uXL8x8fAADAIiYkoc2bN2/YsOGqq67KvrJw4cI77rhDRP7973/v27cv/28BAABgBROS0IwZMy677LJeL958883qg/b29vy/BQAAgBVMSEI33nhj3xfLy8tHjx4tIpMmTcr/WwAAAFjBqucJpVKpzz777Etf+tLFF19s0bcAAADIk5nPE+qpublZRBYvXpz7l1RVVfV9kfYZAADIU78ZQ7EqCT377LOTJk1atGhR7l9C6AEAAFbomzGy2ciSJLR37976+vpHH3107NixVowPAABgCvPPCaXT6Xvuueeuu+6aNWuW6YMDAACYyPwkdP/990+bNu322283fWQAAABzmbw7tnnzZsMw6urqzB0WAADACmYmocbGxr/97W8PP/ywiWMCAABYx7QktH379vXr1z/88MO9Tkl3dHSkUqkLLrjArG8EAABgFnPOCW3btu2BBx6oq6sbN25cz9d379596623fvGLXzTluwAAAJjLhDWhl19++c477xSRnpewisjJkydFZP78+SUlJfl/FwAAANPlm4RaWloGr4ldd911eX4LAAAAi+SbhGbNmsWzoQEAgEtZdQMrAACA85GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAfw2YhFpbW0cw3OHDh7dv375z5850Op3HrAAAAAphdN+X3njjjbVr1+7evXvPnj25D9TS0nLvvfdOmDBhypQpJ0+eXLp06dy5c++6666xY8eaN1sAAAAznZGEWlpaNmzY0NzcnEqlxowZk/soLS0tkUiktrb2pptuUq8cPXr0+uuvf+uttxKJhJnzBQAAMM8Zu2MXXXRRIpGora0d7igrV6686KKLsjFIRM4999wf//jHTU1NL730kgnTBAAAsMAZSai8vFxEJk2aNKwhjh8/vn///nPPPbfX6+eff76INDc35zdDAAAAq/RzYrqoqGgEA73++uuHDh3q+cr7778vIl/96ldHNjMAAACrmdCiHzdu3JQpU1Kp1LJlyz799FP1Yjqd3rRpU0VFxdy5c/P/FgAAAFYw53lCy5cvF5FXX331pptuOnz4sIjU1tYeP348kUjQHQMAAI7VT4t+BL797W+vWLHivvvue/PNN6+77rqvfe1ro0aN+vvf/15aWpr7IFVVVX1fHNljjQAAALL6zRiKOUlIREKh0DnnnLNy5cpkMvnyyy/fe++9w4pBQugBAADW6JsxstnIzNs2Pv7446997WtlZWWpVGr58uWrV682cXAAAADTmbYmtHLlyv/7v//btGlTR0fHLbfc8t///nfjxo2fffbZPffcY9a3AAAAMJc5a0J1dXWbNm36/e9/X1RUNHHixCeeeGLmzJkiomnatm3bTPkWAAAApjMhCR09evTBBx+cPn36xRdfrF4pLS196KGHpk6dKiJ/+ctf8v8WAAAAVjAhCb322msnT54MBAI9XywtLVXnhHbu3Jn/twAAALCCaeeEuru7e70yY8aMMWPG9L2FAwDykUwm29rakslkR0dHMplMJpNlZWVlZWXl5eVlZWWzZ8+2e4IA3GQkSWj37t0vvvji4sWLL7jgAhH55je/ec4557z22mvpdHrUqM8XmVKpVCqVuvrqq02bLAB/SyaTO3bsqK+vLykpqaioEJHy8vKKiooTJ050dnbu2rVLROrr6ysrK6urqysrK+2eLwAX6CcJdXZ2ikgqlTp16lTfO8jS6fTixYu7urreeuuthx9+WESKi4t//etfL1++fO3atXfffXf2Mx988MELL7zw9ttvt3L+AHwhmUxqmnbgwIGKioo5c+aUlJT0fLekpKSsrExlo87OzgMHDqxZs6asrGzZsmVlZWU2TRmAO5yRhJqbm59//vnGxkYRSaVSCxcuvOKKK8LhsFr7ySotLe3q6powYUL2le9///tjx469//7733zzze9973sismXLlvHjx//1r38d7vMVAaCXtra2NWvWVFVVzZkzZ8hPLikpqaysnDx5sspD8+fPZ78MwCDO6nu+xxZVVVU8YxpAX1u2bNm6devMmTNHsLqTTCZbW1urq6vnzZtnxdwAuFc2eJh2YhoATKdi0OzZs3tth+WorKxs5syZW7duFRHCEIB+mXnbBgCYqK2trb6+fubMmSOLQUpJScns2bObmpra2tpMnBsAzyAJAXAoTdOqq6vzP/KsimaapiWTSVMmBsBLSEIAnEjTNPV8IFNGq6ioKCkpqa+vN2U0AF5CEgLgRDt27Jg8ebKJA1ZWVrJBBqAvkhAAx9mxY4daxTFxTDXajh07TBwTgAeQhAA4Tn19vXpMormqqqrYIAPQC0kIgLNkrxIzfeSysrITJ06wRwagJ5IQAGdpa2uz7oqM4uJii0YG4FIkIQCOY+4JoV4jsyYEoCeSEABnaW1ttTQJWTQyAJciCQHwkeLi4o6ODrtnAcBBSEIAnKW8vNy6wZPJpKXjA3AdkhAAZ6msrLR02ca649gA3IgkBMBxTpw4YdHIyWSysrLSosEBuBFJCICzWLpm09nZad3gANyIJATAWcrKyiZPnmxF1729vX327NnsjgHoiSQEwHHmz5/f3t5u+rBtbW3V1dWmDwvA1UhCABynsrJy8uTJyWTSxDHb29snT57MISEAvZCEADhRdXX1rl27TDzW09bWNn/+fLNGA+AZJCEATjR79uw5c+bs2rXLlNGampouu+wyFoQA9EUSAuBQ6nRz/ken1ZWu4XDYjEkB8BqSEACHUvGlo6MjnzDU1tbW0dFBDAIwEJIQAOcqKytbtmzZhAkTtm7dOtwzQ52dnU1NTd3d3ffddx/NeQADGW33BABgMGVlZfPnzy8vL9+6dWtFRUUuZ306OzsPHDjQ2to6f/78efPmFWCSANyLNSEATldWVjavo6N261a1OLRr166BCvadnZ1tbW1bt27t7u5etmfPvHHjCjxVAK7DmhAAN4jHyxKJcDCYTCZ37NjR2tra1NRUUlJSXFxcUlLS2dmpslFZWVl1dfXSpUtFRP7f/5NIRPbvt3nmAJztrO7ubrvnICJSVVXV2tpq9ywAOFI8LrouDQ09X1PRJ5lMJpPJstN6f2FNjQSDEo0WbKYA3CIbPFgTAuB4sVivGCSnL2od4ih0IiE1NRIKSSBg2eQAuBvnhAA4W02NhMMSDI7kawMBCQYlHjd5SgA8hDUhAA6m66Lrks8mfjQqNTWi6yPMUgC8jjUhAA4Wj0sikdcIgYBEoxKJmDQhAF5DEgLgVJomIpL/46GDQQkEMqMBwJlIQgCcKh43p/alloU4LQSgPyQhAI4Uj0swaNrhHrUsxB4ZgD44MQ3AeQxDYjGTH4qoGvWGQaMeQE+sCQFwnkhEYjGTI0sgIOEwy0IAeiEJAXAY1Zy34sHQoZAYhui6+SMDcC2SEACHyb85PxAa9QD6IAkBcBKzmvMDCYdp1APoiRPTAJwkEul7xZjJ1NFp68IWAFdhTQiAY0QiI79iLHfqMjL2yACICGtCAJzCMETTTG7OD4TLyACcxpoQAGewojk/EJ46DeA0khAAB9B1MQxLmvMDCQZp1AMQkhAAR4hErGrODyQQkESC00IABkxCra2teQ6dTqf/85//bNu2LZVK5TkUAC/TtMwp5gJTl5GxRwb4Wz8npt944421a9fu3r17z549Ixu0oaHhiSee6OjomDNnzvTp0/ObIQCvK0BzfiCqUR8KcRkZ4FtnJKGWlpYNGzY0NzenUqkxY8aMYLgjR4786le/ev3111etWjVv3jyTJgnAuwrTnB+IWouy7qnWABzvjN2xiy66KJFI1NbWjmys99577/rrr3/zzTc3bdpEDAIwNF0XTbM5hUSjmZvOAPjSGUmovLxcRCZNmjSCgY4cOfLDH/7w/fffX7du3bRp08yZHQBvc8JiDI16wN/6OTFdVFQ0goF+9rOfvf/++7fccsvll1+e96wA+ICmiWE44tYLtTfHZWSAL5nTon/mmWdeffXV4uLiW265xZQBAXifExaEFJaFAB8zJwmtW7dORH7wgx+MGzfu+PHj27Zta2lpSafTpgwOwIPicXua8wOhUQ/4lQn3jjU3Nx88eFBEJk2atGTJkn/9619dXV0nT54sKyurra299tprcxynqqqq74v5P9YIgOMYhsRitjXnB0KjHvCufjOGYkISeumll9QH77zzzm9/+9uJEyeeOnXqd7/73eOPP/7zn/989OjR3/3ud3MZh9AD+IW9zfmBBAISDjtozw6AefpmjGw2MmF37MCBAyIybdq0VatWTZw4UUSKiopWrlx56aWXikg8HmebDMDnVGXdmWkjFKJRD/iNCUnoyJEjIvLlL3+51+uRSEREOjo6tm3blv93AeARTl50UUenuYwM8BMTkpB6GvUXvvCFXq/X1NSoD44dO5b/dwHgBaqp7oTm/EDU0Wka9YBvmJCExo8fLyJ9r1ktLi4uLi7Of3wA3hGPSzRq9yQGRaMe8BkTktBXvvIVEXn77bf7GX3UKBE577zz8v8uAFwvHpdg0HEHpftSk2SPDPAHE5KQ6sn/97//PXz4cK+3Tp06dd5551VXV+f/XQC4m2rOO3xBKIvLyADfGEkS2r179+rVqw8dOqT+MhAILFiwQESeffbZnp+2Z8+ekydP3nLLLWplCICvRSISi7nmUT3ZRj0Ar+sno3R2dopIKpU6depU33fT6fTixYs3bty4YsWK7IsrVqyYPn16XV3dvn371Cuffvrpvffe+61vfWvJkiXWzByAe+i6GIZrFoSUUEgMg2UhwPPOeLJic3Pz888/39jYKCKpVGrhwoVXXHFFOBy+4IILen5aaWlpV1fXhAkTsq+UlJQkEona2tobb7zxRz/60bnnnvvcc8/Nnj176dKlhfnbAOBoTm7ODyTbqN+/3+6pALDQWd3d3XbPQUSkqqqKZ0wD3qRp8sgjjrtbI0fq/g0n1/4BjEg2eJhw2wYADCYScWsMktOXkZGEAO/iLDMAKznzirHcBQI06gFvY00IgGUMQzTN9edsolGpqRFdd3GeAzAw1oQAWMZdzfmB8NRpwNNIQgCs4cbm/EDUahCNesCLSEIArBGJuK85PxDuqAe8iyQEwALxeOassWeoO+rZIwM8hyQEwAIuumIsd4mEaJoYht3zAGAmkhAAs7m9OT8QtcrFshDgLbToAZhK10XTxBkPrzdfNCpTp0oo5MGcB/gVa0IATOXGK8ZyFwhIIsGyEOAlJCEA5lHHaLx9N4VaDdI0e2cBwCwkIQDm8faCkMKDFgFvIQkBMIn3mvMDUY16Hi8EeAInpgGYwTAkFnP9FWO5U3fUG4br7xIBfI81IQBm8MYVY7kLBCQcZo8M8ACSEIC86brougcfpTi4UCjzNw7AzUhCAPLmh4PSfXEZGeAJJCEA+VF9cm835weijk7TqAfcjCQEID/xuO/2xbJo1APuRxICkId4XIJBXzTnB6L+9tkjA1yLFj2AkfJbc34g0ajU1Iiu+zoRAq7FmhCAkfJbc34g7JEBbkYSAjAiui6G4d8TQr0Eg2IYNOoBNyIJARgRfzbnB0KjHnAtkhCA4VO9cY7F9BQO06gH3IgT0wCGLxKRhga7J+E86jIyfz5aCXAt1oQADFMkIuEwC0L9CARo1AOuw5oQgOHQddE0mvMDolEPuA1rQgCGIx6nOT8YGvWA25CEAORM02jOD02tBtGoB1yCJAQgZzTnc0GjHnAVkhCA3MTjmRPBGJK6o549MsANSEIAchOLsS82DIlEZjMRgLORhADkgOb8cKn1M5aFAMejRQ9gKKo5391t9zzcJhqVqVMlFCJBAk7GmhCAoXBQemQCAUkkODoNOBxJCMCg1EVa3CAxMuroNJeRAQ5GEgIwqHicg9Ijx4MWAccjCQEYGM35/KllIfbIAKfixDSAARiGxGJcMWYCdUe9YXBLCeBArAkBGEAkwhVj5ggEJBxmjwxwJpIQgP7ouug6J4RMEwpl/pECcBiSEID+0Jw3F5eRAU5FEgLQB815K4TDNOoBByIJAegjEmFfzBI06gHnGTAJtba25jNuR0dHY2PjsWPH8hkEgA24Ysw6waAEg+yRAY7STxJ64403Fi1adP311+cz7k9+8pNbb721ra0tn0EAFJphiKaxIGShaJSj04CjnPE8oZaWlg0bNjQ3N6dSqTFjxox40PXr1+/atSvvuQEoOJrzVss+dZpVN8AZzlgTuuiiixKJRG1tbT4jvvnmm48//nh+swJgB10Xw2BByHLBoBgGy0KAQ5yRhMrLy0Vk0qRJIx7uxIkTy5YtW716db7zAlB4NOcLg0Y94CT9nBMqKioa8XCrV6++6qqrqqur85gSADuodjdbNoWhGvX0yAAHMPPescbGxpaWls2bN5s4JoACiUSkocHuSfiJuowsFOJUFmAv054ndOTIkdra2jVr1owdO9asMQEUCM35wgsEJBhkWQiwnWlrQrW1teFwuKqqasQj9Pu1eT7WCMDQdF00jTvnbRCNSk2N6DoZFLDaIPnEnCT0zDPPfPzxx0uWLMlnEEIPYA91UJo9msKjUQ8USt+Mkc1GJuyOvfPOO+vWrfvDH/6Q/1AACk3TxDC4Ysw2KgPRqAfsk28SSqfTv/zlL3/xi19ccMEFpkwIQEHRnLcXjXrAbvnujiUSibfffrupqampqanvuw899NBzzz339a9//brrrsvzGwEwXzyeObcLGwWDmUY9z7QE7JBvEtq/f//HH3/89NNP9/uufnrJlyQEOFEsRnPeEWjUA/bJNwmFQqGrr7667+u33nqriNx9992VlZUXXnhhnt8FgPlqamjOO0UgIOEwO5WALfJNQtOmTZs2bdpA715++eVXXHFFnt8CgPnUdejd3XbPA6eFQjTqAVuM5MT07t27V69efejQIdNnA6BAWH5wGo5OAzbpJwl1dnaKSCqVOnXqVN930+n04sWLN27cuGLFCstnB8AK6ooxmvNOo45Oq387AArljN2x5ubm559/vrGxUURSqdTChQuvuOKKcDjcqyFfWlra1dU1YcKEgs4UgFlYEHKm7LIQIRUooLO6nXFQoKqqimdMA4UQj4thkIScq6ZGAgH+BQFWywYPM++iB+B0hiGxGFeMOZpq1HN0GigU0+6iB+ACkYjEYjy0xtGyjXoABUESAnxDNed5kLHzhUJiGFxGBhQGSQjwjXicJ0q7A416oIBIQoA/qG42R0/cIhymUQ8UBiemAX+IRFgQchl1dJpGPWAx1oQAH1CPqGFByF0CAQkG2SMDrMaaEOB1hiGaRnPelaJRGvWA1VgTAryO5rx7qaPTNOoBK5GEAE/TdTEMmvMuFgzSqAcsRRICPC0S4d4Gd1M3b3BaCLAMSQjwLk3LnLqFq6k76tkjA6xBEgK8KxJhX8wjEgnRNDEMu+cBeBBJCPAomvNeotb2WBYCLECLHvAiXRdNk+5uu+cB89CoB6zBmhDgRfE4B6W9hkY9YA2SEOA56kAJtzR4j1oN4jIywFQkIcBzWBDyKpaFAAuQhABvicdpznsZjXrAbCQhwEMMQ2IxFoQ8jkY9YCqSEOAhqjnPFWPeFghIOMyyEGAWWvSAV+i66DrNeV8IhWjUA2ZhTQjwCg5K+4c6Os1lZIAZSEKAJ6hmNc15/1BHp2nUA3kjCQGeEI9zxZi/0KgHTEISAtwvHpdgkCMjvqP+pbNHBuSHE9OAy6nm/P79ds8DduAyMiBvrAkBLheJSCxGc96naNQDeSMJAW6m62IYnBDytVBIDEN03e55AG5FEgLcjOY8aNQD+SEJAa6lGtQcEIF6sDiNemBEODENuFYkIg0Ndk8CzpBISE0ND5QCRoA1IcCd1BVjLAhBCQRo1AMjw5oQ4EK6LppGcx5noFEPjAhrQoALxeM059EbT50GRoQkBLgNzXkMRK0G0agHhoMkBLhNJEJzHv2jUQ8MH0kIcJV4PHM2FuiXuqOePTIgZyQhwFViMfbFMIREQjRNDMPueQDuQBIC3IPmPHKhVg1ZFgJyQ4secAnVnO/utnsecINoVKZOlVCI3AwMiTUhwCW4Ygy5CwQkkWBZCMgFSQhwA3Xsg7sUkDu1GsRlZMBQSEKAG7AghOHiQYtAbkhCgOPRnMfIqEY9jxcCBsWJacDZDENiMa4YwwipO+oNg7tZgIEMuCbU2to63LHS6fTOnTu3b99+7Nix/GYF4LRIhCvGMHKBgITD7JEBg+hnTeiNN95Yu3bt7t279+zZk/tAdXV1dXV1n3zyifrLWbNm/eY3vwnwxzeQD10XXZeGBrvnATcLhbijHhjEGWtCLS0tkUhk0aJFr7766rBGWbVq1dq1a8ePHx8MBsvLy9VQCxYsGMHCEoDPcVAa+eMyMmBQZyShiy66KJFI1NbWDmuInTt3/vOf/9y4cWNDQ0NdXd0rr7wSjUZF5NixY8uXLzdzsoCvqP4zzXnkLxyWQIBGPdCvM5KQWs6ZNGnSsIbYvHnzhg0brrrqquwrCxcuvOOOO0Tk3//+9759+8yYJ+A/8ThXjME0NOqBAfRzYrqoqGhYQ8yYMeOyyy7r9eLNN9+sPmhvbx/ZzABfi8clGORgB0yj/nNijwzow4QW/Y033tj3xfLy8tGjR3/22WfDXWECQHMelohGOToN9GXVkxVTqdRnn332pS996eKLL7boWwCeRXMeVuCp00B/rHqyYnNzs4gsXrw49y+pqqrq+yLtM/iOrothcEIIlggGJR5nWQg+1G/GUKxKQs8+++ykSZMWLVqU+5cQegARmvOwUrZRz94rfKZvxshmI0t2x/bu3VtfX/+///u/Y8eOtWJ8wLNUz5nf12EdGvXAmcxfE0qn0/fcc89dd901a9Ys0wcHPC4S4YnSsJy6jEzdzwr4nvlrQvfff/+0adNuv/1200cGPC4SkXCYBSFYLhDIHBgCYPqa0ObNmw3DqKurM3dYwPt0XTSN0xsoEBr1wGlmrgk1Njb+7W9/++Mf/2jimIBfxOM051E4NOqB00xLQtu3b1+/fv2f/vSnXqekOzo6Dh06ZNZ3AbxJ02jOo9DUapCu2zsLwHYjSUK7d+9evXp1z3yzbdu2Bx54oK6ubty4cb0+89Zbb/3iF7+Y7zQBb6M5j8LjjnpARPo9J9TZ2SkiqVTq1KlTfe8gS6fTixcv7urqeuuttx5++GERefnll++8804R6XkJq4icPHlSRObPn19SUmLR7AEviMczJ1iBAlP1Me76hb+dkYSam5uff/75xsZGEUmlUgsXLrziiivC4fAFF1zQ89NKS0u7uromTJggIi0tLYPXxK677joLpg14SCxGcx62UY36UIgzavCts7q7u+2eg4hIVVUVz5iGH6m9CbbGYCP+I4QvZYOHVbdtABiaas4747cR+Fc0KlOnSijEFi38yaq76AEMjYPScIJAQBIJjk7Dt0hCgE3UxU/hsL2zAEROH53mMjL4EkkIsAmFHTgHD1qEj5GEADvQnIfTqGUh9sjgP5yYBgrOMCQW44oxOI5q1BsGjXr4CmtCQMFFIlwxBicKBCQcZo8MfkMSAgpL10XXOSEEhwqFMv+JAr5BEgIKi+Y8nIzLyOA/JCGggGjOw/nCYRr18BVOTAMFFIlwxRhcQB2dJrLDH1gTAgolEpFwmOY8XEA94oE9MvgDa0JAQRiGaBrNebhGNCo1NaLrZHd4HmtCQEHQnIe78NRp+AZJCLCeroth0JyHywSDYhg06uF5JCHAejTn4UY06uEPJCHAYqqNzGELuJFq1LNHBk8jCQEWi0TYF4OLJRKiaWIYds8DsApJCLASzXm4nWrUsywE76JFD1hG10XTpLvb7nkA+aFRD09jTQiwDAel4Q006uFpJCHAGupoBfcVwBvUahCXkcGLSEKANVgQgpewLATvIgkBFojHM+dMAc8IBmnUw5NIQoDZDENiMZrz8CAa9fAikhBgNprz8KpAQMJhloXgMbToAVPpuug6zXl4VihEox4ew5oQYCoOSsPbuIwMnkMSAsyjOsY05+Ft6ug0jXp417DzZwAAIABJREFUBUkIME88zkFpeB+NengLSQgwSTwuwSCHJ+ALalmIPTJ4AiemATOo5vz+/XbPAyiURIKj0/AG1oQAM0QiEotJIGD3PIBCoVEPryAJAXlTzXlOCMFvQiExDNF1u+cB5IUkBOQtHpeGBrsnARQcjXp4AkkIyI/qEnNUAv4UDtOoh9txYhrITyTCghB8TR2d5jFacC3WhIA8cMUYEAhIMMgeGdyLNSFgpAxDNI3mPCDRKI16uBdrQsBI0ZwHFJ46DTcjCQEjoutiGDTngQy1GkSjHi5EEgJGJBLhznngczTq4VokIWD4NC1zShRAlrqMjD0yuA1JCBi+SIR9MaAfiYRomhiG3fMAhoEkBAwTzXlgIGqtlGUhuIolSai1tdWKYQH76bpoGieEgAFFo5mb+ACXMDkJvfHGG4sWLbr++uvNHRZwinicGAQMhkY93Ma0JNTS0hKJRBYtWvTqq6+aNSbgLOoABLcKAINTe8dcRgaXMC0JXXTRRYlEora21qwBAcdhQQjIBctCcBXTklB5ebmITJo0yawBAWeJx2nOA7lSjXoeLwQ3MPnesaKiInMHBBzBMCQW44oxYBjUHfWGwY00cDha9EAOVHOeP9CB3AUCEg6zRwbn4y56YCiqEtzdbfc8ALcJhbijHs7HmhAwFA5KAyPDZWRwAwetCVVVVfV9kYc0wmaqCUxzHhiZYFAeeUQ0jf+JYK9+M4bioCRE6IETsSAE5CO7LEQSgq36ZoxsNmJ3DBhYPC7BIEccgLyo/4nYI4NTOWhNCHAWmvOAWaJRjk7DsVgTAgYQiUgsRnMeMAGNejgYSQjoj66LYUg0avc8AK8IhcQwuKMeDkQSAvrDQWnAXDTq4VQkIaAP1ZznQANgLvWgdu6oh8OYfGK6s7NTRFKp1KlTp7iDDG4ViUhDg92TALxIXUZGox5OYloSam5ufv755xsbG0UklUotXLjwiiuuCIfDF1xwgVnfAigE9eATFoQAKwQCmUY9u89wDNOS0De+8Y1vfOMbZo0G2EPXRdNozgMWolEPh+GcENBDPE5zHrCWOjpNox6OQRICTqM5DxSGWg2iUQ9nIAkBp3F2ASgMGvVwEpIQICIi8XjmLCeAAggGJRBgjwxOQBICREQkFmNfDCioREI0TQzD7nnA70hCAM15wA5qFZZlIdiNu+jhe6o5391t9zwA/4lGZepUCYX4PQQ2Yk0IvscVY4BdAgFJJFgWgr1IQvA3dQUSz/4H7KJWg7iMDPYhCcHf4nEOSgN24kGLsBtJCD5Gcx5wAtWo5/FCsAknpuFXhiGxGFeMAY6g7qg3DO66QeGxJgS/ikS4YgxwikBAwmH2yGALkhB8SddF1zkhBDhIKJT5HxMoLJIQfInmPOA0XEYGm5CE4D805wFnCoclEKBRjwIjCcF/aM4DjkWjHgVHEoLPRCISDNKcBxxK/e/JHhkKiBY9/MQwRNNozgOOFo1KTY3oOr+xoDBYE4Kf0JwHnI+nTqOwSELwDV0Xw+CEEOACwaAYBo16FAZJCL5Bcx5wCxr1KCCSEPxB9XI5dgC4hWrUs0cG65GE4A+RCPtigMskEqJpYhh2zwMeRxKCD0QiEg6zIAS4TCAgwSDLQrAaLXp4na7TnAfcikY9rMeaELwuHqc5D7gVjXpYjyQET1OHDDghBLiXWg2iUQ/LkITgaTTnAbejUQ+LkYTgXfF45sQlAFcLBmnUwzokIXhXLMa+GOARNOphGZIQPIrmPOAlNOphGVr08CLVnO/utnseAMxDox7WYE0IXsRBacB7ODoNa5CE4DnqirFw2N5ZADCfOjqt/h8HTEISgufE4xyUBryJBy3CAiQheEs8LsEgxwgAz1LLQuyRwTycmIaHGIbEYlwxBnhcIiE1NWIY3KIDU7AmBA+JRLhiDPC+QEDCYZaFYBaSELxC10XXOSEE+EIoJIbBZWQwBUkIXkFzHvAPGvUwD0kInkBzHvCbcJhGPUzBiWl4QiQiDQ12TwJAYamj0/wKhPywJgT344oxwJ/UZWTskSE/rAnB5QxDNI3mPOBTXEaGvLEmBJejOQ/4GU+dRt76SUKpVKq5uXnv3r0jGO7w4cPbt2/fuXNnOp3Oe27AUHRdDIPmPOBrwSCNeuSj9+5YXV1dIpGorq4+fPjw0aNH77vvvhkzZuQyUEtLy7333jthwoQpU6acPHly6dKlc+fOveuuu8aOHWvBtAEREYlEaM4Dfpdt1LNLjhE5IwmtXLnyH//4x9NPPz1t2jQReeCBBxYtWqRp2uWXXz74KC0tLZFIpLa29qabblKvHD169Prrr3/rrbcS/KCCRTQtc14SgM+Fw/LII9y+jJH5fHdsy5YtmzZtikQiKgaJyJ133jlu3LilS5eeOHFi8FFWrlx50UUXZWOQiJx77rk//vGPm5qaXnrpJSvmDUgkwp96ADISCdE0MQy75wH3ySShdDq9Zs0aEbn22ms/f2/UqGuuuebgwYOPPfbYIEMcP358//795557bq/Xzz//fBFpbm42ecqA0JwHcCa1QszRaQxfJgk1NjYePHhwzJgx2QUhZdasWSLy5JNPDjnQ66+/fujQoZ6vvP/++yLy1a9+1bTJAoqui6ZxQgjAGaLRzP2DwHBkktCLL74oIhdffHGvt9W6zrvvvrtv376Bhhg3btyUKVNSqdSyZcs+/fRT9WI6nd60aVNFRcXcuXMtmTj8jCvGAPRFox4jkklCra2tIlJRUdHr7UsuuUR90NbWNsgoy5cvF5FXX331pptuOnz4sIjU1tYeP348kUjQHYPJ1FEAnq8PoC+1Y85lZBiOTBJ6++23RaS4uLjX26NHZ8plHR0dg4zy7W9/e8WKFSLy5ptvXnfddT/96U+PHz/+97//vW+0AvLFghCAgbAshOHLBJ2uri4RKSoqGujzBtkdU0Kh0DnnnLNy5cpkMvnyyy/fe++9paWlw5pKVVVV3xfVYhWQEY/TnAcwmGBQAgEa9eil34yh5Hrv2Nlnnz3k53z88cdf+9rX9u3bl0wmly9fvnfv3l/84he5zpHQgyEZhsRi3DkPYAjqjvpQiHt4kNU3Y2SzUWZ3LLsL1kv20ozp06cP/j1WrlxZX1+fSCQ2b96sCmgbN2783e9+N+JJA73RnAeQi0BAwmH2yJCjTBKaOHGiiGSbX1nJZFJ9MH78+EFGqaur27Rp0+9///uioqKJEyc+8cQTM2fOFBFN07Zt22b+rOFDqhzLCSEAuQiFaNQjR5kkdOmll4rI8ePHe72tTlKLSK/nDPV09OjRBx98cPr06dkSfmlp6UMPPTR16lQR+ctf/mL6pOFHHJQGkLvsZWTAUDJJqKamRkR27tzZ6+2PPvpIRCoqKqZMmTLQEK+99trJkycDZ27HlpaWrl69ut8xgWFTnVia8wByp45O06jHUDJJaO7cuaWlpR9++OF7773X8+2mpiYRWbBgwZADdXd393plxowZY8aM6XsLBzBs1EAADBeNeuQmk4SKiopuu+02EXnhhRey76XT6VdeeaW8vPzmm2/u+TW7d+9evXp19m6Nb37zm+ecc85rr72WPV6tpFKpVCp19dVXW/t3AM+LxyUY5KA0gGFTy0LskWFQn99Fv2TJkurqak3Tjhw5ol5Zv359R0fH2rVrx40bl/20dDq9ePHijRs3qkcpikhxcfGvf/3rZDK5du3ankM/+OCDF1544e2332793wW8SzXnWRACMDKJBEenMbgzyvPr1q2LRqM33HDDlVde2d7e/sEHHzz11FMzZszo9TWlpaVdXV0TJkzIvvL9739/7Nix999//5tvvvm9731PRLZs2TJ+/Pi//vWvw32+InCGSERiMR4KAmCEso161pUxgLP6nu+xRVVVFU9WRG+6LpGI7N9v9zwAuJlhSE2NJBKEIfSUDR6jhvxUwDY05wHkj0Y9BkUSglOp7iu/wwHIXzhMox4DyfXeMaDQIhGuGANgGnUZGY8lQx+sCcGRuGIMgLkCAQkG2SNDX6wJwXkMQzSNg9IATBaNSk2N6Dq/ZaEn1oTgPDTnAViBp06jPyQhOIyui2HwKEUAllCrQTxoET2QhOAwkQjNeQBWoVGPPkhCcJJ4PHOqEQAsoi4jY48Mp5GE4CRcMQagABIJ0TQxDLvnAUcgCcExaM4DKAy19syyEESEFj2cQtdF08QZt+AB8D4a9TiNNSE4A1eMASgkGvU4jSQEB1Ab9jwFH0AhqdUgLiPzPZIQHIAFIQCFx7IQRIQkBPvRnAdgF9Wo5/FC/saJadjKMCQW44oxALZRd9QbBjf8+BZrQrCVas7zBxAAuwQCEg6zR+ZnrAnBProuuk5zHoDNQiEa9X7GmhDsw0FpAE7AZWT+RhKCTVRzleY8ACdQR6dp1PsSSQg2ice5YgyAU9Co9zGSEOwQj0swyJY8AAdRfyixR+Y/nJhGwdGcB+BMXEbmS6wJoeAiEYnFaM4DcBz2yHyJJITC0nUxDE4IAXCoYFAMQ3Td7nmgcEhCKCya8wCcjEa9/5CEUECqocoGPAAnUw++p1HvG5yYRgFFItLQYPckAGAo6jIyHnjmD6wJoVDUFWMsCAFwvkCARr1/sCaEgtB10TSa8wBcg0a9b7AmhIKIx2nOA3ATGvW+QRKC9WjOA3AjtRpEo97rSEKwXiRCcx6A+9Co9weSECwWj2fOHgKA66g76tkj8zSSECwWi7EvBsDFEgnRNDEMu+cBq5CEYCWa8wDcTq1qsyzkXbToYRnVnO/utnseAJCfaFSmTpVQiN/rPIk1IViGK8YAeEMgIIkER6e9iiQEa6gre3hWPQBvUEenuYzMi0hCsEY8zkFpAN7Bgxa9iyQEC9CcB+A9almIPTLP4cQ0zGYYEotxxRgAD1J31BsGdwd5CWtCMFskwhVjALwpEJBwmD0yjyEJwVS6LrrOCSEAnhUKZf6gg1eQhGAqmvMAvI3LyDynnySUSqWam5v37t2b59DpdPo///nPtm3bUqlUnkPBHWjOo7CSyWRbW9uOHTva2tqSyaTd04FvhMM06r2k94npurq6RCJRXV19+PDho0eP3nfffTNmzBjuoA0NDU888URHR8ecOXOmT59u0lTheJGINDTYPQl4XDKZ3LFjR2tra1tbW0lJiYgUFxer18vKykSkurp69uzZ6mPAKmpZiF/8POGs7h6XIaxcufIf//jH008/PW3aNBF54IEH/vznP2uadvnll+c43JEjR371q1+9/vrrq1atmjdvXu7zqKqqam1tHdbU4SxqrZitMVhGZaD6+vqqqqqysrK+Waezs1NE2traOjs7Kysrq6urKysr7Zgp/IE/9FwuGzw+T0JbtmxZtmzZHXfc8T//8z/qlXQ6fdVVV40ZM+aFF15Qv3UN7r333rv55pu7uroeeeQRlaVGMCG4kmHI1Kmyfz+VMVhky5YtW7duraioyCXcdHZ2HjhwoLOzc+bMmcP6lQwYBsOQmhpJJHh2mktlg0fmnFA6nV6zZo2IXHvttdlPGjVq1DXXXHPw4MHHHntsyBGPHDnywx/+8P3331+3bt1wYxBcj+Y8LJNMJtesWbN169bZs2fnuMZTUlJSWVlZWVm5devWNWvWcIQIluCp016RSUKNjY0HDx4cM2ZMrxAza9YsEXnyySeHHOhnP/vZ+++/f8stt+S+lQaP0HUxDJrzsIKKQSdOnJgzZ446FZS7kpKS2bNnn3XWWYQhWCUYFMOgUe92mST04osvisjFF1/c6+3zzz9fRN599919+/YNMsozzzzz6quvFhcX33LLLdbMEw5Gcx6W0TStrKxs5syZI/tytThUXl6u1rwBk9Go94RMElJbZRUVFb3evuSSS9QHbW1tg4yybt06EfnBD34wbty448ePb9u2raWlJZ1Omz9fOI3qkbJNDgts2bIlmUxWVVXlOc7kyZNFRKPzDCuoRj17ZG6WadG//fbbcrqMesbbozOf0NHRMdAQzc3NBw8eFJFJkyYtWbLkX//6V1dX18mTJ8vKympra3sePIIH0ZyHNdra2rZu3Tpnzpz8hyopKZk5c+aOHTt27Ngxe/bs/AcEzqAuIwuFOCvpUpmg09XVJSJFRUUDfd4gu2MvvfSS+uCdd9757W9/O3HixFOnTv3ud797/PHHf/7zn48ePfq73/1uLlPp9zc/CmWOph6nwYIQLFBfXz/iTbG+VBiqr68nCcF8gYAEg5wTcLhBVpdzvYv+7LPPHuitAwcOiMi0adNWrVqlXikqKlq5cuWePXv+9a9/xePx73znO6NGDX2tB6HHZXRdNI0752GFtra2tra2/PfFelJr3m1tbTxkCOaLRqWmRnSd3wwdq2/GyP4Jkwko2V2wXrJnfQZ5VPSRI0dE5Mtf/nKv1yORiIh0dHRs27Zt2FOG86lfgFgNhgWamppMXBBSSkpKKioqmpqazB0WEKFR726ZJDRx4kQR+fTTT3u9na2ejh8/fqAhxowZIyJf+MIXer1eU1OjPjh27JgZU4WTaJoYBk+ah0V27NhhxXUZZWVlg5c/gJFTq0E06l0ok4QuvfRSETl+/Hivt9VJahEZ5GGJKiT1vWa1uLg4lydTw5XYEYdl1IViw316UC7UmIQhWIJGvWtlkpBav9m5c2evtz/66CMRqaiomDJlykBDfOUrX5EememM0UeNEpHzzjvPpNnCGeLxzAlBwALZu1QBlwkGadS7USYJzZ07t7S09MMPP3zvvfd6vq321BcsWDDIEKon/9///vfw4cO93jp16tR5551XXV1t5pRhu1iMJ0rDOpY+D7q8vJw1IVgokcgcHoB7ZJJQUVHRbbfdJiIvvPBC9r10Ov3KK6+Ul5fffPPNPb9m9+7dq1evPnTokPrLQCCgotKzzz7b89P27Nlz8uTJW265JZfiGFyjpobmPCzV0dFh6ZrQIE9HA/KVbdTDPT7PKEuWLKmurtY0TXXBRGT9+vUdHR1r164dN25c9tPS6fTixYs3bty4YsWK7IsrVqyYPn16XV1d9rFDn3766b333vutb31ryZIlBfkbQUHouug6J4RgqfLy8hMnTtg9C2CkotHMH5VwiTPK8+vWrYtGozfccMOVV17Z3t7+wQcfPPXUUzNmzOj1NaWlpV1dXRMmTMi+UlJSkkgkamtrb7zxxh/96Efnnnvuc889N3v27KVLlxbibwIFw0FpFERnZ6d1I/NwRVgre3Sax625xBlJqKSkZPXq1YN/wahRo/p9PtCECRPWr1+f/cvFixebMj84iLq2ieY8LFZZWWndU3+sy1jA54JBeeQR0TT+wHQFTvAgZ/E4B6VRAGVlZdbtjp04cYJnTMNyPGjRVUhCyE08LsEgB6VRAGVlZZMnT7aiQdbe3t7Z2UlFH4WgGvU8XsgNSELIgWHQnEchVVdXW3ERYTKZDLNbgYJJJETXadQ7H0kIOYhEJBbjijEUTGVl5YkTJ0w/09Pe3s7WGAonEJBwmGUh5yMJYSiqDsqCEAqorKzssssuM/cRiG1tbbNnz2ZrDAUVColh0Kh3OJIQhkJzHnaYP39+Z2dne3u7KaMlk8mOjg62xlBoXEbmBiQhDIrmPGxSVla2bNmytra2/PfIOjs7m5qaiEGwRzgsgUDmz1I4EkkIg4pE2BeDXcrKyubMmbNjx458wlBnZ+euXbvmz5/PCSHYJpGgUe9kJCEMLBLhijHYa968eSoMjWybLJlMbt26tbq6et68eabPDciVuoyMPTKnGj30p8CfDEM0jafFw3bz5s2rrKzcsGHDcB+K2NbW1tHRsWzZMlaDYL9oVGpqRNf53dKBWBPCAGjOwzEqKytra2u7u7u3bt065Mmhzs7Otra2+vp6YhAchKdOO9hZ3d3dds9BRKSqqsqKB6lhhHSd6wPhQMlksr6+fvfu3aoMX1ZWVlJSUlxcrB4+dOLEiY6OjmQyOX/+fArzcBzDkJoaSSRYFnKIbPAgCaE/U6fyvyscK5lMtrW1qT8xksmkupejsrKyvLxcRDgSBOfil0wnyQYPzgmhD03LnO8DHKmsrGz27NmzZ8+2eyLAMKnLyLjN2mE4J4Q+aM4DgEUSCdE0LiNzFJIQzkRzHgCso1bcOTrtJOyOoQddF00TZxwdAwBvolHvMKwJoQeuGAMAq9GodxiSEE5TW9fczQQAVlOrQVxG5gwkIZzGghAAFAbLQk5CEoKIiMTjNOcBoHCyjXrYjSQEEcOQWIzmPAAUFI16ZyAJgeY8ANghEJBwmGUh29Gi9z1dF12nOQ8ANgiFaNTbjjUh3+OgNADYRR2djkTsnoevkYT8TXU4ac4DgF3U0Wka9fYhCfkbFwECgL1o1NuNJORj8bgEg2xOA4DN1B/F7JHZhBPTfqWa8/v32z0PAACXkdmJNSG/ikQkFpNAwO55AABo1NuJJORLui6GwQkhAHCQUEgMQ3Td7nn4DknIl2jOA4DT0Ki3CUnIf1RXk61oAHCacJhGfeFxYtp/IhFpaLB7EgCA/iQSUlPDY94KiTUhn+GKMQBwskCARn2BsSbkJ4YhmkZzHgAcjUZ9YbEm5Cc05wHA+XjqdGGRhHyD5jwAuIVaDaJRXxAkId+IRGjOA4A70KgvIJKQP8TjmVN4AABXUHfUs0dmPZKQP8Ri7IsBgMskEqJpYhh2z8PjSEI+QHMeANxIreWzLGQxWvRep+uiadLdbfc8AADDF43K1KkSCvHbrHVYE/I6rhgDAPcKBCSRYFnIUiQhT1MbzDy1HQDcS60GcRmZZUhCnsaCEAC4HQ9atFg/SSiVSjU3N+/duzefcTs6OhobG48dO5bPIMgLzXkA8AbVqOfxQtbofWK6rq4ukUhUV1cfPnz46NGj991334wZM0Yw7k9+8pNdu3Y9/vjjV1xxhRnzxDAZhsRiXDEGAB6h7qg3DG5MMt0ZSWjlypX/+Mc/nn766WnTponIAw88sGjRIk3TLr/88mENun79+l27dpk5TQwXV4wBgJcEAhIOc+bBCp/vjm3ZsmXTpk2RSETFIBG58847x40bt3Tp0hMnTuQ+4ptvvvn444+bPE0Mi66LrvMoRQDwlFAo88c7TJVJQul0es2aNSJy7bXXfv7eqFHXXHPNwYMHH3vssRyHO3HixLJly1avXm36RDEM/NIAAN7DZWTWyCShxsbGgwcPjhkzJrsgpMyaNUtEnnzyyRyHW7169VVXXVVdXW3uLDEMqmlJcx4AvEcdnaZRb6pMEnrxxRdF5OKLL+719vnnny8i77777r59+4Ycq7GxsaWl5e677zZ7khiOeJx9MQDwJhr1FsgkodbWVhGpqKjo9fYll1yiPmhraxt8oCNHjtTW1q5Zs2bs2LFmTxI5i8clGKQ5DwCepf6QZ4/MPJnu2Ntvvy0ixcXFvd8enfmEjo6OwQeqra0Nh8NVVVVmzxA5ozkPAH4QjUpNjeg6v/eaIhN0urq6RKSoqGigzxt8d+yZZ575+OOPlyxZks9U+k1RarEKOaE5DwB+kN0jIwnlbJCVmlzvoj/77LMHeuudd95Zt27dU089Nex5nYnQkxddF8PghBAA+EIwKPE4y0K565sxstkoc04ouwvWSzqdVh9Mnz59oE/45S9/+Ytf/OKCCy4wYaYYMZrzAOAfNOrNkwlAEydObG9v//TTT3u9nUwm1Qfjx4/v9+sTicTbb7/d1NTU1NTU992HHnroueee+/rXv37dddeZN2f0oRqV/GYAAP4RDssjj4im8diUPGWS0KWXXtre3n78+PFeb6uT1CLS6zlDWfv37//444+ffvrpft/VTz8KkyRkrUhEGhrsngQAoLDUZWTqIUMYqUwSqqmpef7553fu3Nnr7Y8++khEKioqpkyZ0u/Xh0Khq6++uu/rt956q4jcfffdlZWVF154oZlTRi+RiITDLAgBgO8EApkDQ5yOyEMmCc2dO3fVqlUffvjhe++9N3HixOzbas9rwYIFA339tGnTBlouEpHLL7+cu+itpeuiaTTnAcCnaNTnLXNiuqio6LbbbhORF154IfteOp1+5ZVXysvLb7755p5fs3v37tWrVx86dKiQE0X/4nGa8wDgXzx1Om+f30W/ZMmS6upqTdOOHDmiXlm/fn1HR8fatWvHjRuX/bR0Or148eKNGzeuWLGi0JNFL5pGcx4A/E6tBnFH/UidUZ5ft25dNBq94YYbrrzyyvb29g8++OCpp56aMWNGr68pLS3t6uqaMGFCAeeJ/rA3DADINuo5KTEiZ3V3d9s9BxGRqqoqnqw4POqZWlTGAAAimRIZuwQ5ywaPUUN+KhwqFuO/eABARiKROTKBYSIJuRPNeQBAT9lGPYYp13vH4CCqOe+MbU0AgFNEozJ1qoRC/J48LKwJuRAHpQEAfQUCkkhwGdlwkYTcRl0xxi0zAIC+1M0b6icFckMScpt4nIPSAID+8aDF4SMJuUo8njkTBwBAv9SyEHtkOePEtHsYhsRiPDgLADAEdUe9YXAXUy5YE3KPSIQrxgAAQwsEJBxmjyxHJCGX0HXRdU4IAQByEgplfnBgKCQhl6A5DwDIXfYyMgyFJOQGNOcBAMMVDtOozwVJyA0iEfbFAADDRqM+ByQhx+OKMQDAyASDEgyyRzY4WvTOZhiiaTTnAQAjFI1KTY3oOr9RD4Q1IWejOQ8AyAdPnR4KScjBdF0MgxNCAIC8BINiGDTqB0IScjCa8wCA/NGoHxRJyKlU75FtXQBA/lSjnj2y/pCEnIrmPADARImEaJoYht3zcBySkCPRnAcAmCsQkGCQZaG+aNE7j67TnAcAmI9GfX9YE3IedVCa5jwAwFw06vtDEnIYtYnLFWMAACuo1SAa9T2QhByG5jwAwDo06vsgCTlJPJ450QYAgEWCQRr1PZGEHMMwJBajOQ8AsByN+h5IQo5Bcx4AUBiBgITDLAsptOidQddF16W72+55AAD8IRSiUa+wJuQMHJQGABRfUIzvAAAXUUlEQVQSR6dPIwk5gLpijOY8AKCQ1NFp9TPIx0hCDhCPc1AaAFBoPGhRREhC9ovHJRhkmxYAYAO1LOTvPTJOTNtKNee5YgwAYJdEwudHp1kTslUkIrEYV4wBAGzj+0Y9Scg+qjnPCSEAgL1CITEM315GRhKyD815AIAT+LtRTxKyCc15AIBzhMO+bdRzYtomkYg0NNg9CQAATlNHp/33KzprQnbgijEAgNMEAhIM+nCPjDWhgjMM0TSa8wAAx4lGfdioZ02o4GjOAwCcyZdPnSYJFZaui2HQnAcAOFQw6LdGPUmosCIRmvMAAOcKBCSR8NVpIZJQAWla5jwaAACOpS4j880eGUmogCIR9sUAAC6QSIimiWHYPY9C6CcJpVKp5ubmvXv3DnesdDq9c+fO7du3Hzt2zIy5eQvNeQCAW6gdDH8sC/Vu0dfV1SUSierq6sOHDx89evS+++6bMWNGLgPV1dXV1dV98skn6i9nzZr1m9/8JkBDStF10TTp7rZ7HgAA5MY3jfoz1oRWrly5YcOGRx99dO3atY8++uh3vvOdRYsW7dy5c8hRVq1atXbt2vHjxweDwfLychFpaWlZsGBBa2urVRN3F64YAwC4i28a9Z8noS1btmzatCkSiUybNk29cuedd44bN27p0qUnTpwYZIidO3f+85//3LhxY0NDQ11d3SuvvBKNRkXk2LFjy5cvt3T27qC2Wv33/HIAgLup1SCvX0aWSULpdHrNmjUicu21137+3qhR11xzzcGDBx977LFBhti8efOGDRuuuuqq7CsLFy684447ROTf//73vn37LJm4i7AgBABwI38sC2WSUGNj48GDB8eMGZNdEFJmzZolIk8++eQgQ8yYMeOyyy7r9eLNN9+sPmhvbzdtsm4Uj9OcBwC4lWrUe/rxQpkk9OKLL4rIxRdf3Ovt888/X0TefffdQZZ2brzxxr4vlpeXjx49WkQmTZpk1lzdxzAkFmNBCADgYolE5oIEj8okIXW0uaKiotfbl1xyifqgra1tWOOmUqnPPvvsS1/6Ut905SOqOU+BDgDgXoGAhMMe3iPLtOjffvttESkuLu799ujMJ3R0dAxr3ObmZhFZvHhxvhN0L10XXac5DwBwvVDIw436TNDp6uoSkaKiooE+b7gHn5999tlJkyYtWrQo9y+pqqrq+6KLe/gclAYAeIM6Oh2JyP79dk9lhPrNGErvJysO5Oyzz879++3du7e+vv7RRx8dO3Zs7l/l4tDTl+oc0pwHAHhDMCiPPCKa5tIfbX0zRjYbZc4JZXfBekmn0+qD6dOn5/jN0un0Pffcc9ddd6nemU/F41wxBgDwDu826jNJaOLEiSLy6aef9no7mUyqD8aPH5/jiPfff/+0adNuv/12k2boQvG4BIOe3EwFAPiX+tHmuUZ9Zino0ksvbW9vP378eK+31UlqEen1nKGBbN682TCMuro6E6foMqo579qdVAAABuTFy8gya0I1NTUi0veKsY8++khEKioqpkyZMuRYjY2Nf/vb3/74xz+aPUlXiUQkFqM5DwDwIC826jNJaO7cuaWlpR9++OF7773X8+2mpiYRWbBgwZADbd++ff369X/60596nZLu6Og4dOiQeRN2NvXsKU4IAQC8KhQSwxBdt3sepskkoaKiottuu01EXnjhhex76XT6lVdeKS8vz16doezevXv16tU98822bdseeOCBurq6cePG9frMW2+99Ytf/KKFfweOQnMeAOBt2Ua9V3xeGVuyZMn27ds1Tfv+978/YcIEEVm/fn1HR8ef//znnvkmnU4vXry4q6vrrbfeevjhh0Xk5ZdfvvPOO0Wk5yWsInLy5EkRmT9/fklJSWH+ZmymmvMe2joFAKAf4bCrG/W9nFGeX7duXTQaveGGG6688sr29vYPPvjgqaeemjFjRq+vKS0t7erqUmmppaVl8JrYddddZ/qkHSoSkYYGuycBAID1EgmpqfFGEjqr2xnXQVRVVbn7yYpqnZCtMQCAT7j8B182eOT6jGkMRtdF02jOAwB8xCuN+lF2T8AT4nGa8wAAf/HKU6dJQnmjOQ8A8Ce1GuTyRj1JKG+RiHt3SQEAGDlPNOpJQvmJxyUQcPsWKQAAIxQMSiDg6j0yklB+YjH2xQAAvpZIiKaJYdg9jxEiCeUhEpFwmAUhAICvqb0R1y4L0aIfKdWcd8bTmAAAsFM0KlOnSijkxtUB1oRGiivGAABQAgFJJFy6LEQSGhG1IeqJp4wDAGACtRqkruB0FZLQiLAgBABAT6590CJJaPhozgMA0Jdq1Lvt8UKcmB4mw5BYjCvGAADoh7qj3jBcdAMVa0LDFIlwxRgAAP0LBCQcdtceGUloOHRddJ1HKQIAMKBQKPPj0iVIQsPBQWkAAAbntsvISEI5U81AmvMAAAxOHZ12SaOeJJSzeJx9MQAAhuaqRj1JKDeRiASDNOcBAMiJ+qHphj0yWvQ5MAzRNJrzAAAMQzQqNTWi6w5fR2BNKAc05wEAGC6X7JGRhIai62IYnBACAGDYgkExDIc36klCQ6E5DwDAyLihUU8SGpRqADp7gxMAAOcKhx3eqOfE9KAiEWlosHsSAAC4mbqMTD1kyHlYExpYJCLhMAtCAADkJRCQYNCxR6dZExqArtOcBwDAHA5u1LMmNIB4nOY8AADmcHCjniTUH02jOQ8AgJnUapDzGvUkof7QnAcAwFxObdSThPqIxzNnuwAAgIlUfcxhe2QkoT5iMfbFAACwRCKROYLiGCShM9GcBwDAOs5r1NOi70E157u77Z4HAADeFY3K1KkSCjlk3YE1oR44KA0AgNUCAUkknHN0miR0mroSJRy2dxYAAHifOjrtjMvISEKnxeMclAYAoBCc9KBFkpCI0JwHAKCw1LKQA/bI/HJiOplMlpWV9f+eYUgsxhVjAAAUlLqj3jDsvdvKs0komUzu2LGjo6MjmUy2tbWpF8tOq6qqmj17duZTIxGuGAMAoNACAQmHJRKRhgb1wpYtWwb6wV1eXj5v3jwrZnFWtzNK41VVVa2traYMpTJQfX29+gdXVlZWXFxcUlLS2dkpIidOnOjs7GxvbxeRysrK6gsvrLzmGprzAADYwDCkpib5hz/sGDu2vr6+pKSkoqIi+4NbRDo7O9UP7mQy2dnZWVlZWV1dXVlZmf93zgYPryWhNWvWHDhwoKKiYsh/TJ2dnQcOHGhtbZ0/Y8a8n/40/28NAACGa8vdd29NpSoqKiZPnqzSz0DUD+729vY5c+bkvz7kwSSUTCY1TUsmk9XV1bl/lfrH2tHRsWzZsgEPEgEAALPZ+4M7Gzw80h1ra2tbsWLFWWedNax/miJSUlJSWVlZXl6+Zs2a7K4kAACwlCk/uLds2ZL/TLyQhJLJ5Jo1a/LZOKysrKyqqlLJ1Ny5AQCAXkz5wT1z5sympqb8VzG8kIQ0Tauurs5zb0sdr16zZo1ZswIAAP3SNK2qqirPH9zqeLWW94OqTU5CqVSqubl579695g47iDVr1gz2rKDhUMk0/3+mAABgIGoHxpT+V0VFRXl5eZ4/uM1MQnV1dd/85jc3bdoUj8fnz5+/Z88eEwfv144dO9ra2oa7xTiImf+/vfuPibp+4Dj+ToF2N8SNz2n+4GZrwvlj/KgVdSxqrjYYdW7W0JbkaKzSmqvJX7ll2g/SOWnWBFkWbGLYGrkBMWPRYuHdoC1gVvNuymyXEHqfzCYnFnz4/vFp92UHot7n87mTz+f5+Ot8D9/vt/f2vfeL9/tz78vLU+vUq0IAABCh3nSj48KdkZERCAS0LNy6JaFdu3bV1tYePXq0urr66NGjTz75ZFlZWV9fn171z8jv9+fl5elYod1ud7lcXq9XxzoBAICqtbXV6XTqWKF6Rtba2hpzDfokoba2ti+++OLFF1/MzMxUS7Zv356amrpjx45r167p0sSMfD6f7h99V9OlvnUCAAAhhM/n0+VcbCpJkmRZjvkzTzokIUVR1AeNS0pK/l/vvHlFRUVDQ0ONjY3am5hRW1ub0+mc/RamGKgV+nw+fasFAMDifD6fQQu33W6PeeHWIQl1dXUNDQ2lpKRENoRU+fn5QoimpibtTcwoFAoZdBei0+nkgAwAAH35/X7jFu6Y72fWIQl1dHQIIVauXBlVvnjxYiHEhQsXBgcHtbcyXSAQMOgN1T2uAgAA4y7ts9lsiTwdU1PY9AegVq9erb4w6LEbWZYNiixa3lAAADAjvW690VeS9irOnTsnhLDZbNFVJ/1XeSgU0t5KnMmyLPbsSXQvAAAwD+O2MOx2+7Vr12JLWjokobGxMSFEcnLyjX7gFk/HXC7X9MIbHfsZ926KyOnY+fMG1Q8AgNXIqakJbH3GjKHSIQnd1Pz582/lx27rWSdJksLhcKw9uon/aq6vN6h+AACsRhJC2rkzHA4btJERDodn2RCanjEi2UiH54Qip2BRFEVRX6xatUp7K9Op9wcYUbNet4ADAIAISZIMumVw9hg0Ox2S0NKlS4UQ169fjyqPxJSFCxdqb2U6Q5+6ugMf6QIAYE4z7jxHyxaGDkkoJydHCHH16tWocvVJaiFE1D1DenG5XMFg0Iiag8HgLAeKAAAgBsYt3FrOiHRIQuvWrRNCTP+KsStXrgghnE7nihUrtLcyndvtNu50zO12G1EzAACWlZWVpX7CS/eag8Ggx+OJ7e/qkISKi4vT0tIuX748PDw8tVy9prm0tFR7EzOSJCkjI0P3dBkIBIhBAADoTpKk3Nxc3RfuYDDodrsT+ZxQcnLy1q1bhRDt7e2RQkVRTp065XA4Nm/erL2JG/F4PLpf2xgMBgsKCvStEwAACCE8Ho/ue0KBQEDLwq3Pd9FXVFQUFBQ0NDT8+eefaklNTU0oFKqurk418v6ArKysjIyM/v5+vSr0er0ZGRl8cAwAACNIkvTEE0/ouHAHAgGNC7c+SUgIcejQoUceeWTjxo27d++uqKj45ptvjh8//vDDD+tV/42Ul5eHw2FdttrU7aXKykrtVQEAgBm53W6bzabLkY4sy6FQSOPCfdfk5KT2rmjncrli/hZZWZbfe+89t9ut5bImWZa9Xm9lZSUbQgAAGEpduPPy8rTcWRMOhzs7O2NeuCPBQ7c9oQSSJGnjxo0+ny/mgBkMBolBAADEh7pw9/f3x7xwy7Lc2dlZXl6ufeGOx7dtxIHb7c7Kyjpw4IAQ4nbflP7+/nA4TAwCACButCzcgUBAPRTTZeE2w+lYhCzLPp+vs7PT6XTe9N0Jh8O///57MBjMyMjg2SAAAOIvgQt3JHiYKgmpAoGA1+sdGBiQJMnpdIopX52hXvKtXuvk9/s9Hk9WVhZbQQAAJJAsy62trerCLUmS3W6/0cItSZLH49Hl2j8zJyGVGjP9fr8sy7Is2+129d1U32WXy/X000/r2BwAANDipgu3lusTpzN/EooiyzJfqgoAwFyhXsBo3NodCR4meWL6pohBAADMIXFbuM3wKXoAAIDYkIQAAIB1kYQAAIB1kYQAAIB1kYQAAIB1kYQAAIB1kYQAAIB1WSUJuVyuRHcB8cNwWwrDbSkMt6XEZ7itkoQAAACmIwkBAADrIgkBAADrIgkBAADrIgkBAADrIgkBAADrIgkBAADrumtycjLRfRCCKyIAAEB8+f1+ceckIQAAgPjjdAwAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFiXJZLQxMRET0/P2bNnE90R6IMBRRS/35/oLkA3jCYURenr6+vu7v7777/j0FxSHNpIrLq6uvr6+oKCgkuXLv31119VVVXZ2dmJ7hRip3FAn3nmmaGhoaklFRUVL730kt7dRJz89NNP1dXVAwMDp0+fTnRfoJWW0WRqm0ZdXV1dXd3o6Kj6x/z8/Hfffffee+81rkWTJ6Fdu3a1tLR8+eWXmZmZQoiDBw+WlZU1NDTcf//9ie4aYqFxQNva2n755ZepJUlJSRs2bDCkrzBYb29vbW1tT0/PxMRESkpKorsDTTSOJlPbNN55551jx44tW7bsoYce+vnnn0OhUG9vb2lpaWNjo8vlMqjRuyYnJw2qOuHa2toqKytfffXV119/XS1RFKWwsDAlJaW9vd1msyW2e7hd2ge0pKTkueeeczgckRKHw5Gfn29Uj2GkUCjkcDg+//zzPXv2pKSksCc0p2kcTaa2OfT19b322mv79u0rLCxUS9T/EkKINWvWnDhxwqB2TbsnpCjKgQMHhBAlJSWRwnnz5hUVFR07dqyxsZFd07lF+4CePHkyPT19y5YtxnYU8aIue8uXL090R6ADLaPJ1DaN5ubm2tra3NzcSMnzzz9/6dKlmpqaX3/9dXBw8L777jOiXdM+Md3V1TU0NJSSkqIeo0SovyU0NTUlqF+IkfYBPXToELvl5pOcnJzoLkA3sY0mU9s0srOzp8Yg1ebNm9UXwWDQoHZNm4Q6OjqEECtXrowqX7x4sRDiwoULg4ODCegWYqVxQL/99ttAILBz584HHnhg586dfDgFMAemtpls2rRpeqHD4UhKShJGbgCbNgmp88HpdEaVr169Wn0RCATi3SdooHFAP/74Y/XF6Ohoc3Pz+vXrd+/eff36dQN6CiB+mNqmNzExMT4+vmTJkum/CevFtM8JnTt3Tggx/SlaNVoKIUKhULz7BA00Dujx48cDgcDw8HBXV1dLS8v4+HhTU9Nvv/125MiR+fPnG9RnAEZjapteT0+PEMLQ58BMuyc0NjYmZj115nRsbtE4oDabLTc3t7i4+IMPPvj+++8fe+wxIYTX6/3www917yqAuGFqm95XX321fPnysrIy45owbRK6KX5dMJlbH9BFixZ98sknTz31lBCivr4+PneYAjAaU9t8zp4929raunfv3rvvvtu4VkybhCKHJlEURVFfrFq1Ko7dgVa6D+j777+/bNmy8fHx3t5erZ0DcMdgapuGoihvvvnmG2+8YfTVUKZNQkuXLhVCTH9uTpZl9cXChQvj3SdooPuA2my2Z599VggRudMdgAkwtU1j3759mZmZ27ZtM7oh0yahnJwcIcTVq1ejytUHb4UQUdfS4A5nxICuWbNGCGHopiuA+GNqm0Bzc/P58+erqqri0JZpk9C6deuEEH19fVHlV65cEUI4nc4VK1YkoFuIlREDqp6sTb/IC8CcxtSe67q6uk6cOPHRRx/FpznTJqHi4uK0tLTLly8PDw9PLfd6vUKI0tLSBPULMTJiQH/88ceioiL13A2AaTC157Tu7u6amprDhw9H7eqFQqGRkREjWjRtEkpOTt66dasQor29PVKoKMqpU6ccDkfk9m7MFbc1oAMDA/v374/MmVAo1NHREQ6Ho37m5MmTb731lvF9B6APprbp/fDDDwcPHqyrq0tNTZ1aPjAw8PLLLy9YsMCIRk17s6IQoqKioru7u6GhYcOGDenp6UKImpqaUCj02WefRb3FmBNucUAVRdmyZcvY2NiZM2c+/fRTIcTevXtbW1uXLFmyY8eOkpKS0dHRlpaWxsbGw4cPL1q0KGH/HuhBXQUnJib+/fdfvoNsrpt9NJnapvfdd99t375dCBH5LnrVP//8I4TweDx2u92Idu+anJw0ot47RDgcfvvtt/v6+h599NFgMHjx4sWqqqrs7OxE9wsxupUBVRTl8ccfv3jx4vr16/fv3y+E6Onp2bZtW+SDJAsWLNi0adMrr7ySlpaWgH8DdNLT0/P11193dXX98ccfQoicnJwHH3ywvLz8nnvuSXTXcNtuZTSZ2ubW29v7wgsvzPIDR44ciUpIejF5ElKNjIycOXPG4XCsXbs20X2BDm46oCMjI6dPny4sLIwcM09MTHi9XkVR0tPT165dO2+eac+FARNjasMIlkhCAAAAMyI+AwAA6/ofWkooI1Uii9QAAAAASUVORK5CYII=\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image4.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image5.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image6.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44491,"title":"Shuffle","description":"Shuffle a vector by breaking it up to segments of |n| elements, and rearranging them in a reversed order.\r\n\r\nFor example, the vector:\r\n\r\n vector = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\r\n\r\nshould be shffuled by segments of |n=3| like so:\r\n\r\n cetvor = [8,9,10,   5,6,7,   2,3,4,   1]\r\n\r\nThe shuffled vector should have the same dimensions as the original one.\r\n\r\n*You must call the functions \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44486 push()\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44490 pop()\u003e.*","description_html":"\u003cp\u003eShuffle a vector by breaking it up to segments of \u003ctt\u003en\u003c/tt\u003e elements, and rearranging them in a reversed order.\u003c/p\u003e\u003cp\u003eFor example, the vector:\u003c/p\u003e\u003cpre\u003e vector = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\u003c/pre\u003e\u003cp\u003eshould be shffuled by segments of \u003ctt\u003en=3\u003c/tt\u003e like so:\u003c/p\u003e\u003cpre\u003e cetvor = [8,9,10,   5,6,7,   2,3,4,   1]\u003c/pre\u003e\u003cp\u003eThe shuffled vector should have the same dimensions as the original one.\u003c/p\u003e\u003cp\u003e\u003cb\u003eYou must call the functions \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44486\"\u003epush()\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44490\"\u003epop()\u003c/a\u003e.\u003c/b\u003e\u003c/p\u003e","function_template":"function cetvor = shuffle(vector, n)\r\n    cetvor = vector;\r\nend\r\n\r\n% You must call the following functions from the shuffle() function\r\n% (copy-paste your solutions)\r\nfunction [v, n] = push(v, x)\r\n    n = [];\r\nend\r\n\r\nfunction [v, w] = pop(v, n)\r\n    w = [];\r\nend","test_suite":"%%\r\nfiletext = fileread('shuffle.m');\r\nassert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 1;\r\nw_correct = 8 : -1 : 1;\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1; 2; 3; 4; 5; 6; 7; 8];\r\nn = 2;\r\nw_correct = [7;8;  5;6;  3;4;  1;2];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 3;\r\nw_correct = [6,7,8,  3,4,5,  1,2];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1; 2; 3; 4; 5; 6; 7; 8];\r\nn = 4;\r\nw_correct = [5;6;7;8;  1;2;3;4];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 5;\r\nw_correct = [4,5,6,7,8,  1,2,3];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1; 2; 3; 4; 5; 6; 7; 8];\r\nn = 6;\r\nw_correct = [3;4;5;6;7;8;  1;2];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 7;\r\nw_correct = [2,3,4,5,6,7,8,  1];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1; 2; 3; 4; 5; 6; 7; 8];\r\nn = 8;\r\nw_correct = [1;2;3;4;5;6;7;8];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 9;\r\nw_correct = [1,2,3,4,5,6,7,8];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":140356,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":333,"test_suite_updated_at":"2018-01-07T22:04:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-01-07T21:23:35.000Z","updated_at":"2026-04-03T03:05:46.000Z","published_at":"2018-01-07T22:04:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eShuffle a vector by breaking it up to segments of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements, and rearranging them in a reversed order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the vector:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ vector = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eshould be shffuled by segments of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e like so:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ cetvor = [8,9,10,   5,6,7,   2,3,4,   1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe shuffled vector should have the same dimensions as the original one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou must call the functions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44486\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epush()\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44490\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epop()\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":52709,"title":"Easy Sequences 19: Length of Prime-sided Rectangle with Maximum Area","description":"A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\r\n                                       \r\nGiven an area limit 'n', find the length (i.e. the longer side if sides are unequal) of the prime-sided rectangle, with the largest area less than or equal to 'n'. \r\nIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u003c 100. No other combination of prime sides will produce an area greater than 95 for area \u003c= 100.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 492px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 318px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                       \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"390\" height=\"312\" style=\"vertical-align: baseline;width: 390px;height: 312px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; text-decoration: underline; text-decoration-line: underline; \"\u003earea limit\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e 'n', find the length\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e (i.e. the longer side if sides are unequal) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eof the prime-sided rectangle, with the largest area less than or equal to 'n'. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u0026lt; 100. No other combination of prime sides will produce an area greater than 95 for area \u0026lt;= 100.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function length = maxPrimeRec(n)\r\n    l \u003e= w; % l is the larger side\r\n    isprime(l) == 1; isprime(w) == 1; % both sides are primes\r\n    l*w \u003c= n; % area should be less than or equal to n\r\n    length = 'l such that l*w is the largest area possible';\r\nend","test_suite":"%%\r\nn = 25;\r\nl_correct = 5;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = 100;\r\nl_correct = 19;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nns = 1000:10000;\r\nls = arrayfun(@(n) maxPrimeRec(n),ns);\r\nys = [sum(ls) ls(7500:7529)];\r\nys_correct = [10870381 2833 2833 2833 2833 773 773 773 4253 181 181 127 127 2837 2837 ... \r\n    2837 2837 2837 2837 2837 4259 1217 1217 1217 4261 4261 4261 4261 4261 4261 4261];\r\nassert(isequal(ys,ys_correct))\r\n%%\r\nn = 1000000;\r\nl_correct = 1321;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = 100000000;\r\nl_correct = 77101;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax);\r\nl_correct = 715827881;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax)*109 - 1000000009;\r\nl_correct = 7574033;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax)*109 + 1000000009;\r\nl_correct = 2156657959;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax-1)*1111;\r\nl_correct = 9920021;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nfiletext = fileread('maxPrimeRec.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2021-09-15T07:53:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-14T21:01:26.000Z","updated_at":"2026-02-24T12:09:19.000Z","published_at":"2021-09-15T07:53:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"312\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"390\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003earea limit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 'n', find the length\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e. the longer side if sides are unequal) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eof the prime-sided rectangle, with the largest area less than or equal to 'n'. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u0026lt; 100. No other combination of prime sides will produce an area greater than 95 for area \u0026lt;= 100.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3098,"title":"Scrabble Scores - 13","description":"This problem integrates components of \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11 Scrabble Scores - 11\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Scrabble Scores - 12\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\r\n\r\nRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\r\n\r\nYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\r\n\r\n * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\r\n\r\nThe center multiplier square will be left blank, since it's already covered by a tile.\r\n\r\nRelated problems:\r\n\r\nPrevious problem: 12 - \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Word score optimization (first word)\u003e.","description_html":"\u003cp\u003eThis problem integrates components of \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11\"\u003eScrabble Scores - 11\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eScrabble Scores - 12\u003c/a\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\u003c/p\u003e\u003cp\u003eRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/p\u003e\u003cp\u003eYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\u003c/p\u003e\u003cpre\u003e * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\u003c/pre\u003e\u003cp\u003eThe center multiplier square will be left blank, since it's already covered by a tile.\u003c/p\u003e\u003cp\u003eRelated problems:\u003c/p\u003e\u003cp\u003ePrevious problem: 12 - \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eWord score optimization (first word)\u003c/a\u003e.\u003c/p\u003e","function_template":"function [score,max_word] = scrabble_scores_13(words,mult,first_word)\r\n\r\nscore = 0;\r\nmax_word = {''};\r\n\r\nend","test_suite":"%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 39;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T'];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 30;\r\nmax_word_corr = {'maltha'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = [' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T '];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 45;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'thinning'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'eodnirl'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'diner','doter','droit','drone','elint','eloin','enrol','ident','idler','indol','inert','inlet','inter','intro','irone','lento','lined','liner','lirot','liter','litre','loden','loner','nerol','niter','nitre','nitro','noted','noter','oiled','oiler','olden','older','oldie','olein','oriel','redon','relit','reoil','riled','ronde','teind','teloi','tenor','tilde','tiled','tiler','tined','tired','toile','toled','tondi','toned','toner','trend','tried','trine','triol','trode','trone','dentil','dinero','dotier','editor','entoil','indole','ironed','linted','linter','loiter','neroli','norite','orient','retold','rident','rioted','rodent','roiled','rondel','tinder','tirled','toiled','toiler','tonier','trined','triode','lentoid','retinol','tendril','trindle'};\r\nwords{2} = {'dhole','diner','drone','eloin','enrol','helio','heron','hider','hired','holed','honed','honer','horde','idler','indol','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','rhino','riled','ronde','dehorn','dinero','heroin','hinder','hoiden','holden','holder','holier','hondle','honied','horned','indole','ironed','neroli','roiled','rondel','hordein','inholder'};\r\nwords{3} = {'diner','drone','eloin','enrol','idler','indie','indol','indri','iodin','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','riled','ronde','dinero','indole','inlier','iodine','ironed','linier','neroli','oilier','roiled','rondel'};\r\nwords{4} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{5} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{6} = {'diner','drone','eloin','enrol','idler','indie','indol','indri','iodin','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','riled','ronde','dinero','indole','inlier','iodine','ironed','linier','neroli','oilier','roiled','rondel'};\r\nwords{7} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{8} = {'deign','diner','dinge','dingo','dirge','dogie','doing','drone','eloin','enrol','gelid','genro','geoid','giron','glide','goner','gored','gride','grind','groin','idler','indol','ingle','irone','liger','lined','liner','lingo','loden','lodge','login','loner','longe','nerol','ogled','ogler','oiled','oiler','olden','older','oldie','olein','oriel','redon','reign','renig','reoil','ridge','riled','ronde','dinero','dinger','dingle','doling','dongle','eloign','engild','engird','eringo','gilder','girdle','girned','glider','golden','golder','ignore','indole','ironed','legion','linger','lodger','logier','longed','longer','neroli','reding','regild','region','ridgel','ringed','roiled','rondel','eroding','glenoid','gloried','godlier','groined','ignored','lording','negroid','redoing'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';'   D       D   ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n\t\tmax_score_corr = 33;\r\n\t\tmax_word_corr = {'godlier'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   '];\r\n\t\tmax_score_corr = 16;\r\n\t\tmax_word_corr = {'indole','iodine','ironed','endrin','linden'};\r\n\tcase 3\r\n\t\tmult = ['T   d     d   T';' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T '];\r\n\t\tmax_score_corr = 45;\r\n\t\tmax_word_corr = {'hordein'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'novels'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'dmvxeao'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'ad','ae','am','an','ax','da','de','do','ed','em','en','ex','ma','me','mo','na','ne','no','od','oe','om','on','ox','ado','and','ane','ave','avo','axe','dam','dan','den','dev','dex','doe','dom','don','emo','end','eon','mad','mae','man','max','med','men','moa','mod','mon','nae','nam','nav','nod','nom','oda','ode','oma','one','ova','van','vex','voe','vox','aeon','amen','axed','axon','dame','damn','dean','demo','deva','dome','dona','done','dove','exam','exon','made','mane','mano','mead','mean','mend','meno','moan','mode','move','moxa','name','nave','nema','node','noma','nome','nova','odea','omen','oven','oxen','vane','vena','vend','admen','amend','anode','axmen','axone','daven','demon','devon','doven','maned','maven','maxed','menad','monad','monde','moved','named','nomad','novae','vaned','venom','daemon','moaned'};\r\nwords{2} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dev','dex','doe','dom','emo','mad','mae','max','med','moa','mod','moo','oda','ode','oma','ova','oxo','vex','voe','vox','axed','dame','demo','deva','dome','doom','dove','exam','made','mead','mode','mood','move','moxa','odea','maxed','mooed','moved'};\r\nwords{3} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dev','dex','doe','dom','emo','mad','mae','max','med','moa','mod','oda','ode','oma','ova','vav','vex','voe','vox','axed','dame','demo','deva','dome','dove','exam','made','mead','mode','move','moxa','odea','maxed','moved'};\r\nwords{4} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dee','dev','dex','doe','dom','eme','emo','eve','mad','mae','max','med','moa','mod','oda','ode','oma','ova','vee','vex','voe','vox','axed','dame','deem','deme','demo','deva','dome','dove','eave','exam','exed','made','mead','meed','mode','move','moxa','odea','adeem','deave','eaved','edema','evade','maxed','moved','vexed','oedema'};\r\nwords{5} = {'ad','ae','al','am','ax','da','de','do','ed','el','em','ex','la','lo','ma','me','mo','od','oe','om','ox','ado','ale','ave','avo','axe','dal','dam','del','dev','dex','doe','dol','dom','eld','elm','emo','lad','lam','lav','lax','lea','led','lev','lex','lox','mad','mae','max','med','mel','moa','mod','mol','oda','ode','old','ole','oma','ova','vex','voe','vox','alme','aloe','axed','axel','axle','dale','dame','deal','demo','deva','dole','dome','dove','exam','lade','lame','lave','lead','leva','levo','load','loam','lode','love','made','male','mead','meal','meld','mode','mola','mold','mole','move','moxa','odea','olde','olea','oval','vale','veal','vela','veld','vole','amole','axled','dolma','domal','laevo','lamed','laved','loved','loxed','maxed','medal','modal','model','moved','voled','voxel','loamed'};\r\nwords{6} = {'ad','ae','am','as','ax','da','de','do','ed','em','es','ex','ma','me','mo','od','oe','om','os','ox','so','ado','ads','ave','avo','axe','dam','das','dev','dex','doe','dom','dos','eds','emo','ems','mad','mae','mas','max','med','moa','mod','mos','oda','ode','ods','oes','oma','oms','ose','ova','sad','sae','sax','sea','sev','sex','sod','som','sox','vas','vex','voe','vox','ados','aves','avos','axed','axes','dame','dams','demo','deva','devs','does','dome','doms','dosa','dose','dove','emos','exam','made','mads','maes','mead','meds','mesa','moas','mode','mods','move','moxa','odas','odea','odes','omas','oxes','sade','same','save','seam','soda','soma','some','vase','voes','dames','demos','devas','domes','doves','exams','maxed','maxes','meads','modes','moved','moves','moxas','oaves','saved','soave','vadose','vamose','vamosed'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';'   D       D   ';' D   t   t   D '];\r\n\t\tmax_score_corr = 37;\r\n\t\tmax_word_corr = {'vox'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  '];\r\n\t\tmax_score_corr = 25;\r\n\t\tmax_word_corr = {'vox'};\r\n\tcase 3\r\n\t\tmult = [' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D'];\r\n\t\tmax_score_corr = 35;\r\n\t\tmax_word_corr = {'voxel'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'zoologist'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aehcmdi'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aced','ache','acid','acme','adze','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cazh','cedi','chad','chai','cham','chem','chez','chia','chid','dace','dame','daze','dice','dime','each','emic','hade','haed','haem','hame','haze','head','hide','hied','iced','idea','idem','mace','mach','made','maid','maze','mead','mech','mica','mice','zeda','ached','aimed','amice','amide','azide','chide','chime','demic','hazed','hemic','maced','mache','maize','mazed','media','medic','miche','chimed','haemic','miched','zaideh'};\r\nwords{2} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{3} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{4} = {'aced','ache','acid','acme','ahed','ahem','aide','alec','alme','amid','amie','cade','cadi','caid','calm','came','cami','cedi','ceil','chad','chai','cham','chem','chia','chid','clad','clam','dace','dahl','dale','dame','deal','deil','deli','dhal','dial','dice','diel','dime','each','elhi','emic','hade','haed','haem','hail','hale','halm','hame','head','heal','heil','held','helm','hide','hied','hila','iced','idea','idem','idle','ilea','lace','lade','laic','laid','lame','lead','lech','lice','lich','lied','lima','lime','mace','mach','made','maid','mail','male','mead','meal','mech','meld','mica','mice','mild','mile','ached','ailed','aimed','alcid','almeh','amice','amide','camel','chela','chide','chiel','child','chile','chime','clade','claim','clime','decal','demic','email','haled','halid','hemal','hemic','ideal','ileac','laced','laich','lamed','leach','limed','maced','mache','macle','maile','malic','medal','media','medic','melic','miche','milch','calmed','chield','childe','chimed','chimla','haemic','hailed','halide','heliac','hiemal','lamedh','macled','mailed','malice','medial','miched','camelid','claimed','decimal','declaim','medical'};\r\nwords{5} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{6} = {'aced','ache','acid','acme','aged','ahed','ahem','aide','amid','amie','cade','cadi','cage','caid','came','cami','cedi','chad','chai','cham','chem','chia','chid','dace','dame','dice','dime','each','egad','emic','gach','gadi','gaed','game','gied','hade','haed','haem','hame','head','hide','hied','iced','idea','idem','mace','mach','made','mage','magi','maid','mead','mech','mega','mica','mice','ached','aimed','amice','amide','cadge','caged','chide','chime','demic','gamed','gamic','hemic','image','maced','mache','magic','media','medic','miche','midge','chimed','degami','gached','haemic','imaged','miched'};\r\nwords{7} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cedi','chad','chai','cham','chem','chia','chid','dace','dame','dice','dime','each','emic','hade','haed','haem','hame','head','hide','hied','iced','idea','idem','imid','mace','mach','made','maid','mead','mech','mica','mice','midi','ached','aimed','amice','amici','amide','chide','chime','demic','hemic','imide','maced','mache','media','medic','medii','miche','amidic','chimed','haemic','miched'};\r\nwords{8} = {'aced','aces','ache','acid','acme','ahed','ahem','ahis','aide','aids','aims','amid','amie','amis','asci','cade','cadi','cads','caid','came','cami','cams','case','cash','cedi','chad','chai','cham','chem','chia','chid','chis','dace','dahs','dais','dame','dams','dash','desi','dice','dies','dime','dims','disc','dish','each','edhs','emic','hade','haed','haem','haes','hame','hams','head','hems','hide','hied','hies','hims','iced','ices','ichs','idea','idem','ides','mace','mach','macs','made','mads','maes','maid','mash','mead','mech','meds','mesa','mesh','mica','mice','mics','mids','mise','sade','sadi','said','same','scad','scam','seam','semi','shad','sham','shea','shed','shim','sice','side','sidh','sima','ached','aches','acids','acmes','aides','aimed','amice','amide','amids','amies','asdic','ashed','aside','cades','cadis','caids','cames','camis','cased','cedis','chads','chais','chams','chase','chasm','chems','chias','chide','chime','daces','dames','dashi','deash','deism','demic','deshi','dices','dimes','disme','emics','hades','haems','hames','heads','hemic','hides','ideas','maced','maces','mache','machs','maids','meads','mechs','media','medic','mesic','micas','miche','sadhe','saice','shade','shame','shied','sidhe','amices','amides','camise','cashed','chaise','chased','chiasm','chides','chimed','chimes','emdash','haemic','maches','mashed','mashie','medias','medics','miched','miches','sachem','samech','schema','shamed','simcha','chamise','chasmed'};\r\nwords{9} = {'aced','ache','acid','acme','adit','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cate','cedi','chad','chai','cham','chat','chem','chia','chid','chit','cite','dace','dame','date','dice','diet','dime','dita','dite','each','eath','echt','edit','emic','emit','etch','etic','hade','haed','haem','haet','hame','hate','head','heat','hide','hied','iced','idea','idem','itch','item','mace','mach','made','maid','mate','math','mead','meat','mech','meta','meth','mica','mice','mite','tace','tach','tame','team','tech','thae','them','tide','tied','time','ached','acted','admit','aimed','aitch','amice','amide','cadet','cheat','chide','chime','cited','death','demic','demit','dicta','ditch','edict','ethic','hated','hemic','maced','mache','match','mated','media','medic','miche','tache','tamed','teach','theca','timed','chimed','dacite','detach','haemic','itched','miched','hematic','matched'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';' d   T   T   d ';'   D       D   ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n\t\tmax_score_corr = 117;\r\n\t\tmax_word_corr = {'haemoid'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T'];\r\n\t\tmax_score_corr = 28;\r\n\t\tmax_word_corr = {'medico'};\r\n\tcase 3\r\n\t\tmult = ['T   d     d   T';' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T ';'T   d     d   T'];\r\n\t\tmax_score_corr = 63;\r\n\t\tmax_word_corr = {'decimal'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2015-03-20T18:02:10.000Z","rescore_all_solutions":false,"group_id":40,"created_at":"2015-03-20T01:53:26.000Z","updated_at":"2026-04-02T20:22:25.000Z","published_at":"2015-03-20T01:53:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem integrates components of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eScrabble Scores - 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eScrabble Scores - 12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ * D: double word\\n * T: triple word\\n * Q: quadruple word\\n * d: double letter\\n * t: triple letter\\n * q: quadruple letter]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe center multiplier square will be left blank, since it's already covered by a tile.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 12 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWord score optimization (first word)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42580,"title":"Conic equation","description":"A conic of revolution (around the |z| axis) can be defined by the equation\r\n\r\n   s^2 – 2*R*z + (k+1)*z^2 = 0\r\n\r\nwhere |s^2=x^2+y^2|, |R| is the vertex radius of curvature, and |k| is the conic constant: |k\u003c-1| for a hyperbola, |k=-1| for a parabola, |-1\u003ck\u003c0| for a tall ellipse, |k=0| for a sphere, and |k\u003e0| for a short ellipse.\r\n\r\nWrite a function |z=conic(s,R,k)| to calculate height |z| as a function of radius |s| for given |R| and |k|.  Choose the branch of the solution that gives |z=s^2/(2*R)+...| for small values of |s|.  This defines a concave surface for |R\u003e0| and a convex surface for |R\u003c0|.  \r\n\r\nThe trick is to get full machine precision for all values of |s| and |R|.  The test suite will require a relative error less than |4*eps|, where |eps| is the machine precision.\r\n\r\nHint (added 2015/09/03): the straightforward solution is \r\n\r\n   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \r\n\r\nbut this does not work if |k=-1|, gives the wrong branch of the solution if |R\u003c0|, and is subject to severe roundoff error if |s^2| is small compared to |R^2|.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\r\n","description_html":"\u003cp\u003eA conic of revolution (around the \u003ctt\u003ez\u003c/tt\u003e axis) can be defined by the equation\u003c/p\u003e\u003cpre\u003e   s^2 – 2*R*z + (k+1)*z^2 = 0\u003c/pre\u003e\u003cp\u003ewhere \u003ctt\u003es^2=x^2+y^2\u003c/tt\u003e, \u003ctt\u003eR\u003c/tt\u003e is the vertex radius of curvature, and \u003ctt\u003ek\u003c/tt\u003e is the conic constant: \u003ctt\u003ek\u0026lt;-1\u003c/tt\u003e for a hyperbola, \u003ctt\u003ek=-1\u003c/tt\u003e for a parabola, \u003ctt\u003e-1\u0026lt;k\u0026lt;0\u003c/tt\u003e for a tall ellipse, \u003ctt\u003ek=0\u003c/tt\u003e for a sphere, and \u003ctt\u003ek\u0026gt;0\u003c/tt\u003e for a short ellipse.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003ez=conic(s,R,k)\u003c/tt\u003e to calculate height \u003ctt\u003ez\u003c/tt\u003e as a function of radius \u003ctt\u003es\u003c/tt\u003e for given \u003ctt\u003eR\u003c/tt\u003e and \u003ctt\u003ek\u003c/tt\u003e.  Choose the branch of the solution that gives \u003ctt\u003ez=s^2/(2*R)+...\u003c/tt\u003e for small values of \u003ctt\u003es\u003c/tt\u003e.  This defines a concave surface for \u003ctt\u003eR\u0026gt;0\u003c/tt\u003e and a convex surface for \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eThe trick is to get full machine precision for all values of \u003ctt\u003es\u003c/tt\u003e and \u003ctt\u003eR\u003c/tt\u003e.  The test suite will require a relative error less than \u003ctt\u003e4*eps\u003c/tt\u003e, where \u003ctt\u003eeps\u003c/tt\u003e is the machine precision.\u003c/p\u003e\u003cp\u003eHint (added 2015/09/03): the straightforward solution is\u003c/p\u003e\u003cpre\u003e   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1), \u003c/pre\u003e\u003cp\u003ebut this does not work if \u003ctt\u003ek=-1\u003c/tt\u003e, gives the wrong branch of the solution if \u003ctt\u003eR\u0026lt;0\u003c/tt\u003e, and is subject to severe roundoff error if \u003ctt\u003es^2\u003c/tt\u003e is small compared to \u003ctt\u003eR^2\u003c/tt\u003e.  It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/p\u003e","function_template":"function z=conic(s,R,k)\r\nz=0;\r\nend","test_suite":"%%\r\nR=5;\r\nk=-1;\r\ns=-5:5;\r\nz=[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=-5;\r\nk=-1;\r\ns=-5:5;\r\nz=-[25 16 9 4 1 0 1 4 9 16 25]/10;\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6;\r\nk=0;\r\ns=0:0.125:2;\r\nz=[0 0.001302224649086391 0.005210595859100573 ...\r\n   0.01173021649825800 0.02086962844930099 ...\r\n   0.03264086885999461 0.04705955010467117 ...\r\n   0.06414496470811713 0.08392021690038396 ...\r\n   0.1064123829368584 0.1316527028472488 ...\r\n   0.1596768068881667 0.1905249806888747 ...\r\n   0.2242424739260392 0.2608798583755018 ...\r\n   0.3004934424110011 0.3431457505076198];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=6800;\r\nk=-2;\r\ns=10.^(-9:9);\r\nz=[7.352941176470588e-23 7.352941176470588e-21 ...\r\n   7.352941176470588e-19 7.352941176470588e-17 ...\r\n   7.352941176470588e-15 7.352941176470588e-13 ...\r\n   7.352941176470548e-11 7.352941176466613e-9 ...\r\n   7.352941176073046e-7 0.00007352941136716365 ...\r\n   0.007352937201052538 0.7352543677216725 ...\r\n   73.13611097583313 5292.973166264779 93430.93334894173 ...\r\n   993223.1197327390 9.993202311999733e6 9.99932002312e7 ...\r\n   9.9999320002312e8];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nR=exp(1);\r\nk=pi;\r\ns=10.^(-7:0);\r\nz=[1.839397205857214e-15 1.839397205857469e-13 ...\r\n   1.839397205882986e-11 1.839397208434684e-09 ...\r\n   1.839397463604480e-07 0.00001839422981299153 ...\r\n   0.001841981926630790 0.2212216213343403];\r\nt=arrayfun(@(x)conic(x,R,k),s);\r\nassert(all(abs(t-z)\u003c=4*eps*abs(z)))\r\n%%\r\nt=fileread('conic.m');\r\nassert(isempty(findstr(t,'roots')))\r\nassert(isempty(findstr(t,'fzero')))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":245,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":37,"created_at":"2015-08-26T21:39:35.000Z","updated_at":"2026-04-08T11:17:23.000Z","published_at":"2015-08-26T22:21:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA conic of revolution (around the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e axis) can be defined by the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   s^2 – 2*R*z + (k+1)*z^2 = 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2=x^2+y^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the vertex radius of curvature, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the conic constant:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026lt;-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a hyperbola,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a parabola,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-1\u0026lt;k\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a tall ellipse,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a sphere, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for a short ellipse.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=conic(s,R,k)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to calculate height\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as a function of radius\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for given\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Choose the branch of the solution that gives\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ez=s^2/(2*R)+...\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for small values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This defines a concave surface for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026gt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and a convex surface for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe trick is to get full machine precision for all values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The test suite will require a relative error less than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4*eps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeps\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the machine precision.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint (added 2015/09/03): the straightforward solution is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   z = (R-sqrt(R^2-(k+1)*s^2))/(k+1),]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut this does not work if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek=-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, gives the wrong branch of the solution if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u0026lt;0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and is subject to severe roundoff error if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is small compared to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR^2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. It is possible, however, to find a mathematically equivalent form of the solution that solves all three problems at once.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44779,"title":"Don't be mean.  Be nice!","description":"For this problem, you will be given a range of single digits R, and a separate number K.  You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\r\n\r\nFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4.  The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\r\n\r\nIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\r\n\r\n* 120\r\n* 210\r\n* 201\r\n* 102\r\n\r\nbut not 012 or 021 for the purposes of this calculation.\r\n\r\nYou can assume that R will always have at least K digits, and there will be no repeating digits in R.","description_html":"\u003cp\u003eFor this problem, you will be given a range of single digits R, and a separate number K.  You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\u003c/p\u003e\u003cp\u003eFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4.  The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\u003c/p\u003e\u003cp\u003eIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\u003c/p\u003e\u003cul\u003e\u003cli\u003e120\u003c/li\u003e\u003cli\u003e210\u003c/li\u003e\u003cli\u003e201\u003c/li\u003e\u003cli\u003e102\u003c/li\u003e\u003c/ul\u003e\u003cp\u003ebut not 012 or 021 for the purposes of this calculation.\u003c/p\u003e\u003cp\u003eYou can assume that R will always have at least K digits, and there will be no repeating digits in R.\u003c/p\u003e","function_template":"function y = dont_be_mean(R,k)\r\n  y = k.^R;\r\nend","test_suite":"%%\r\nR=1:4;k=2;y_correct = 27.5;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=0:8;k=3;y_correct = 493.3125;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=[1 2 4 6 8];k=4;y_correct = 4666.2;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=[2 8 6 7 4 5];k=1;y_correct = 5.33333333333333;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=0:9;\r\ny=0;\r\nfor k=1:8\r\n    y=y+dont_be_mean(R,k);\r\nend\r\ny_correct=61042519.44444444;\r\nassert(abs(y-y_correct)\u003c1e-3)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":68,"created_at":"2018-11-07T18:32:08.000Z","updated_at":"2026-04-09T15:34:44.000Z","published_at":"2018-11-07T18:32:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, you will be given a range of single digits R, and a separate number K. You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4. The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e201\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e102\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut not 012 or 021 for the purposes of this calculation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can assume that R will always have at least K digits, and there will be no repeating digits in R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1187,"title":"Knave in the middle attack","description":"This is a Matlab adaptation of the \u003chttp://en.wikipedia.org/wiki/Knights_and_Knaves Knights and Knaves\u003e logical puzzles, mixed with the famous \u003chttp://en.wikipedia.org/wiki/Man-in-the-middle_attack man-in-the-middle attack\u003e in computer security. \r\n\r\nYou are in an island where all inhabitants are either _Knights_, who always tell the truth, or _Knaves_, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.  \r\n\r\n*Details:*\r\n\r\nYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function _function answer=F(question)_ takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question; _true_ means 'yes' and _false_ means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\r\n\r\n* *A*: Islander's type. A is a logical variable: true for a Knight, false for a Knave\r\n* *X*: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g. _x\u003e1_).\r\n* *F*: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\r\n\r\nThe function handles associated with a Knight and a Knave look, respectively, something like:\r\n\r\n  function answer = Knight(question)\r\n    A = true;\r\n    X = @(x)x\u003e10;\r\n    F = @Knight;\r\n    answer = eval(question);\r\n  end\r\n\r\n  function answer = Knave(question)\r\n    A = false;\r\n    X = @(x)x\u003e10;\r\n    F = @Knave;\r\n    answer = ~eval(question);\r\n  end\r\n\r\nOf course the values of X will be different and unknown to you.\r\n\r\nA few examples:\r\n\r\n Knight('A==true') == true\r\n\r\nThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question. \r\n\r\n Knave('A|X(1)') == true\r\n\r\nThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\r\n\r\n Knave('F(''A'')') == false\r\n\r\nThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\r\n\r\nYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\r\n\r\n your_function(@Knight,str) should return Knave(str)\r\n your_function(@Knave,str) should return Knight(str)\r\n\r\nYour function might query the function handle of the islander with whatever questions it sees fit before responding.\r\n\r\n*Examples:*\r\n\r\n your_function(@Knight,'A==true') == true;\r\n\r\n your_function(@Knave,'A==true') == true; \r\n\r\nThis question asks whether the islander is a Knight; both Knights and Knaves would respond _true_ to this question.\r\n\r\n your_function(@Knight,'F(''A==true'')==true') == false; \r\n\r\n your_function (@Knave,'F(''A==true'')==true') == true; \r\n\r\nThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\r\n\r\n your_function(@Knight,'X(3)~=X(2)') == true\r\n\r\n your_function(@Knave,'X(3)~=X(2)') == false \r\n\r\n(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 914.5px; vertical-align: baseline; perspective-origin: 332px 914.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis is a Matlab adaptation of the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Knights_and_Knaves\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKnights and Knaves\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e logical puzzles, mixed with the famous\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Man-in-the-middle_attack\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eman-in-the-middle attack\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in computer security.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 94.5px; white-space: pre-wrap; perspective-origin: 309px 94.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are in an island where all inhabitants are either\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eKnights\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, who always tell the truth, or\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eKnaves\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eDetails:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 52.5px; white-space: pre-wrap; perspective-origin: 309px 52.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efunction answer=F(question)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e means 'yes' and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efalse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 50px; perspective-origin: 316px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: Islander's type. A is a logical variable: true for a Knight, false for a Knave\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u0026gt;1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function handles associated with a Knight and a Knave look, respectively, something like:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 130px; perspective-origin: 329px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003eanswer = Knight(question)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  A = true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  X = @(x)x\u0026gt;10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  F = @Knight;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  answer = eval(question);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003eanswer = Knave(question)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  A = false;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  X = @(x)x\u0026gt;10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  F = @Knave;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  answer = ~eval(question);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eOf course the values of X will be different and unknown to you.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA few examples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knight(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knave(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A|X(1)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knave(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A'')'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,str) should \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn Knave(str)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,str) should \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn Knight(str)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour function might query the function handle of the islander with whatever questions it sees fit before responding.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight; both Knights and Knaves would respond\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e to this question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A==true'')==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function (@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A==true'')==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; perspective-origin: 309px 31.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'X(3)~=X(2)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'X(3)~=X(2)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 52.5px; white-space: pre-wrap; perspective-origin: 309px 52.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function answer = AnswerGenerator(F,str)\r\n  answer=F(str);\r\nend","test_suite":"%%\r\n% Ask a Knight whether 4 is prime\r\n% (he will respond false; your function should respond true)\r\nA=true; X=@isprime; str='X(4)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knave whether 4 is prime \r\n% (he will respond true; your function should respond false)\r\nA=false; X=@isprime; str='X(4)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% Ask a Knight whether he is a Knight \r\n% (both Knights and Knaves would respond true and so should your function)\r\nA=true; X=@isprime; str='A==true';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knave whether he is a Knight \r\n% (both Knights and Knaves would respond true and so should your function)\r\nA=false; X=@isprime; str='A==true';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knight whether he would respond affirmatively to the question of whether he is a Knight\r\n% (a Knave would respond false to this same question, and so should your function)\r\n% A=true; X=@isprime; str='F(''A==true'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% Ask a Knave whether he would respond affirmatively to the question of whether he is a Knight\r\n% (a Knight would respond true to this same question, and so should your function)\r\n% A=false; X=@isprime; str='F(''A==true'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=true; X=@isprime; str='diff(X(2:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=false; X=@isprime; str='diff(X(2:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=true; X=@isprime; str='A==X(6)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=false; X=@isprime; str='A==X(6)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=true; X=@isprime; str='A\u0026any(X(1:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=false; X=@isprime; str='A\u0026any(X(1:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% A=true; X=@(x)rem(x,2); str='F(''F(''''X(3)'''')'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% A=false; X=@(x)rem(x,2); str='F(''F(''''X(3)'''')'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),true))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":14,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2020-09-29T00:03:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-07T22:12:02.000Z","updated_at":"2026-04-15T04:00:57.000Z","published_at":"2013-01-08T03:23:02.000Z","restored_at":"2017-11-13T15:02:29.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a Matlab adaptation of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Knights_and_Knaves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKnights and Knaves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e logical puzzles, mixed with the famous\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Man-in-the-middle_attack\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eman-in-the-middle attack\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in computer security.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are in an island where all inhabitants are either\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKnights\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, who always tell the truth, or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKnaves\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction answer=F(question)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means 'yes' and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Islander's type. A is a logical variable: true for a Knight, false for a Knave\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function handles associated with a Knight and a Knave look, respectively, something like:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function answer = Knight(question)\\n  A = true;\\n  X = @(x)x\u003e10;\\n  F = @Knight;\\n  answer = eval(question);\\nend\\n\\nfunction answer = Knave(question)\\n  A = false;\\n  X = @(x)x\u003e10;\\n  F = @Knave;\\n  answer = ~eval(question);\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOf course the values of X will be different and unknown to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knight('A==true') == true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knave('A|X(1)') == true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knave('F(''A'')') == false]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,str) should return Knave(str)\\n your_function(@Knave,str) should return Knight(str)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function might query the function handle of the islander with whatever questions it sees fit before responding.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'A==true') == true;\\n\\n your_function(@Knave,'A==true') == true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight; both Knights and Knaves would respond\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to this question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'F(''A==true'')==true') == false; \\n\\n your_function (@Knave,'F(''A==true'')==true') == true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'X(3)~=X(2)') == true\\n\\n your_function(@Knave,'X(3)~=X(2)') == false]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1092,"title":"Decimation","description":"When dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\r\n\r\nThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\r\n\r\nFirst iteration: 1 2 3 4 5 6 7 8 9 10\r\n\r\n1-2-3 4-5-6 7-8-9 10\r\n\r\nPrisoners 3, 6 and 9 will be killed.\r\n\r\nSecond iteration: 1 2 4 5 7 8 10\r\n\r\nBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\r\n\r\nThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\r\n\r\nFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\r\n\r\nFifth iteration:  10-4 10\r\nPrisoner 10 is executed\r\n\r\nSince the sole survivor is prisoner 4, he is released.\r\n\r\nYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\r\n\r\nGood luck!","description_html":"\u003cp\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/p\u003e\u003cp\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\u003c/p\u003e\u003cp\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/p\u003e\u003cp\u003e1-2-3 4-5-6 7-8-9 10\u003c/p\u003e\u003cp\u003ePrisoners 3, 6 and 9 will be killed.\u003c/p\u003e\u003cp\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/p\u003e\u003cp\u003eBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/p\u003e\u003cp\u003eThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/p\u003e\u003cp\u003eFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\u003c/p\u003e\u003cp\u003eFifth iteration:  10-4 10\r\nPrisoner 10 is executed\u003c/p\u003e\u003cp\u003eSince the sole survivor is prisoner 4, he is released.\u003c/p\u003e\u003cp\u003eYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\u003c/p\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function survivor=decimate(num_prisoners,kill_every)\r\nsurvivor=4;\r\nend","test_suite":"%%\r\nassert(isequal(decimate(10,3),4))\r\n%%\r\nassert(isequal(decimate(1024,3),676))\r\n%%\r\nassert(isequal(decimate(2012,50),543))\r\n%%\r\nassert(isequal(decimate(30,5),3))\r\n%%\r\nassert(isequal(decimate(10,10),8))\r\n%%\r\nassert(isequal(decimate(2048,2),1))","published":true,"deleted":false,"likes_count":20,"comments_count":12,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":314,"test_suite_updated_at":"2012-12-04T21:28:04.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2012-12-04T19:47:49.000Z","updated_at":"2026-04-08T14:49:07.000Z","published_at":"2012-12-04T19:53:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn. The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences. Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others. Instead of killing every tenth prisoner, he chooses a number (kill_every). If kill_every=3, he kills every third prisoner. If kill_every=5, he kills every fifth prisoner. He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left. For example, if there are 10 prisoners, and kill_every=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-2-3 4-5-6 7-8-9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrisoners 3, 6 and 9 will be killed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBecause Prisoner 10 was counted during the first iteration, the executions will proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThird iteration: 1 4 5 8 10 8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFourth Iteration: 10-4-5 10 Prisoner 5 is executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFifth iteration: 10-4 10 Prisoner 10 is executed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince the sole survivor is prisoner 4, he is released.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are an unlucky prisoner caught by Carnage Maximum. Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day. Your job is to figure out which prisoner you need to be in order to survive. Write a MATLAB script that takes the values of num_prisoners and kill_every. The output will be survivor, which is the position of the person who survives. If you write your script quickly enough, that person will be you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44345,"title":"MATLAB Counter","description":"Write a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b. \r\n\r\nE.g.,\r\n\r\n  \u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n  \u003e\u003e f()\r\n  ans =\r\n       0\r\n  \u003e\u003e f()\r\n  ans =\r\n       1\r\n  \u003e\u003e f()\r\n  ans =\r\n       2\r\n\r\n\r\n","description_html":"\u003cp\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/p\u003e\u003cp\u003eE.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     0\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     2\r\n\u003c/pre\u003e","function_template":"function y = counter(x,b)\r\n  y = x;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','counter.m')\r\n\r\n%%\r\nf = counter(0,1);\r\nassert(isequal(f(),0))\r\nassert(isequal(f(),1))\r\nassert(isequal(2,f()))\r\nassert(isequal(3,f()))\r\n\r\n%%\r\nf = counter(1,0);\r\nassert(isequal(f(),1))\r\nassert(isequal(f(),1))\r\nassert(isequal(1,f()))\r\nassert(isequal(1,f()))\r\n\r\n%%\r\nf = counter(10,2);\r\nassert(isequal(f(),10))\r\nassert(isequal(f(),12))\r\nassert(isequal(14,f()))\r\nassert(isequal(16,f()))\r\n\r\n%%\r\nf = counter(0,5);\r\ny_correct = [0, 5, 10, 15, 20, 55];\r\nassert(isequal([f() f() f() f() f() f()+f()],y_correct))\r\n\r\n%%\r\nx0 = randi(10);\r\nb = randi(10);\r\nf = counter(x0,b);\r\ny_correct = x0 + (0:1000)*b;\r\nassert(isequal(arrayfun(@(n)f(),0:1000),y_correct))","published":true,"deleted":false,"likes_count":23,"comments_count":9,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":301,"test_suite_updated_at":"2017-10-17T00:19:49.000Z","rescore_all_solutions":false,"group_id":34,"created_at":"2017-09-24T01:58:21.000Z","updated_at":"2026-04-13T19:23:03.000Z","published_at":"2017-10-16T01:45:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\\n\u003e\u003e f()\\nans =\\n     0\\n\u003e\u003e f()\\nans =\\n     1\\n\u003e\u003e f()\\nans =\\n     2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42503,"title":"Generating random matrix with given probability mass function","description":"Inspired by \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities Problem 2356. Simulating the selection of a state with given probabilities\u003e, let's consider a similar yet more useful problem. Write a function\r\n\r\n                             x = rndsampling(m,n,prob)\r\n\r\nto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u003e0) == 1 and sum(prob) == 1.","description_html":"\u003cp\u003eInspired by \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities\"\u003eProblem 2356. Simulating the selection of a state with given probabilities\u003c/a\u003e, let's consider a similar yet more useful problem. Write a function\u003c/p\u003e\u003cpre\u003e                             x = rndsampling(m,n,prob)\u003c/pre\u003e\u003cp\u003eto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u0026gt;0) == 1 and sum(prob) == 1.\u003c/p\u003e","function_template":"function x = rndsampling(m,n,prob);\r\n  x = rand(m,n)\r\nend","test_suite":"%%\r\nrnd = sort(rand(randi([10,20]),1));\r\nprob = vertcat(rnd(1,:),diff(rnd,1,1),1-rnd(end,:));\r\nsz = [1 1e5;1e5 1;1e3 1e2;randi([100 200], 100, 2)];\r\nsz = sz(randi(size(sz,1)),:);\r\nx = rndsampling(sz(1),sz(2),prob);\r\nprob_est = histcounts(x,1:numel(prob)+1,'Normalization','probability').';\r\nerr = mean(abs(prob_est - prob))\r\nassert(err \u003c 0.005 \u0026\u0026 isequal(size(x),sz) \u0026\u0026 all(~isnan(x(:))));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":108,"test_suite_updated_at":"2015-08-13T18:44:59.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-11T19:26:49.000Z","updated_at":"2026-04-16T11:26:02.000Z","published_at":"2015-08-11T19:26:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2356. Simulating the selection of a state with given probabilities\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, let's consider a similar yet more useful problem. Write a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                             x = rndsampling(m,n,prob)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u0026gt;0) == 1 and sum(prob) == 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1288,"title":"Balanced Ternary Numbers: Easy as |, |-, |o","description":"This problem concerns the so-called \u003chttp://en.wikipedia.org/wiki/Balanced_ternary balanced ternary\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1. \r\n\r\nIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \"|\" for one, \"o\" for zero (that's a lower-case O), and \"-\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \"|o-\". Thus\r\n \r\n dec 8  =\u003e bt \"|o-\"\r\n\r\nHere are some more examples.\r\n\r\n dec 3  =\u003e bt \"|o\"\r\n dec 15 =\u003e bt \"|--o\"\r\n dec 52 =\u003e bt \"|-o-|\"\r\n \r\nGiven an integer d, return the string bt. Leading zeros should always be suppressed.","description_html":"\u003cp\u003eThis problem concerns the so-called \u003ca href = \"http://en.wikipedia.org/wiki/Balanced_ternary\"\u003ebalanced ternary\u003c/a\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1.\u003c/p\u003e\u003cp\u003eIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \"|\" for one, \"o\" for zero (that's a lower-case O), and \"-\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \"|o-\". Thus\u003c/p\u003e\u003cpre\u003e dec 8  =\u003e bt \"|o-\"\u003c/pre\u003e\u003cp\u003eHere are some more examples.\u003c/p\u003e\u003cpre\u003e dec 3  =\u003e bt \"|o\"\r\n dec 15 =\u003e bt \"|--o\"\r\n dec 52 =\u003e bt \"|-o-|\"\u003c/pre\u003e\u003cp\u003eGiven an integer d, return the string bt. Leading zeros should always be suppressed.\u003c/p\u003e","function_template":"function bt = balanced_ternary(d)\r\n  bt = 'o';\r\nend","test_suite":"%%\r\nd = 3;\r\nbt_correct = '|o';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 52;\r\nbt_correct = '|-o-|';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 182;\r\nbt_correct = '|-|-|-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 26;\r\nbt_correct = '|oo-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = -5;\r\nbt_correct = '-||';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = -164;\r\nbt_correct = '-|oo-|';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 512;\r\nbt_correct = '|-o|oo-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":74,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-02-21T23:26:14.000Z","updated_at":"2026-04-03T19:20:00.000Z","published_at":"2013-02-21T23:36:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem concerns the so-called\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Balanced_ternary\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ebalanced ternary\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \\\"|\\\" for one, \\\"o\\\" for zero (that's a lower-case O), and \\\"-\\\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \\\"|o-\\\". Thus\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ dec 8  =\u003e bt \\\"|o-\\\"]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere are some more examples.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ dec 3  =\u003e bt \\\"|o\\\"\\n dec 15 =\u003e bt \\\"|--o\\\"\\n dec 52 =\u003e bt \\\"|-o-|\\\"]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer d, return the string bt. Leading zeros should always be suppressed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":81,"title":"Mandelbrot Numbers","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nFor any complex c, we can continue this iteration until either\r\nabs(z(n+1)) \u003e 2 or n == lim, then return the iteration count n.\r\n\r\n* If c = 0   and lim = 3, then z = [0 0 0] and n = 3.\r\n* If c = 1   and lim = 5, then z = [1 2], and n = length(z) or 2.\r\n* If c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\r\n\r\nFor a matrix of complex numbers C, return a corresponding matrix N such\r\nthat each element of N is the iteration count n for each complex number c\r\nin the matrix C, subject to the iteration count limit of lim.\r\n\r\nIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments\r\nwith MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf \r\nChapter 10, Mandelbrot Set (PDF)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 296.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 148.083px; transform-origin: 407px 148.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot Set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is built around a simple iterative equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(1)   = c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(n+1) = z(n)^2 + c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 142.5px 8px; transform-origin: 142.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.5px 8px; transform-origin: 226.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 149.5px 8px; transform-origin: 149.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCleve Moler has a whole chapter on the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in his book \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/moler/exm/chapters.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eExperiments with MATLAB\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = mandelbrot(C,lim)\r\n  N = ones(size(C));\r\nend","test_suite":"%%\r\nC = 0;\r\nlim = 5;\r\nN_correct = 5;\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\nC = [0 0.5; 1 4];\r\nlim = 5;\r\nN_correct = [5 4; 2 1];\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\ni = sqrt(-1);\r\nC = [i 1 -2*i -2];\r\nlim = 10;\r\nN_correct = [10 2 1 10];\r\nassert(isequal(mandelbrot(C,lim),N_correct))","published":true,"deleted":false,"likes_count":17,"comments_count":9,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1778,"test_suite_updated_at":"2012-01-26T03:21:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:28.000Z","updated_at":"2026-04-13T19:34:30.000Z","published_at":"2012-01-18T01:00:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in his book \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/moler/exm/chapters.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExperiments with MATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59516,"title":"Determine aquifer properties: slug test","description":"An important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems 59152, 49473,  and 59147, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity  of the aquifer are determined. \r\nInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement  of water in the well is given as a function of time  by\r\n\r\nwhere  is the initial displacement,  is the radius of the well casing,  is the radius of the well screen,  is the length of the well screen, and  is the effective distance over which the water table returns to its undisturbed level. If the distance  from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness , then \r\n\r\nIf ,\r\n\r\nBouwer and Rice provided the coefficients , , and  in a figure, and Yang and Yeh (2004) fit the curves as functions of :\r\n\r\n\r\n\r\nWrite a function that computes the distance  and determines the hydraulic conductivity  by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1075.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 537.75px; transform-origin: 407px 537.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.358px 8px; transform-origin: 382.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59152\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59152\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/49743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e49473\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59147\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.4667px 8px; transform-origin: 89.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.56667px 8px; transform-origin: 9.56667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer are determined. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.933px 8px; transform-origin: 383.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.075px 8px; transform-origin: 152.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of water in the well is given as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"181\" height=\"42\" alt=\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\" style=\"width: 181px; height: 42px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAACXklEQVRYR+1XOy9FQRB2exoqlYKChNB4hJ5GjYhO4vEDSChFSNB71CIevYRSIvGImoKEhoqGnu+TnWTOOXdf13EjcTaZ7N5z5sx8+83szN5SzR8dpT+Kq6YAFhuZgrF/w9gadtoJGUzt+AW/dyFHkGvzrhnzPGQcUqv0P7A+hmwoXS+BoTl2AUu9xtod5mHIg8X6KJ7vq3djWB94kaQUQoHd4rtW8+0i5lWHIw2MzLZD3n4DWD2MvirDPZ6QbOP9lNE/xTwUC4r6IYzFMqDZnYWPrd8Cphk4hBMCtY00uy2OXHTiDWHsGRYajRUfAzPQ2zS6PCQDleRXSChZAu7V1nwM8PSNGH0fuz9iLJYBzW5FZULQ+kKpGYjN4YZKwxgSyncoSRVn/bpxoJtUYWR+tcXuROu7GOuG4pVS9jFwAl1pXetYsz1VPFzAFmB1xVi+xNzn8fKp3rOosrimBze7DHmEsAc/QXjSM53BBUz3Rx8DZIqMcbBpN5VxJjraFr/pgGTalgtYCAPCiC7CNnZ5YutSoCVddvB8WtNrAxbCgLbja/LS1sodCiEggcUGLKYRhzR53uvmIBlm8ExSJlH3bMB8DGi2dBG2XXPEuQtYIo/LAdNhJABXfyRb5xC5q9nqVwiwBGgNzHU13oNzhkNurdRlsk5ApMELi0z+M4iuYz8CpsOT91qKryuUVsbyBqPt5Zb8eYOUvC1X46RcJFqe73aRJ0C5EmmfUmAz/w2qCczWkvqx+y51sL7JqCYw+iO4JQibtwxepzL/UasNLDg1CmDBVBnFgrGCsVgGYvW/AKlmkikkpPNvAAAAAElFTkSuQmCC\" width=\"19\" height=\"20\" alt=\"H0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.6333px 8px; transform-origin: 83.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the initial displacement, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" alt=\"rc\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1833px 8px; transform-origin: 99.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well casing, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well screen, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"20\" alt=\"Le\" style=\"width: 16px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the length of the well screen, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.475px 8px; transform-origin: 302.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"Lw\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.0416667px 8px; transform-origin: 0.0416667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"305.5\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\" style=\"width: 305.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"20\" alt=\"Lw = h\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.9px; text-align: left; transform-origin: 384px 21.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\" style=\"width: 203px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.525px 8px; transform-origin: 132.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBouwer and Rice provided the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.15px 8px; transform-origin: 206.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMoAAAAoCAYAAAC/6WUhAAAJW0lEQVR4Xu2cW+jlUxTHZ97J7YkHpswDueca0ZBLiSTlnhQNHiQPJjxIHhBK8uASNUmuSVIKhYhcHtzjgRoST27xzvqM3xpr1uy1f3vvc86v85+zf7X6n//57dtv7f1d+7vWXr+zfl2/uga6BkY1sH60RC/QNdA1sK4DpS+CroECDXSgFCipF5lUA2dLb7+LfDJpryOddaAs02wsfiz7ShfXidyz+K6ae/hZaj68wDEeLG0fJ/J8zQg7UGq0tbbLApLXRG5cNmtt1Hq8fP5YZD+R3xao7vuk7YNELintY9WAooqpsialylzicoDkfZGrlhgkqO8xkQ0i50ygS10DRWDZ3YGiVGOTKP5kkT1E3phoIiaY6+IuPpSS74psydSAkkDLrhTZ35X7aKh/74It/V/S/i0ij46M8265f+4wn1HRX+TGqyLsHt8HhdDL1pH+tlddBaDAR88cJoBnXjWgsFBY/AcUwgrj8qspi74uWzBA6A7L/oQIlKiEdlH+OTPO++WzAvl6+cz/GEau20VSfhlU7y2Ro0UiMG1vYHcHil0b/wz/rBJQWPQ/iIxZaasndpbvzBcnyOcpIlBVVEjGRHTsdTNO79f4+9Fz0C/gPMkqwX/uQMlpZ+3fq91NeGJrqaEvh4uUWPhZtKWAvlYaKfUfb5OyUDCub0UOTQyACJrSyMflM9TSXwqorEHoQJllepe/Lpz/mWCBRKNnoV483Jxq94Uq3SFSSg8ZHv7FicM4oVkp/8uWeUHKRI47gHovc79Tr+Vf680j1J3hUmmh1ErTmbXCN8j/Oce6eXCuIhRqWyWglUrTFFEyQO0v+ywRmKiDfggO7Bk9UN9RdtYM/BzLdNTw9YHDX6wNiyZHQaAPt4qcNtQ5TP7+JPKFyAMiU/B8+zSEWjeL1JxJeP9ko9TPOrnRwqr4Xvus8YWs//G39JUKAPgyZ2TmQGlcOIYcUJh4tuDTRU4VgetZC8P9R4YycNmabbNCj3MrOubMq7I8l7VcOLKwek6xl4z2gmFCWAAAzIdap6IzSjtqjCEUiDnlgvefIrJo/wT9cr6T8jGiyVcjwP2UPjWaNRb10vYVVOEOmlMilfcRIe/mJRE6VUDowqCjQ4beSqyPj0S0oiAK9+XaywFFF0jkFOIUEzniSlEZ5fV+e7eOMRz5yUGfU+wu+Cdfi2SjOU5hUCDmiCtyflvnLKr3jdx4SqQmrYY6uu6szhn7RSKXD+uV3QaHf6xtXZchPSu1NhbBbOVYnT9EiCJgOQFOyeQvI1A04oIhiABozxZQvuWy9l6qvvLkqXYSXZAYBg4Ka4ACuNQK1/o2LQDSlJUSI6vt+3Me3y/z84HIyyJvipRSR/QVOvylQLGWUZ2mKQ6hWpQf1Yl2FEs3cjzZRoPsIrLgTwFFrbQH2DyfLdVWLVB00WpbNb5N67O0pKyk6CHGmhwxvUrXtR13Vl+lDXqLOnqS2aq5BdaLgGJ3yxxQrK/it3s9+EoBRWnbsgPF0svanah12tht7xKpiaxZg2XpoaVjrdQ8fO5SoKAIHUjE41uVNVW9CCg21p4Dit05LI2yljilaF2AOeqlgZEjRRmRU8uufrMIOVvni5DHlMvdqt1RSs4l5jlXtSkr2rcN+dqd3RqyWqDrRhD6ZTVAUSRPbRnnNTklQIni8YwhAgr3cmBT6pXi/Jq0SdQH53QsmKDjo95XIl+KRJm2LKgfRUp9lJJziXnNBe3UpqxQx4evLT30vktLuHlmZ9474bkFlVPmMjrzlnLktuycL6LvenBSjCHRmD1Wjjaj03HqEVlkAQCoFFB0cXgrqRY0crprwsMtaSuM6yyRGtqka6MlZYW6Y2krNmqXO2D0a1TnNgxglOwoNrFOY+w1g7CDWkag2EWS27KtE5kyFBoyx4pznsL1uQgZsWMRQdVLCijqQ3laoHWiMasBKIkojZ1LpIwfOwIJlzn6FxlNze4NT8KDimNA8IAvPdsb1VUJUOy7DOqn2MnhoQmrLfpgKrdTldzLnaNY3htFe5R6phaz7ihbGy1sDii6M6SsnT5TaszqO5WEeWsdYR1vDb2xc9SSskJ9G76OWE1JGb9eGM8RIiGwUkBBwVxYQeWRmr5hLQ91AcmFImshVJwDit3pUrF03VXRCwdaPq+IhcZVc7psJysHFB13Dii5XKdssp8MwvP+MWDpqTcL0mcWazbHMXJvgwhnGZ6aqS9RCzLPRiKDZtdoLhHS6h8dZ1mSB4qN4MC1yVU6T0QPbfzW9qe7bztfps9WyZHDbKmVT9XhXXPyvlKhTJ9TxGm4XlAThOtFkYiCzQqUaHFDKXiW3MtQ1kdjnFHkh7VBGvzm4Xn8ItQoFvScF6jIeyObwVM//Aze2y+lRapLS7v4LgKKPw8ao54679lyHig2Pwl6dYWIP9lUKhDdXyaA8DykMPjXRgFLKm1CkyIJv3Lhb2AMtonkXin1kxjpYOydiBSIS3aUCCi5F7c03UMXfu282V1MF5sFD3QW3fl8sdqUFdq+WkRT6nWc6CoKkVsqicEHvJEvxXrGl0y9q7JDJyU+Sq0CV7E8Vgzg3SlyrFEAWcjq2LMjkSCZohy5HUU5d4565ehS63lF6TwqdSMPkORZcgOfFeF5/Y9ZaNkxK1/a96zlinXTgTKrqv97GejBweql3omwPbDzvCPik/QW4czbflvOLEo1Y4McHIbuLfKZCL6CD/DwHcaj9GyndAwt5XS3Tfmcu7TXgdKi4v/rYCFZFKVZuiwUfsxAF662lAOK+hDe2czVST1V8S+OVKpEI4ZjQQCapWxtykrlcIqLV+mjA6VYr8mCegBW8j6O0rPUOx65RT924FiT1wRA3xZpOSSMNKU+lKdTjBsapruKPuMUyZZjs1qthw6UMZXm7/tM1oekuD1TYnvn55KuESGPK/oBOo0m1qawEGwgUFFzhkVffkebRQsayFBHXt/0hGLZY4NF0r+a8de8FrKj3Q6UGhWny9q4faoEURfCy3oWZcvoucNN8qV9ESkVStYfYHhayrIIidQQhq0ByexPu2sLNn2Hu0RDXxHxfhhBiZpfWVnEWJvb7EBpVt1OFbFSvDa9ScSmr3wq/6+FrIX5aCHfCjR17E3DKcbR1EcHSpPaeqVV00AHyqrNeH/eJg10oDSprVdaNQ10oKzajPfnbdJAB0qT2nqlVdNAB8qqzXh/3iYN/Av404xHdxwSBQAAAABJRU5ErkJggg==\" width=\"101\" height=\"20\" alt=\"x = log10(Le/R)\" style=\"width: 101px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"332.5\" height=\"19.5\" alt=\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\" style=\"width: 332.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"342\" height=\"19.5\" alt=\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\" style=\"width: 342px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"351\" height=\"19.5\" alt=\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\" style=\"width: 351px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136px 8px; transform-origin: 136px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.258px 8px; transform-origin: 132.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and determines the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.625px 8px; transform-origin: 83.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 412.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 206.35px; text-align: left; transform-origin: 384px 206.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"455\" height=\"407\" style=\"vertical-align: baseline;width: 455px;height: 407px\" src=\"data:image/png;base64,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\" alt=\"Schematic of the Bouwer-Rice slug test\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h)\r\n%  t = measurement time\r\n%  H = displacement\r\n%  rc = casing radius\r\n%  R = screen radius\r\n%  Le = screen length\r\n%  Lw = distance from undisturbed water table to bottom of well\r\n%  h = initial saturated thickness\r\n  Re = ln(Re/R) = [1.1/ln(Lw/R) + [A+B*ln((h-Lw)/R)]/(Le/R)]^{-1}\r\n  K = rc^2*log(Re/R)*log(H(1)/H)/(2*Le*t);\r\nend","test_suite":"%%\r\nt = 0:2:16;             %  Measurement times (sec)                                                 \r\nrc = 0.05;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 3;                 %  Screen length (m)\r\nLw = 5;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.5 0.645 0.372 0.195 0.13 0.067 0.044 0.023 0.015];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 2.82e-4;\r\nRe_correct = 1.11;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:5:40;             %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 3.5;               %  Screen length (m)\r\nLw = 15;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [0.8 0.404 0.204 0.103 5.21e-2 2.63e-2 1.33e-2 6.72e-3 3.4e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 9.4e-5;\r\nRe_correct = 4.065;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 14;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 0.978 0.562 0.323 0.186 0.107 6.15e-2 3.53e-2 2.03e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 2.179;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 28;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 1.11 0.719 0.467 0.304 0.197 0.128 8.35e-2 5.43e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 5.592;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:60:480;           %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 5;                 %  Screen length (m)\r\nLw = 30;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 30;                 %  Undisturbed saturated thickness (m)\r\nH = [1.3 0.651 0.326 0.163 8.16e-2 4.09e-2 2.05e-2 1.02e-2 5.13e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 7.43e-6;\r\nRe_correct = 5.608;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nfiletext = fileread('BouwerRice.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-30T14:18:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-30T13:54:14.000Z","updated_at":"2026-02-12T15:36:49.000Z","published_at":"2023-12-30T14:04:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59152\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e59152\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/49743\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e49473\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e59147\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer are determined. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of water in the well is given as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH = H_0 \\\\exp\\\\left(-\\\\frac{2 K L_e t}{r_c^2 \\\\ln(R_e/R)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the initial displacement, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well casing, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well screen, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Le\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the length of the well screen, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{A+B\\\\ln((h-L_w)/R)}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw = h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w = h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{C}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBouwer and Rice provided the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = log10(Le/R)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = \\\\log_{10}(L_e/R)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and determines the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"407\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"455\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Schematic of the Bouwer-Rice slug test\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59217,"title":"List lunar triangular numbers without duplication","description":"Triangular numbers—which are the subject of Cody Problems 5, 291, 44289, 44732, 45833, 55680, 55695, and 55705—are the sums of consecutive integers. For example, the 10th triangular number is the sum of the numbers 1 to 10, or 55. \r\nLunar addition, which is the subject of Cody Problem 44785, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\r\nWrite a function to compute the th lunar triangular number without duplicating any terms. For example, the 10th lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11th lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.683px 8px; transform-origin: 192.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangular numbers—which are the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/5\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44289\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44289\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44732\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44732\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45833\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45833\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55680\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55680\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55695\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55695\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55705\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55705\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.2px 8px; transform-origin: 18.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—are the sums of consecutive integers. For example, the 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 186.3px 8px; transform-origin: 186.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangular number is the sum of the numbers 1 to 10, or 55. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118.642px 8px; transform-origin: 118.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLunar addition, which is the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44785\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 44785\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.608px 8px; transform-origin: 199.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.6583px 8px; transform-origin: 98.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 238.45px 8px; transform-origin: 238.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth lunar triangular number without duplicating any terms. For example, the 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.45px 8px; transform-origin: 19.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.042px 8px; transform-origin: 168.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = lunarTriNum(n)\r\n  y = num2str(n);\r\nend","test_suite":"%%\r\ns = char(48:57);\r\nfor n = 0:9\r\n    assert(strcmp(lunarTriNum(n),s(n+1)));\r\nend\r\n\r\n%%\r\nassert(strcmp(lunarTriNum(10),'19'))\r\n\r\n%%\r\nfor k = 1:1000\r\n    n = randi(10000);\r\n    assert(isequal(sum(lunarTriNum(n)-'0'),n))\r\nend\r\n\r\n%%\r\nn = 77;\r\np_correct = 215233605;\r\nassert(isequal(prod(lunarTriNum(n)-'0'),p_correct))\r\n\r\n%%\r\nn = 134;\r\np_correct = 183014339639688;\r\nassert(isequal(prod(lunarTriNum(n)-'0'),p_correct))\r\n\r\n%%\r\nn = 6259;\r\nlen_correct = 696;\r\nassert(isequal(length(lunarTriNum(n)),len_correct))\r\n\r\n%%\r\nn = 5*(10.^(1:7));\r\np = primes(1e8);\r\nx_correct = [267 4103 256889 33082235 4266286911 523279276675 61893416706717];\r\nfor k = 1:length(n)\r\n    a = str2num(reshape(lunarTriNum(n(k)),[],2));\r\n    x(k) = sum(a+p(1:size(a,1))');\r\nend\r\nassert(isequal(x,x_correct))\r\n\r\n%%\r\nfiletext = fileread('lunarTriNum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-11-25T14:58:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-11-25T14:57:46.000Z","updated_at":"2023-11-25T14:58:06.000Z","published_at":"2023-11-25T14:58:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangular numbers—which are the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/291\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44289\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44289\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44732\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44732\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45833\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45833\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55680\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55680\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55695\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55695\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55705\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55705\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—are the sums of consecutive integers. For example, the 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangular number is the sum of the numbers 1 to 10, or 55. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLunar addition, which is the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44785\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 44785\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth lunar triangular number without duplicating any terms. For example, the 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44374,"title":"Tautology","description":"Check if the given expression is always true. For example, the sentence\r\n\r\n  '~(A \u0026 B) == (~A | ~B)'\r\n\r\nis always true.\r\n\r\nCharacters in the input sequences may include *~ \u0026 | == ( )*, whitespace, 0 for false, 1 for true and letters for variables.","description_html":"\u003cp\u003eCheck if the given expression is always true. For example, the sentence\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e'~(A \u0026 B) == (~A | ~B)'\r\n\u003c/pre\u003e\u003cp\u003eis always true.\u003c/p\u003e\u003cp\u003eCharacters in the input sequences may include \u003cb\u003e~ \u0026 | == ( )\u003c/b\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/p\u003e","function_template":"function y = tautology(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = '0';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1\u0026A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A\u0026B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|~A';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '0==0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(A \u0026 B) == (~A | ~B)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(Z \u0026 Y) == (~Y | ~Z)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|~A|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nassert(isequal(tautology('(A|B)|C'),false));\r\n%%\r\nassert(isequal(tautology('(A|B)|(C == C)'),true));\r\n%%\r\nassert(isequal(tautology('(A == B)|(B == C)|(C == A)'),true));\r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(0))))))'),false)); \r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(~0))))))'),true));\r\n% provided by Alfonso:\r\nassert(isequal(tautology('((0\u00261)|~B)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((0\u0026~B)\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)\u0026~A)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((0|~B)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((1\u00260)|B)'),false)); \r\n%%\r\nassert(isequal(tautology('((1\u00261)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('((1|0)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|A)|0)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|~A)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u00261)|~A)|A'),true)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~A)\u0026~B)|~A'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~B)\u00261)|B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|0)\u00261)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|A)\u0026A)|~A'),true)); \r\n%%\r\nassert(isequal(tautology('((B|0)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((B|1)\u0026B)\u0026A'),false)); \r\n%%\r\nassert(isequal(tautology('((B|A)|~A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)\u00260)\u0026B'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|0)'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|~A)|1'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|A)|~B)\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|B)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~B)\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('((~B\u00260)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('(0\u00261)|1\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('(0|~A\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(1|A\u00260)'),true)); \r\n%%\r\nassert(isequal(tautology('(A\u0026A\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('(A\u0026~A|1)'),true)); \r\n%%\r\nassert(isequal(tautology('(A|1)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(A|A)|A|1'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u00261)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u0026~B)\u0026~B\u00260'),false)); \r\n%%\r\nassert(isequal(tautology('(B|~B)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A\u0026B\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|0)|~B\u0026~A'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|1)|1'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|B\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|B)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|~A)|0'),false)); \r\n%%\r\nassert(isequal(tautology('(~B\u00260)\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('1\u0026B|~B|0'),true)); \r\n%%\r\nassert(isequal(tautology('B\u00261\u0026A\u00261'),false)); \r\n%%\r\nassert(isequal(tautology('~A\u00260\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('~B\u00260\u0026~A|B'),false)); \r\n%%\r\nassert(isequal(tautology('~B|1|1|~B'),true)); \r\n%%\r\nassert(isequal(tautology('~B|~B\u00261|1'),true));\r\n%%\r\nassert(isequal(tautology('A==~A'),false));\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":30,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2017-10-31T07:45:16.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-10T23:20:08.000Z","updated_at":"2026-02-03T08:59:32.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck if the given expression is always true. For example, the sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA['~(A \u0026 B) == (~A | ~B)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis always true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCharacters in the input sequences may include\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~ \u0026amp; | == ( )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56423,"title":"French Conundrum","description":"The French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\r\nThe battle-ground is in a form of a 2-D rectangular lattice spanning from (0,0) to (m,n). In order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position (although relative, consider it to be 0,0) to the end point (m,n).\r\nHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\r\n\r\nThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\r\n\r\nGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 285px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 142.5px; transform-origin: 407px 142.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357px 8px; transform-origin: 357px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 228.5px 8px; transform-origin: 228.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe battle-ground is in a form of a 2-D rectangular lattice spanning from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15px 8px; transform-origin: 15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(0,0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(m,n). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(although relative, consider it to be 0,0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the end point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5px 8px; transform-origin: 19.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(m,n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 291px 8px; transform-origin: 291px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357px 8px; transform-origin: 357px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = henridnum(m,n)\r\n  y = f(m,n);\r\nend","test_suite":"%%\r\nfiletext = fileread('henridnum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || ...\r\n          contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nassert(isequal(henridnum(1,1),3))\r\n\r\n%%\r\nassert(isequal(henridnum(1,3),7))\r\n\r\n%%\r\nassert(isequal(henridnum(3,2),(3+2)^2))\r\n\r\n%%\r\nassert(isequal(henridnum(2,8),145))\r\n\r\n%%\r\nassert(isequal(henridnum(5,5),1683))\r\n\r\n%%\r\nfor i=0:9\r\n    assert(isequal(henridnum(i,1),2*i+1))\r\nend\r\n\r\n%%\r\nassert(isequal(henridnum(6,4),1289))\r\n\r\n%%\r\nassert(isequal(henridnum(7,6),19825))\r\n\r\n%%\r\nassert(isequal(henridnum(3,3),(3+3+1)*3*3))\r\n\r\n%%\r\nassert(isequal(henridnum(8,6),40081))\r\n\r\n%%\r\nassert(isequal(henridnum(10,10),8097453))\r\n\r\n%%\r\nassert(isequal(henridnum(5,3),(5*3)^2+3+3))\r\n\r\n%%\r\nassert(isequal(henridnum(3,7),575))\r\n\r\n%%\r\nassert(isequal(henridnum(11,9),7059735))\r\n\r\n%%\r\nassert(isequal(henridnum(4,2),4*2*5+1))\r\n\r\n%%\r\nassert(isequal(henridnum(8,7),108545))\r\n\r\n%%\r\nassert(isequal(henridnum(11,13),224298231))\r\n\r\n%%\r\nassert(isequal(henridnum(12,12),251595969))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2022-10-27T11:34:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-26T17:38:03.000Z","updated_at":"2025-09-19T20:55:15.000Z","published_at":"2022-10-27T11:34:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe battle-ground is in a form of a 2-D rectangular lattice spanning from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(m,n). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eIn order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(although relative, consider it to be 0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e to the end point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(m,n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58019,"title":"Factor a number into Fermi-Dirac primes","description":"Cody Problem 58018 asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, . \r\nWrite a function analogous to factor(n) that factors the number  into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58018\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 58018\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"18\" alt=\"2250 = 2x5x9x25\" style=\"width: 122px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function analogous to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efactor(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that factors the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = factorFD(n)\r\n  y = factor(n).^n;\r\nend","test_suite":"%%\r\nassert(isequal(factorFD(1),1))\r\n\r\n%%\r\np = primes(1000);\r\nfor q = p\r\n    assert(isequal(factorFD(q),q))\r\nend\r\n\r\n%%\r\nassert(isequal(factorFD(56),[2 4 7]))\r\n\r\n%%\r\nassert(isequal(factorFD(64),[4 16]))\r\n\r\n%%\r\nassert(isequal(factorFD(644),[4 7 23]))\r\n\r\n%%\r\nassert(isequal(factorFD(2250),[2 5 9 25]))\r\n\r\n%%\r\nassert(isequal(factorFD(6444),[4 9 179]))\r\n\r\n%%\r\nassert(isequal(factorFD(64444),[4 16111]))\r\n\r\n%%\r\nassert(isequal(factorFD(644444),[4 73 2207]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(5784354),[2 9 211 1523]))\r\n\r\n%%\r\nassert(isequal(factorFD(11739420),[4 5 9 11 49 121]))\r\n\r\n%%\r\nassert(isequal(factorFD(28437991),[17 103 109 149]))\r\n\r\n%%\r\nassert(isequal(factorFD(1106427169),[841 961 1369]))\r\n\r\n%%\r\nassert(isequal(factorFD(753345263125),[13 73 529 625 2401]))\r\n\r\n%%\r\nassert(isequal(factorFD(159360553668481),[14641 83521 130321]))\r\n\r\n%%\r\nassert(isequal(factorFD(2760834326158300),[4 7 25 49 10201 7890481]))\r\n\r\n%%\r\nfiletext = fileread('factorFD.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-28T23:50:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-25T01:29:47.000Z","updated_at":"2025-03-02T18:40:23.000Z","published_at":"2023-04-25T01:29:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58018\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 58018\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2250 = 2x5x9x25\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2250 = 2 \\\\cdot5\\\\cdot9\\\\cdot25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function analogous to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efactor(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that factors the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60406,"title":"Alert a city about a spill","description":"Problem statement\r\nCody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s maximum contaminant level (MCL). As in CP 54750, the spill of mass  will be assumed instantaneous at position  and time  and mixed over the cross section (with area ). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with  \r\n\r\nwhere  is the mean velocity of the river,  is the discharge or volumetric flow rate, and  is a dispersion coefficient, which describes spreading by several mechanisms. \r\nWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position  downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return 'The MCL is not exceeded.' Please note that the MCL is given in mg/L, whereas other variables are given in SI units. \r\nDetails\r\nMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of Seo and Cheong (1998):\r\n\r\nwhere  is the width of the channel (assumed rectangular here),  is the water depth, and  is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\r\n\r\nwhere  is the gravitational acceleration,  is the longitudinal slope of the channel,  is the hydraulic radius, and  is the wetted perimeter. For a rectangular channel, . \r\nIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 690.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345.017px; transform-origin: 407px 345.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 7.79167px; transform-origin: 63.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/54750\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 54750\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 307.167px 7.79167px; transform-origin: 307.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.9px 7.79167px; transform-origin: 129.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (MCL). As in CP 54750, the spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3417px 7.79167px; transform-origin: 23.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assumed instantaneous at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2333px 7.79167px; transform-origin: 34.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and mixed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.79167px; transform-origin: 104.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6083px 7.79167px; transform-origin: 62.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20px; text-align: left; transform-origin: 384px 20px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZkAAABQCAYAAADLNQgGAAAZDklEQVR4Xu2d++t3S1XHj3+AVOZPBnHoAgpGkWkhFSiYURCB2gUlDiSVBUJ3byWhZVeKA3ZDoR/UivKHpHtQkCFmF4yKglPxUBIEVlZ/QK3XOZ93zzrjzN5r9n3vz9qwOM/5fvaeWbNmzazrrHnGI/kkBZICSYGkQFJgJQo8Y6V2s9mkQFIgKZAUSAo8kkImmSApkBRICiQFVqNACpnVSJsNJwWSAkmBpEAKmeSBpEBSICmQFFiNAilkViNtNpwU2I0Cn249v83gNw1+ezcssuOzUOBbDdHPNHjzGginkFmDqtlmUmA/CiBgftfgzwy+fT80sucTUWBVnkkhcyJOSFSTAiMU0GbBay9MaiUFHAU+3/79TIN/NfinCmXgnScMfmVp5SSFTPJhUuA6FMB64flKg3+/zrByJDMo8A327c8afJpr40fs3++uCBsE0R8tLWhSyMyYvfw0KXAgCrCRsKG8xOCvDoRXorIfBb7Kun7c4BU3nuD/33MTOD9n/625U+GhXzb4NoNfWAL1FDJLUDHbSArsSwECtz9v8I03LXRfbOq9oyX/mMGrDdLKmj5DP2yf/pfBjweawLJ9baF0IGh+y+A/DT63MRf08SaDLzP4k0A/g6+kkJlLwfw+KbAvBeTi+H1DAy30iM9VBYziHEM0Lzfpz7KXn9P4ILqhf599/6jBWGIH79WE0f/e+n92Q8gQn/lTg2cNCKIwn6WQCZPqUC+ymZByWD74WaNaIhrN84sG0JAWMZEPRa1rI4O2+tlLbAYrkYmN+P0GX2FQCziv1O0mzTK2zzD4IYMvcj1iJSAA/s6gdF0iZJ5bfIPrinXX4+bEPfrAIGLRlMRAyPyjwecMUOlL7bcPGvyqwSzlJYXMJry4SicwKwzgmbulmZQIsDg+WiyK19j/55mKVaZqtUblJvv+iZvNaojdGla227tum+ja/e3VvuIY6v8LAgIDKwP34dRNXNlgX2NtRC0g8NPaJ/g/di6GTLOvN5jlNkshsxdbLtOvfKdqLcoMaL9eOB11k1qGStdsRZvMf9jwhjTSPUfPRvotB8ZvKdr4dfh71ijZfWPPEnEPhNvbDb7YIOrBYE7eYNCKx3i8UWSxeMasnsGxppAZY4Vj//4Phh6uEj1fbf8Ys0akQfmRRTSvY1Pi/rDDXfI6g6MG+yUEcRuhEV/58UpbNCtLbk7iHq0HqwNrdSj2gpLxowYRt5nmpMdrMZvPUsicl/WlZeD/VQ78GIPLVEYzkXDi+yFGPy+Frov5IhrmyuSRxnx13mLj/rijZURh0zetNGKak6uRtToUE8EiwqUVsWYR9pyD6Ym7zua1FDIrr7QVm5cfGJ8uTMYz5mfVYT3+ixbMM9UnvOLQsukRCki7PLKbEyv7z0c2yCtMtI/HRN1K+qZlhfp465ilqgD9mBcjmpFWmxPFZsZwqc5nCpnzsjkTT1zl9QbkvY8JDGmWHNYj20eWzCTGOS/ZTo+5XB5Yr9FEj60HLYt5zLKu4aW04DKYzbifZ9Aqi7L1GNWfBD7/P2SZePz0TTl/jPGVBu8wkHcC4fHfBv9j0Mo+I1tsSMFEqH2tQWkRIczIKB2L5+hsTVSIPm0uUsjsxZrz+8UXi6B5nwGphjxojrWaVVr0aL6/bgCz6EHYXC21dD51j9uCMsqiG9oeIxGO0UQUNrFvMiDN2W+uii/60igE1o90oJN1KJyjChtWHlAmCLCeP9XgRa5NxsvD2m0JGTwTCIpawoGSA0p3GgLtvY1vajyj+O+YxfRJ36aQ2WMJzu9TJjJM/REDCY2WpiE3GQJIGwBYTNJM5qOfLcyggILM3Yt9Rp+9nypzKqrAoASxgcr/T39y46oUCkIVF++RDp2WRwEilmXEytNhyTH3t+aFqtsvNyj3c+0TKJ+ltYIge6NBND6jOe12r6eQ6V0+x3hfGWJaxGJKsCsZXe9Kq5R/lXePrA0fg9LHwkIb1NGTNVqbXoSa+paNkZIoBKpxCx/R2vYKWzR1Wd+0EgQkGKBVVJGQ+83v51gq7zTAMmo9PRahF6gRYfr/faaQibD98d7xlgnYeZPdM0Dt4JV/N8rEx6PAfWI0WZvcmFxzhIxPsUfQvNVgLC2/HF6k3MsYSTitPxar0DhpK5qEwTe4rlrZYP7MTXR/LhXJsbFN/V0us6hb8Ml+ooOYilR+tzwFlP7oTWnP7BIcSoHEXyyGnmLeLz+CbHEqBeQq61rkUzub8d0cIeM1+W7XzA1nvx6mDiOSiuw9CJH4UyR1WXMctYwY31ZCRhZT17zMETJsWGR7+BpaZCp82AD/qjIlCDSPaQRTGeEev1Omh7dCakKmdqLYa4k9THyPdD7amH28Ihrr2GsMc4QMOPfGJMpxwvsvmDl4DkAOuehKhS2yl9bWrkfTn7mJWkZeyEQE4xyy+ArO4fNPEcKURPhm+wOlImB0AscE4h7cXtLf9U0r22nOQO/9W90b4stCeOEBc37IgIyzMnA4xby/d3ofZfw6W3GGZI05QkYVgNlfjqwI+fMxUTxrsRPPX9rE+VuPwFCctXc/7+VtLwQjltuT7fcg5dMIYfTHDGqF2XzeeDQ7onew9/x+Lf3RCxmC+aSC8pR+317z/p7pfLSxT3JV7DSIMjGlBw2fmMJ3XUHmno5mvuvXXGSfi7jKNMe9iR0IdbLFwtbFjLErLhO2tKJCxgsO/HHfYTDkApMmM+Uw1ozxX/5Tf97F1yryGpDKzJSaRvlOpEDe5Ql6ogF2L+4dxyYtP6zt3nAl8+p7bwqszn4dNTnFZ5ZFhIzc10MWiua4K+Zh9Gqdu1mDBaQEhHGMCJlSwETuFpjKZGsQ5UptttIffbCU8daY3methBnkSsQ78VgmuSl2HK/iR2Ft13CVAiXLpYzLKCU3sv9sMXQfI8OzM1QJWetz6MiAb0/KOcr6WGxIvNFD6zn0kQUXtrbGhEx5cC9aUloEO6qpO4fIe37buqDKM2hr8qdUit1zrNn3Qwp4JeIsawp+GyruyOZIfPefDT5m8AEDfzeKPy9DbT4UoynpzGvyUemm/knrrEwWYA+lTAxHB4b2Tx/jIR71PQYkUI0dltR3PTGcOTTp5sUhIVNmT/SarTrFO2dA+e1DCkiQtJIppPnV5skLIVrsncszz4O/AZQN7Q8MvKuXRVq7ZZR3qaZALSn/8Pda6XoWHw9xSjZQNhRuHlU7cw4T+s1sTDE8ylxJQW0JRT8mcC5d617Brf1+pHGq1hgKHrzxwOBTDIiNcpA0UgqnPB80Vn1Z48fTRCWPWjmpNWjk5ULIHTrEsD4TKbPE1piueJu+KiuMXLsPQrXMyrsn2Px++sbs6jHiQ45jd8w3VY6ExYpQIQlCGZEUFfUH/Hy8itF414M/ZV/Snd++zgBNm7bZKEnjZ+GrnpWoM8edIVdnNIvpCDOiQp6t0iXQjt84kf54MR/gz/dvM4D3a78fYYzCAVxfZvDlN3z19z+0f3CEI6JgQA9uyuSJjleusq3PTUmhDcXcW0Km1HxDjS0w6/Rbao5TmiWFt+dK0il9bPVNiyalRo1GHtXShfuV6OTnQy4Ez7c6nIpmieB5hYEvONgK5LbiYJqXV1k7umUUIYAwe4sBLqAXu40D/KauIyl8ZxIyjFeB/Kibfas1dZV+sH5eahC5iXPJMatqSEhxagmZ0pTd6vBXGcCeSpipi3lqf/ndcSjA5o/lXSuk6C2WWvKD4lZYi1yJgKB4wmDo5kHPszW3iP+ddqdk9QmvM1qgCEg0+sjNjcfhouNjguVDXTf4tFWdea1RSOkJJRC1hIx3lW15+GspS4bFvjXh15rQbLePAnIt1VwIPkuLDb8svOj9zfDQJwxQsNAUWyn7Xoi0lBufoTnFtSH3REhz7CPX6m/LgvxO6+kq3oXViTbSgWj6U/beHldbd1nWLSHjD+1lPGZvlsr+eyigswZo/cRHykd+b/5ey8jpteIjQsZbUFOskSWEzBIKXCvpYWx+FG8YuhNlrI38/SEFUFr+eCcBAxZSmkLu24iQyXLwyd5noYCPJcK3D0YQrwVlfVkTrHgyhIYCtxEh4y2okIvB4e2/nZMVuIQruhd3T36dcxk7yH0WXtsLT5SgvzHwiStb49KV7ZhCZuvpyf7WpIDfSOecG+g5uBoRMoxZ1kjvRu3bD6WMNgi8hCWz9+a2Ju9k23EKLCJk5HKg2y3dZUssBHC+atZUnA3u802/IU+JfUA1xWXge2WNDW3uvUKmN66ylJC5T47IUa9BgUWEjA9UjpVMKAcx5xDmEiY9+GR22Rqsdfw2feA+4uYl1bkMnJLJBXDS+qO3IQ+tgYiQ8W68XpdXCpnj8929YbiIkCk3+6iZzqJ9u8HUvPilLJlodhnBs+feG4dcYLwE9EkFrj3K4VcacivLkDMcnPR/s2uExfOGW9tkk0Uq7UaEjAL/vQobqJ1FyORaOufC+jxD+986UV9EyNCnt2ZwHQylcfI+HXOfzFQB0znORV7PhbEIGTdvZEjI+AVQO3QJsqon5c+syArybjafBMB3tThPRMjMqUqeQmZz9rqrDncVMlDa3+3Qum9b1gtxnFcb5C2Y2/Po0SrUbk+Bhz36k/36q88008V6pdsKFxm8W56e9pt8Tdnyv9eEmqoPhNI9K4Q7i5DZc86z720psJglI7QlRDiUxoMbgsKBLGYCoyy8vQ4FbUva4/YmK7K8pOy4GK+LGbz5XoOXV7opL9xTjazX2bu1oLxPIaY5hIUvv16e+KdPndH5Qvs3dc1o9903IdY78hQyvRTL99emwOJCRggTL3mOAfWYeEhn/HuDSPG3tQd9z+2rEOFvGBHQzu/hGXKX+fHjAvsSAyri8s3fGpSnzlkw/vHxvFaMkLZUgr10l1E/jmKJ9LlEBeYUMvfA0eca42pC5lxkuB9sVYTwZ2zIP3gnw44KmS3IEYnJzMEjhcwc6uW3a1AghcwaVD1wm8TC3mKwRw2jA5NlM9TWFjIMpKu0+mYjP2dHWLe4NMdK8DOv8trURuqt2dIa9u9PdZMembo6rByqa3mWC5COTPA9cVO8LGMx+83ClkKm9yDnflQ5Zs9yLXPXT6QiBO9/l8Gb3HBapYb8zZbErYcqdx+TOnGsFimQGe8u39yTAmnF7En9p/reQsh03d+xP0kOi4HPlo0ImXJ++f/WtSc68tFKmz8sUSYglkJmAtHO+AmaE4z9rDMifyGcvX+aumRrFIDsur/jQrRdcijldc5RIeO/a6Wh+6rE93CMo+t+o3SXTWNjGO/DBnveWYMV84sGvZdBgTv+5DVjOAhATtO3HhVaHKrw4H3e02Zp3a/AnVRlrg8uHy7pWtIX36U5rjvsU7aug7a4G3XVQ1TI+Lu1SnelzqcpTT2yFoln8PhKE2cjatfVEylk+qdX7pEp94L091b/QlZM7y2L0rp7KwFPwZtNGA3Pn1VpafplrbzX23d7ljKfMt41v9G8hQKtayJywrZ1OJebUn/H4IO3MUSFjL9by5fXQnC9ywD32WuC/Kq4zdTirUcgvz83Fio3lkKmf9pkKm6xUbewm2LF+OKRW+FelnipJSj4E/q164v7Z+h6X/igcq7ZvvnFcniBAW6s53UKGX/ZnL86Wy60nlp0fi082/A4a2UUH4MMCepk2D6G9f7ZvbRKJvkDBj1WTFmDaysh4wOtrdP0uCOoHLGnZdjHBdu/nWdlptFcQkLB+t4NsrxXiHjbOw1wj0WqfIM1CsJ333ic/2ffwM3NM5ZGPW3U637VrfCkkIlPiE9/1Fd7aCRsyvj8I/5f4clmr9gB7quthEzL1QBeU9wNWJFvNbhHV5poeWZXS3y1zX9T65USQIo/9goZeS3ABqHCLakk2rzRQBUfhjBVzJHqD0qDxlpn/fL0rOH5FFmmBQnecC2+FDJxwhM3eKEBOfaq4xbySca7GH1zihWj+A3WgmIkWwgZv6C9q4FBomG+x4DU3LHrjUUUxW1aKaSjxDv5C10ZPScf6xLoo4x9wgD+19MjZMqadWojciV3ib93u229ZyxBS9+GEiHCnocUMrEpUDwDBuF0vYLZW2uVTPBfGEQzU9CkKGCqwOSWqbDe1SCtxxejjAo6n8Gz5S2tMc7Y7q1uDXI71A7Xk0otldeO9AiZ8nAlCpGUy/AGe6OM5q5Utg5HuABCsqjDl++lkAlQ1V7xWlHkIqtIq1oI0dP6WiA9mrxuecRlwNMrZMZKa2ictXRj72rgplJSvpWNE3E3IFxeafAOA6xHHrka6A9/9lmDpxH+KN/x2nCu2zYFvUJYFkPtETI+4xFX2fsMlJmGsMAzEC0OTKIO6zaqWE3hjy2+8clD4VBBMuv41Hh3E0zlNZywX9J147V5/hy1hhAQ9C+BMYY5wvBVBv6yuaiQYUN7/LYwxvrh9zIIWroa0PwopY82+JhBufhrfUjAqVy++nlg/6C68ZrnfCJj3vqd7tTRrRE8QH/KVPw1w6UW7+gRMhIMfo36MzNRgeGv3j77tfBKfOryKKSQGV4ZysqCoeSi8ozam2GmA3xo52jzZKlEJqzXitH7ZYphRMhIiCJAsbLQwBgni47nRQZYFvyuhyu3veDwWren8BShfCVXw9x9WNl6ve6auf2e5Xt4BWWGumG159Hb7/ymO3/4d5nl5TV2fpf3oPx7JIXXK6WR949Ma/Ffl7BMITM8pbrzvSzd4rOmwmajdYXQkounJy0V050nYsVIMP6EvV9mwIwJGXD6JQP5ssVUPliJNcIzlEJdXt2Na0FP2Jd7+0ButykC6sgLdgpu2rB6lZspfZ3xG29p9OBfbv5DRxVK3iYZaOjxNc2irvEe3Ld611vSPS77R1LItKdIZm5NantTek62SKRciPCITqzSlctrhBnpmJBBU/uYAYJQ/eJ/lpDVJjfmKihdDZSYUTmPiOWmWbmSq2GJzWDyQl+i8xO0AX8OlTN61H7H0uHxV3KXJYD8+a7SalQyjeKEY0qTiptGz9Uclcxa+z3r98mxpJBpTymMRnptzfTWPfF8HY2p1HrypvRQdVe+jVgxih+1rIwxIeNxlJvKLw4tvqExe8FAe4yLQP0TBlqYUXP7Sq6GpTYPacZZ9r+fotGYjPdU1IRIWcmizGITZt69pjXD3/asedhPtae+iKz9atspZOok9/XJ2CDL56X2B6Uxz/WPS+uvaTrasCO+XGlY1Gj6ywYnSTiijRAc5WkF0aWByVLzWvSQi7Dlaij/3lqYHnVtqN6amrpIrvKdeDNdZv0zGhEy/h16qPF6eTC7pTR5nkfZeqYBFn3Ny9A/mu2+0NqflIKdQqY+UWz8bMT+IJd/c26GWaut0pphk0V4RJiyXBxRFqy5vjS+Wr2msdiIdzWUgtO70SLCeUgAR8d3xfdElzFXzRXHPmdMESHjz3cNuYb8e62UZq0F2nmtwfsNIsrVnDGu8a2E5SSXXwqZT54SEXTIepiTYVb26LUi7wKRFRON+QyVzVefsmR8/SSV3fd41dxqCsCPuWlkAdFeuQmWBQeHzhrUXA1rLKAztukzACMKyBnHuAbOY0KG36kLKLcuwuMlBqV7yx8QFp4oX6wN/65PRGDNPWYQSd9fY+xz2pRSE40LP62vFDJPJ702fFxOLSuGL8pzID0ZZrXJlo/XWw49VkyUgSIxGb8QJST8hu//hsvQn0eIuBqiZw1KVwNnhM7qz47OT897sxZ+T0cXetcrYmWwfyhpwLuUx5IL/LvwK2vkzIeHpdBMsmLgnRQyT19BMoEjMZCh4o+969ILLfy75O1/3CBqxUT7GxMyShxAk/M+f+8eJID5EQPcbGWxSh8QbbkaSkHUorVcDcIDoUOhwTMWFYzOT897sxd/T2f57t1SYLYyk0LmIe9IW4+m6Hm3UDRbaohTfT49pcBJLljaFTIkZMozBt7V5YWHxlCLzfhSMkMxF/9ei96iL+38tcFjK9Dj7DuH5mxpZeTsdEn8l6GAFJkxF/lgbylkniKP98VGqqyW2jgbJaf3o7WMapNSpv6usXEMCRkflC9N4/Kkc+2ypvIOdWjiS9pozIwTd6SKDfJ3+vsBA1+LzFuKrbaWWUrnbUXzMpaMcd4RJuZ7UUCHuul/VrJCCpmnsrcoxFg+H7I/lEG6seB67ZseJvHZKGMniXva1bvyJ9eC/YztZQb/YlC7rwXB+mKDWsozlk7r8TQZeo/v/bskCTy/0d+UsV/1G1mZc85rXZU2Oa7pFFDoYLaym0Jm+iSs8aUspExNXYO6120T9yOWYU9l4OtSI0c2lwL+nGD0WpFmnylk5k7H8t9nBtXyNL16izqIS0LG0nG8q9Mux/d0CshNRqbrIt6UFDLJYkmBa1BgUe3zGiTJUUyggMppDRXA7Wo2hUwXufLlpMChKaBsoIzPHHqaDoscGa7wUO0A6mSkU8hMJl1+mBQ4JAUkaDKud8jpOSxSOiO3qIBhtClkDjvniVhSYDIFVtswJmOUHx6ZAqvySwqZI0994pYUmE4BkgF45pzdmt57fnkmCsArlL7x59QWwz+FzGKkzIaSAkmBpEBSoKRACpnkiaRAUiApkBRYjQL/Bz3CXatp2ptEAAAAAElFTkSuQmCC\" width=\"204.5\" height=\"40\" alt=\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\" style=\"width: 204.5px; height: 40px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61.5\" height=\"18.5\" alt=\"U = Q/A\" style=\"width: 61.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.892px 7.79167px; transform-origin: 101.892px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.858px 7.79167px; transform-origin: 138.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the discharge or volumetric flow rate, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.625px 7.79167px; transform-origin: 48.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.758px 7.79167px; transform-origin: 376.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 218.967px 7.79167px; transform-origin: 218.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.95px 7.79167px; transform-origin: 103.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 103.95px 8.25px; transform-origin: 103.95px 8.25px; \"\u003e'The MCL is not exceeded.' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.242px 7.79167px; transform-origin: 132.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDetails\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 322.725px 7.79167px; transform-origin: 322.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eSeo and Cheong (1998)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.1333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.0667px; text-align: left; transform-origin: 384px 22.0667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"44\" alt=\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\" style=\"width: 190.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.9083px; text-align: left; transform-origin: 384px 31.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.65px 7.79167px; transform-origin: 174.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the channel (assumed rectangular here), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 7.79167px; transform-origin: 74.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"u*\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.6083px 7.79167px; transform-origin: 86.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"21\" alt=\"u* = sqrt(gRS0)\" style=\"width: 90px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"19.5\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 7.79167px; transform-origin: 101.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gravitational acceleration, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.483px 7.79167px; transform-origin: 124.483px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18.5\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 7.79167px; transform-origin: 50.5667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 159.858px 7.79167px; transform-origin: 159.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter. For a rectangular channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"78\" height=\"18\" alt=\"P = B + 2H\" style=\"width: 78px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.00833px 7.79167px; transform-origin: 1.00833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = spillAlert(x,t0,M,Q,B,H,S0,MCL)\r\n% See the tests for the definitions of the variables and note that the MCL is given in mg/L.\r\n  t = datetime(x*B*H/Q);\r\nend","test_suite":"%% Benzene\r\nx = 80000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 26000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.005;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 08 05; 2018 05 28 05 06 05])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Chlorobenzene\r\nx = 79500;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 34000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.1;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 43 39; 2018 05 28 03 41 07])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Atrazine\r\nx = 14300;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2020,7,3,16,35,0);    %  Datetime for spill\r\nM = 5600;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 32;                             %  Width of channel (m)\r\nH = 0.4;                            %  Depth of channel (m)\r\nS0 = 6e-4;                          %  Longitudinal slope of channel\r\nMCL = 0.003;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2020 07 04 00 51 03; 2020 07 04 14 00 39])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Dalapon\r\nx = 4200;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2019,6,13,14,23,0);   %  Datetime for spill\r\nM = 3000;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 15;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.2;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2019 06 13 15 47 17; 2019 06 13 19 39 06])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 2\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 80;                             %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 3\r\nx = 94000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 37;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Nitrate \r\nx = 1600;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2024,4,30,15,20,00);  %  Datetime for spill\r\nM = 140;                            %  Mass of spill (kg)\r\nQ = 14;                             %  Discharge (m3/s)\r\nB = 14;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 5e-4;                          %  Longitudinal slope of channel\r\nMCL = 10;                           %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2024 4 30 15 32 22; 2024 4 30 15 38 03])';\r\nassert(isequal(t,t_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-28T15:13:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-27T17:17:23.000Z","updated_at":"2026-01-25T17:02:57.000Z","published_at":"2024-05-27T17:22:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/54750\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 54750\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MCL). As in CP 54750, the spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will be assumed instantaneous at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and mixed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the discharge or volumetric flow rate, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'The MCL is not exceeded.' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSeo and Cheong (1998)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = 5.915u_*H\\\\left(\\\\frac{B}{H}\\\\right)^{\\\\!\\\\!0.62}\\\\left(\\\\frac{U}{u_*}\\\\right)^{\\\\!\\\\!1.428}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the channel (assumed rectangular here), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u*\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u* = sqrt(gRS0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_* = (g R S_0)^{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\,\\\\rm{m/s^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gravitational acceleration, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter. For a rectangular channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P = B + 2H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = B + 2H\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46636,"title":"Montgomery Multiplication","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMultiply all elements of an input matrix (A) modulo N, given all elements are less than R (2^number of bits). Where gcd(R,N)=1 and N\u0026lt;R. Output the final result, P (in normal form) and all intermediate products (p) in Montgomery form \u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; \"\u003e(\u003c/span\u003e\u003cspan style=\"\"\u003efirst product is just first element of matrix (A)*R modulo N\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; \"\u003e)\u003c/span\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [P,p] = montgomeryMult(a,R,N)\r\n  P=N-1;\r\n  p=mod(a,N);\r\nend","test_suite":"%%\r\nR=2^16;\r\nN=3329;\r\nY=2050;\r\ny =[    1263         470        2922         960         982         369        2562        2142        1318         744];\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44576       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51731       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22389\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n%%\r\nN=3347;\r\nR=2^16;\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44596       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51771       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22389\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\nY=1870;\r\ny=[130,1496,2440,2533,1292,1876,783,751,107,3006];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n%%\r\nR=2^16;\r\nN=3967;\r\nY=3799;\r\ny=[788,2020,2960,1688,2874,3752,1280,2265,1542,1371];\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44596       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51771       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22999\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-30T21:17:47.000Z","updated_at":"2025-10-12T15:14:20.000Z","published_at":"2020-09-30T21:17:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMultiply all elements of an input matrix (A) modulo N, given all elements are less than R (2^number of bits). Where gcd(R,N)=1 and N\u0026lt;R. Output the final result, P (in normal form) and all intermediate products (p) in Montgomery form (first product is just first element of matrix (A)*R modulo N).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44793,"title":"Project Euler 249: Prime Subset Sums","description":"Inspired by Problem 249 of Project Euler.\r\n\u003chttps://projecteuler.net/problem=249\u003e\r\n\r\nLet S = {2, 3, 5, ...} be the set of prime numbers less than N.\r\n\r\nFind the number of subsets of S, the sum of whose elements is a prime number.\r\nEnter the rightmost 16 digits as your answer.\r\nThe answer must be a uint64 integer.","description_html":"\u003cp\u003eInspired by Problem 249 of Project Euler. \u003ca href = \"https://projecteuler.net/problem=249\"\u003ehttps://projecteuler.net/problem=249\u003c/a\u003e\u003c/p\u003e\u003cp\u003eLet S = {2, 3, 5, ...} be the set of prime numbers less than N.\u003c/p\u003e\u003cp\u003eFind the number of subsets of S, the sum of whose elements is a prime number.\r\nEnter the rightmost 16 digits as your answer.\r\nThe answer must be a uint64 integer.\u003c/p\u003e","function_template":"function num = euler249(N)\r\n  num = uint64(7) % answer for N = 10\r\nend","test_suite":"%%\r\ntic;\r\nSUM = euler249(10)\r\ntoc;\r\nassert(isequal(SUM, uint64(7)))\r\n\r\n%%\r\ntic;\r\nSUM = euler249(100)\r\ntoc;\r\nassert(isequal(SUM, uint64(5253640)))\r\n\r\n%%\r\ntic;\r\nSUM = euler249(1000)\r\ntoc;\r\nassert(isequal(SUM, uint64(5725053962252706)))\r\n%%\r\ntic;\r\nSUM = euler249(2000)\r\ntoc;\r\nassert(isequal(SUM, uint64(9536598422264105)))\r\n%%\r\ntic;\r\nSUM = euler249(4900)\r\ntoc;\r\nassert(isequal(SUM, uint64(2455225028344813)))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":8269,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-11-22T00:50:24.000Z","updated_at":"2025-12-15T21:24:15.000Z","published_at":"2018-11-22T00:50:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by Problem 249 of Project Euler.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://projecteuler.net/problem=249\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://projecteuler.net/problem=249\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S = {2, 3, 5, ...} be the set of prime numbers less than N.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of subsets of S, the sum of whose elements is a prime number. Enter the rightmost 16 digits as your answer. The answer must be a uint64 integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2266,"title":"2048 tile game","description":"The popular 2048 game has been implemented here:\r\n\r\nhttp://gabrielecirulli.github.io/2048/\r\n\r\nGiven the board like this:\r\n\r\n  [2 4 8 0\r\n   4 0 0 0\r\n   2 0 0 0\r\n   2 0 4 0]\r\n\r\nYou give the direction\r\n\r\n1 (left)\r\n2 (up)\r\n3 (right)\r\n4 (down)\r\n\r\nThe system here will keep calling your solver.  Score for each board is the biggest tile achieved.  The Cody score is the maximum board score plus the average score across all 200 boards.","description_html":"\u003cp\u003eThe popular 2048 game has been implemented here:\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://gabrielecirulli.github.io/2048/\"\u003ehttp://gabrielecirulli.github.io/2048/\u003c/a\u003e\u003c/p\u003e\u003cp\u003eGiven the board like this:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[2 4 8 0\r\n 4 0 0 0\r\n 2 0 0 0\r\n 2 0 4 0]\r\n\u003c/pre\u003e\u003cp\u003eYou give the direction\u003c/p\u003e\u003cp\u003e1 (left)\r\n2 (up)\r\n3 (right)\r\n4 (down)\u003c/p\u003e\u003cp\u003eThe system here will keep calling your solver.  Score for each board is the biggest tile achieved.  The Cody score is the maximum board score plus the average score across all 200 boards.\u003c/p\u003e","function_template":"function direction = getMove(board)\r\n  direction = 1;\r\nend","test_suite":"%%\r\nfh=fopen('main.m','wt');\r\nfprintf(fh, '%s \\n', 'function out = main(n)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'result = 0;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'for i = 1:n    ');\r\nfprintf(fh, '%s \\n', '    board = zeros(4);');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', '    %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    direction = 1;');\r\nfprintf(fh, '%s \\n', '    while (direction ~= 0)');\r\nfprintf(fh, '%s \\n', '        %pause(0.1)');\r\nfprintf(fh, '%s \\n', '        %clc');\r\nfprintf(fh, '%s \\n', '        direction = getMove(board);');\r\nfprintf(fh, '%s \\n', '        board = updateBoard(board, direction);');\r\nfprintf(fh, '%s \\n', '        %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    end');\r\nfprintf(fh, '%s \\n', '    %figure(1)');\r\nfprintf(fh, '%s \\n', '    %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    %figure(2)');\r\nfprintf(fh, '%s \\n', '    %hist(result,[2 4 8 16 32 64 128 256 512 1024,2048])');\r\nfprintf(fh, '%s \\n', '    %drawnow');\r\nfprintf(fh, '%s \\n', '    result(i) = max(board(:));');\r\nfprintf(fh, '%s \\n', '    %disp([i result(i) max(result)])');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = max(result) + mean(result)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = collapse(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'in = squish(in);');\r\nfprintf(fh, '%s \\n', 'for i = 1:3');\r\nfprintf(fh, '%s \\n', '    result = miniCollapse(in(i:i+1));');\r\nfprintf(fh, '%s \\n', '    out(i:i+1) = result;');\r\nfprintf(fh, '%s \\n', '     in(i:i+1) = result;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = squish(in);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = squish(in);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = in(in ~= 0);');\r\nfprintf(fh, '%s \\n', 'if numel(out) ~= 4');\r\nfprintf(fh, '%s \\n', '    out(4) = 0;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = miniCollapse(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if in(1) == in(2)');\r\nfprintf(fh, '%s \\n', '    out(1) = in(1) * 2;');\r\nfprintf(fh, '%s \\n', '    out(2)  = 0;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    out = in;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = saltBoard(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if nnz(in) == 16');\r\nfprintf(fh, '%s \\n', '    out = nan;');\r\nfprintf(fh, '%s \\n', '    return;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'vi = find(in == 0);');\r\nfprintf(fh, '%s \\n', 'selected = randi(numel(vi));');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'thresh = 0.1;');\r\nfprintf(fh, '%s \\n', 'if (rand \u003c thresh)');\r\nfprintf(fh, '%s \\n', '    salt = 4;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    salt = 2;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = in;');\r\nfprintf(fh, '%s \\n', 'out(vi(selected)) = salt;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function board = updateBoard(board, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'boardOriginal = board;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'board = collapseBoard(board,direction);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if ~isequal(boardOriginal, board)');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function dispBoard(board)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'clf');\r\nfprintf(fh, '%s \\n', 'r = 1;');\r\nfprintf(fh, '%s \\n', 'c = 1;');\r\nfprintf(fh, '%s \\n', 'v = 2;');\r\nfprintf(fh, '%s \\n', 'for r = 1:4');\r\nfprintf(fh, '%s \\n', '    for c = 1:4');\r\nfprintf(fh, '%s \\n', '        v = board(r,c);');\r\nfprintf(fh, '%s \\n', '        dispSquare(r,c,v)');\r\nfprintf(fh, '%s \\n', '    end');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function dispSquare(r,c,v)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'cmap = autumn(12);');\r\nfprintf(fh, '%s \\n', 'absIndex = (r-1)*4 + c;');\r\nfprintf(fh, '%s \\n', 'if v == 0 ');\r\nfprintf(fh, '%s \\n', '    cMapIndex = 1;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    cMapIndex = log2(v) + 1;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'h = subplot(4,4,absIndex);');\r\nfprintf(fh, '%s \\n', 'set(h,''xtick'',[])');\r\nfprintf(fh, '%s \\n', 'set(h,''ytick'',[])');\r\nfprintf(fh, '%s \\n', 'set(h,''color'',cmap(cMapIndex,:))');\r\nfprintf(fh, '%s \\n', '%axis off');\r\nfprintf(fh, '%s \\n', 'text(0.5,0.5,num2str(v), ''fontsize'', 20)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function flag = isMoveDirection(board, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'originalBoard = board;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'board = updateBoard(board, direction);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'flag = ~isequal(board, originalBoard);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = collapseBoard(in, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'rotDirection = direction-1;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'in = rot90(in,rotDirection);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'for r = 1:4');\r\nfprintf(fh, '%s \\n', '    out(r,:) = collapse(in(r,:));');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = rot90(out,-rotDirection);');\r\n\r\nfclose(fh);\r\n\r\nrehash path\r\n%%\r\nn = 200;\r\nscore = main(n)\r\nscore = 4056 - score;\r\n\r\nassert(score \u003c (4056 - 256))\r\nassignin('caller','score',score)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":240,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2014-04-02T17:36:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-04-01T20:01:55.000Z","updated_at":"2026-02-03T10:02:13.000Z","published_at":"2014-04-02T14:29:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe popular 2048 game has been implemented here:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://gabrielecirulli.github.io/2048/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://gabrielecirulli.github.io/2048/\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the board like this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[2 4 8 0\\n 4 0 0 0\\n 2 0 0 0\\n 2 0 4 0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou give the direction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 (left) 2 (up) 3 (right) 4 (down)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe system here will keep calling your solver. Score for each board is the biggest tile achieved. The Cody score is the maximum board score plus the average score across all 200 boards.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60834,"title":"Bell 202 Decoder","description":"Decode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \r\nWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\r\nDuration of each bit is based on the baud-rate.\r\nDigitized audio stream is produced at the sample rate and is smooth between bits.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 66px; transform-origin: 408px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDecode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDuration of each bit is based on the baud-rate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDigitized audio stream is produced at the sample rate and is smooth between bits.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function decodedStream = decodeBell202(audioSignal, sampleRate, bitRate)\r\n decodedStream=audioSignal/bitRate;\r\nend","test_suite":"%%\r\nrng(2718);\r\nbS=num2str(randi(2,1,1e4)-1);\r\nbS(bS==' ')=[];\r\nt = 1/1e5:1/1e5:1/9.2e2;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1e5,920),bS))\r\n%%\r\nrng(2718);\r\nbS=num2str(randi(2,1,1e4)-1);\r\nbS(bS==' ')=[];\r\nt = 1/1e5:1/1e5:1/1e3;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1e5,1e3),bS))\r\n%%\r\nbS='1011110001100110011001110001110101011010101010111000111000111000111100011100110101011001';\r\nt = 1/1.2e5:1/1.2e5:1/600;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1.2e5,600),bS))\r\n%%","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-03-27T15:12:44.000Z","updated_at":"2025-12-07T15:19:32.000Z","published_at":"2025-03-27T15:12:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDecode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDuration of each bit is based on the baud-rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDigitized audio stream is produced at the sample rate and is smooth between bits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60749,"title":"Compute the dispersion coefficient","description":"A contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\r\nG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \r\n\r\nwhere  is the width of the stream,  is the transverse mixing coefficient, and  is the deviation of the velocity profile from the cross-sectional average velocity\r\n\r\nWrite a function that takes a (normalized) velocity profile  specified at several points and computes the quantity \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 187.5px; transform-origin: 407px 187.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"240\" height=\"44\" alt=\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 240px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the stream, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the transverse mixing coefficient, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIAAAAAmCAYAAAAMe5M4AAAAAXNSR0IArs4c6QAABGFJREFUeF7tmluoFlUUx3+HpFLJChVRAhGSMCgFQUUfFEVLw5TQLlogXlAUFTXMW3lDBcEsSrFQCNJuVN4eTHtRUN9EFF8kTCQ0NEu8oYWZ+y/rg/2N88k358ycr5nZGw6Hc9izZq+1/uu/LnuaCKvUFmgqtfZBeQIASg6CAIAAgJJbIJ/qPwH0Bto04/i3gePA33o2MEAzLPg/eOQ54FsDQdLj7AcmAn8GACQ1XQH3BwYooFOTqBQAkMRaBdybBQBUmLwGnAGOFdBmhVIpCwC8CHwPLAJ+LJS1CqhMFgBQhfk6MA24VECbFUqltAHQFtgIHAjRnw+cpA2A7sBCYBlwJR8mKPcp0wbAy4BYYGe5zZof7VsCgEcBjSS1rgP/5EftRCctgp4KynbAXfPVnYoF4gAghZ8HegB9gQHANuDriNmmAFuBgzZavJDIrI3fXAQ925uvegJ9XO01EHgPOOKZ9xFgOfA+8CUwy0Bwf0stADxtguYBv7t+fnSkp3/SnD8O2OwELnBtny4ZmrtaMtv23/kBsLrOQwgAra1nnUere5siuyuwBngTOApMAM55ElSXfWXgWAKs86U/LAUsBtY6BvjJDXXeAS57D/ZziNtlL5/hfn9W95HjNzYCAJWTtKaeLTRT7OOPu1S8wbXcM80PCtpb3k4N5X6wv0cAP9cDAOX2TeZ4IUb08a896FNKHDtkoWRWMougZzdgh0vFQ4BoMCpFfApMqsEONa+D/YgcA+zxPKDaQPVA/xrskJWzspCbhZ5psFmSVDbI+WIfcCMmVftMLZaOskNNAAy3Yc4J4A3gtFlfKUNCRDlaGvpo5JvXDiALPVsbANOBLTHB+Jir/NcDc8xX881fVYEUVwPof0utmIpWjb0s+vU1itbbRj9ZRGfWMougZ2XyKhBEU/VQYLvVaWrTR0a6g/v2jQOAX+Er96vC/A9QPqlU2GKBXwB1ASdT8FQaUaNjJKHORuiZgqmqRPgVvh+MXYBV9snY5Ie16nEAqNzmqbesVI3aNxXo4IqKTkb7uvHT/66moFUjANAIPVMwVZWISgrzg1HX8SssQIdZIV8zVccB4FVgd6RqHOw+JFQx+JH1/a9YZyB2UJtxETictnYZyyuCnmLiD+36XcF4zdVrb7kZzTNuiLfXBj8a5okdvgE0vDvk1XQPpAABQlMj/WjKN9c+PNTlzruWCr5zfeULBohf7YWaF9zM2GFpii+CnhrtfmwsvNIof6xdxctvYlU5W626wC72Vu32ibusqzkK9osKdQCaLIkq1V+eckMEtRyVSNfLn7KJoRggT6sIena0Avwly/FnzR+z3bcY5208ryJQAFD0a6mmqwrUuBQw3toKPaD2QrT/hwnobAgaZbQjpvgtT573zpp3PTWQU6Qr3/9lbPC55+BngS/c5+Pq3ORHte7aV7VachuYU7+HY/sWCAAoOR4CAAIASm6BkqsfGCAAoOQWKLn6gQECAEpugZKrHxig5AC4B9wJDzZ/ROxOAAAAAElFTkSuQmCC\" width=\"64\" height=\"19\" alt=\"u' = u - bar(u)\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103\" height=\"44\" alt=\"ubar = (1/h) integral(u(y),0\u003c=y\u003c=h)\" style=\"width: 103px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a (normalized) velocity profile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30\" height=\"18\" alt=\"u(y)\" style=\"width: 30px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e specified at several points and computes the quantity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"215\" height=\"44\" alt=\"I = -integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 215px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = computeK(y,u)\r\n  I = -integral(u'*integral(integral(u',0,y1),0,y),0,h);\r\nend","test_suite":"%%\r\nny = 1000;\r\ny = linspace(0,1,ny);\r\nu = y.*(1-y);\r\nI = computeK(y,u);\r\nI_correct = 1/7560;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = 2*y;\r\nu(y\u003e1/2) = 2*(1-y(y\u003e1/2));\r\nI = computeK(y,u);\r\nI_correct = 1/480;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 2.5;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.00788915;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 3;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01168232;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 3.2; \r\nb = 3.2;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01192484;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-10-16T01:19:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-16T01:18:30.000Z","updated_at":"2024-10-27T15:58:26.000Z","published_at":"2024-10-16T01:19:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = -\\\\frac{1}{hD}\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the stream, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the transverse mixing coefficient, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u' = u - bar(u)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu^\\\\prime = u-{\\\\bar u}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ubar = (1/h) integral(u(y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\bar u} = \\\\frac{1}{h} \\\\int_0^h u(y) dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a (normalized) velocity profile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u(y)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu(y)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e specified at several points and computes the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = -integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = -\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1949,"title":"Get top 5 Cody Player Emails Automatically","description":"Yes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\r\n\r\nLooking at the list of the players \u003chttp://www.mathworks.com/matlabcentral/cody/players\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \"View Profile Information\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand. \r\n\r\nFor this program, let's say we want the top 5 profiles that give a \"real\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it. \r\n\r\nIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \"mailto:\" and if it is there, the email address is immediately following it. If the string \"mailto:\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\r\n\r\nAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\r\n\r\n*I am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.*\r\n\r\n*If this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \"My Community Profile\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.* ","description_html":"\u003cp\u003eYes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\u003c/p\u003e\u003cp\u003eLooking at the list of the players \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/players\"\u003ehttp://www.mathworks.com/matlabcentral/cody/players\u003c/a\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \"View Profile Information\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand.\u003c/p\u003e\u003cp\u003eFor this program, let's say we want the top 5 profiles that give a \"real\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it.\u003c/p\u003e\u003cp\u003eIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \"mailto:\" and if it is there, the email address is immediately following it. If the string \"mailto:\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\u003c/p\u003e\u003cp\u003eAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\u003c/p\u003e\u003cp\u003e\u003cb\u003eI am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eIf this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \"My Community Profile\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.\u003c/b\u003e\u003c/p\u003e","function_template":"function emails = getCodyEmails()\r\n  emails = {};\r\nend","test_suite":"%%\r\n% My code is below, it's used to generate the expected result.\r\n\r\n%Read in the player page\r\nplayerPage=urlread('http://www.mathworks.com/matlabcentral/cody/players');\r\n\r\n%Find where the web address for each profile starts\r\nstartIdx=strfind(playerPage,'\u003cdiv class=\"grid_53 push_3\"\u003e')+104; \r\n\r\n%Initialize output array\r\nemails={};\r\n\r\n%Get top 5 only\r\nfor i=1:5\r\n    % Get the profile page link\r\n   tempStr=playerPage(startIdx(i):startIdx(i)+100);\r\n   quoteIdx=strfind(tempStr,'\"')-1;\r\n   profilePageLink=['http://www.mathworks.com' tempStr(1:quoteIdx(1))];\r\n   \r\n   profilePage=urlread(profilePageLink);\r\n   % Try and find mailto link\r\n   tStartIdx=strfind(profilePage,'mailto');\r\n   \r\n   %If you could find it\r\n   if ~isempty(tStartIdx)\r\n       % Get the email\r\n       tEndIdx=strfind(profilePage(tStartIdx:tStartIdx+100),'\"')+tStartIdx;\r\n       \r\n       % Add it to our cell array\r\n       emails{length(emails)+1}=profilePage(tStartIdx+7:tEndIdx-2);\r\n   end\r\n    \r\nend\r\n\r\n\r\ntic\r\nyourResponse=getCodyEmails()\r\ntimeElapsed=toc\r\n\r\n\r\nassert(isequal(yourResponse,emails))\r\nassert(isequal(1,timeElapsed\u003e3))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":3743,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-20T05:40:10.000Z","updated_at":"2025-07-31T17:14:24.000Z","published_at":"2013-10-20T05:40:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLooking at the list of the players\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/players\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.mathworks.com/matlabcentral/cody/players\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \\\"View Profile Information\\\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this program, let's say we want the top 5 profiles that give a \\\"real\\\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \\\"mailto:\\\" and if it is there, the email address is immediately following it. If the string \\\"mailto:\\\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \\\"My Community Profile\\\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":53990,"title":"Classify product/digit-sum sequences","description":"Cody Problem 53120 involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\r\nWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved Cody Problem 53120, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \r\nWrite a function to classify the product/digit-sum sequences given the first two terms  and . To encourage solvers to find the pattern, loops are banned, and to allow for large inputs,  and  are specified as strings. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 93px; transform-origin: 407.5px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 309.642px 7.66667px; transform-origin: 309.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.883px 7.66667px; transform-origin: 383.883px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.075px 7.66667px; transform-origin: 103.075px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.017px 7.66667px; transform-origin: 262.017px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.35px 7.66667px; transform-origin: 93.35px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 7.66667px; transform-origin: 77.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are specified as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = PDSseq(a,b)\r\n  c = [1 9 26 62 163];\r\n  y = c(a+b);\r\nend","test_suite":"%%\r\na = '1';\r\nb = '2';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7';\r\nb = '31';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '17';\r\nb = '28';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '51';\r\nb = '77';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '82';\r\nb = '262';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7021';\r\nb = '8878';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264';\r\nb = '412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8675308';\r\nb = '2941300';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '9142534264';\r\nb = '8424812653';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164';\r\nb = '8424812753';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '1352408463575';\r\nb = '9898989898985';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264534264534264534264';\r\nb = '412578412578412578412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '86753088675308867530886753088675308';\r\nb = '28413002941300294130029413002941300';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '914253426491425342649142534264914253463';\r\nb = '842481265384248126538424812653842481265324';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164842481275380314231648424812753';\r\nb = '84248127538031423164842481275380314231648424812756';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '43524084635758031423164842481275380314231648424812753';\r\nb = '98989898989858031423164842481275380614231648424812753';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = num2str(randi(835042)*57);\r\nb = char(randi(9,20,1)+48);\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = repelem('1',1,23);\r\na(randi(23)) = '4';\r\nb = num2str(10^randi(14));\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\nfiletext = fileread('PDSseq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'system') || contains(filetext,'regexp') || contains(filetext,'java') || contains(filetext,'for') || contains(filetext,'while') || contains(filetext,'numpy'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2022-02-05T01:46:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-02-04T04:01:11.000Z","updated_at":"2026-01-15T18:05:52.000Z","published_at":"2022-02-04T04:04:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are specified as strings. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55315,"title":"Chain multiplication - 04","description":"Following up on the problem in 55305, you found the optimal way to multiply a chain of matrices.\r\nHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\r\nFor example, \r\nd= [1, 2, 3, 2] and s = \"A(BC)\".\r\nhere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\r\nFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\r\n\r\nn.b. only valid parenthesization are given in this problem for simplicity.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 273px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 136.5px; transform-origin: 407px 136.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFollowing up on the problem in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55305-chain-multiplication-02\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e55305\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, you found the optimal way to multiply a chain of matrices.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ed= [1, 2, 3, 2] and s = \"A(BC)\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ehere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en.b. only valid parenthesization are given in this problem for simplicity.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = chain_mul_04(s,d)\r\n  y = x;\r\nend","test_suite":"%%\r\nd= [1, 2, 3, 2];\r\ns = \"A(BC)\";\r\ny_correct = 16;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [1, 2, 3, 2];\r\ns = \"(AB)C\";\r\ny_correct = 12;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [40, 20, 30, 10, 30];\r\ns = \"A(B(CD))\";\r\ny_correct = 51000;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [40, 20, 30, 10, 30];\r\ns = \"(AB)(CD)\";\r\ny_correct = 69000;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n\r\n%%\r\nd= [81,213,78,96,2,1,98,102, 1200,4];\r\ns = \"(((AB)C)(DE))((FG)(HI))\";\r\ny_correct = 2460558;\r\nassert(isequal(chain_mul_04(s,d),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":363598,"edited_at":"2022-08-16T22:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-16T21:31:49.000Z","updated_at":"2022-08-16T22:04:11.000Z","published_at":"2022-08-16T22:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollowing up on the problem in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55305-chain-multiplication-02\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e55305\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, you found the optimal way to multiply a chain of matrices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ed= [1, 2, 3, 2] and s = \\\"A(BC)\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en.b. only valid parenthesization are given in this problem for simplicity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54720,"title":"Hyperperfect Numbers","description":"A k-hyperperfect number is a natural number n for which the equality n = 1 + k(σ(n)  − n  − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n).\r\n%Example\r\nsigma(6) = 1 + 2 + 3 + 6 = 12\r\n%for k=1\r\n1 + 1*(12-6-1) = 1 + 5 = 6\r\n\r\n%Example\r\nsigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\r\n%for k=3\r\n1 + 3*(434-325-1) = 1 + 3*108 = 324  \r\n\r\nGiven a number x, return the xth Hyperperfect number (serial/order wise) and corresponding k value.\r\n\r\n\r\nP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 386.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 193.45px; transform-origin: 408px 193.45px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.60833px 8px; transform-origin: 6.60833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Hyperperfect_number\"\u003e\u003cspan style=\"perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 72.3417px 8px; transform-origin: 72.3417px 8px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-hyperperfect number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7917px 8px; transform-origin: 63.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a natural number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.625px 8px; transform-origin: 69.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for which the equality \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.8417px 8px; transform-origin: 19.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e = 1 + \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.64167px 8px; transform-origin: 4.64167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eσ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.25px 8px; transform-origin: 12.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e)  − \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.1417px 8px; transform-origin: 16.1417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e  − 1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5667px 8px; transform-origin: 43.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e holds, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.225px 8px; transform-origin: 4.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eσ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Divisor_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003edivisor function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120.175px 8px; transform-origin: 120.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., the sum of all positive divisors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.9px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 91.95px; transform-origin: 405px 91.95px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 111.65px 8.5px; tab-size: 4; transform-origin: 111.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esigma(6) = 1 + 2 + 3 + 6 = 12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%for k=1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.5px; tab-size: 4; transform-origin: 100.1px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 + 1*(12-6-1) = 1 + 5 = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 8.5px; tab-size: 4; transform-origin: 173.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%for k=3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.5px; tab-size: 4; transform-origin: 142.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 + 3*(434-325-1) = 1 + 3*108 = 324  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.7333px 8px; transform-origin: 51.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8333px 8px; transform-origin: 33.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.4417px 8px; transform-origin: 12.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003exth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.175px 8px; transform-origin: 185.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHyperperfect number (serial/order wise) and corresponding \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.675px 8px; transform-origin: 18.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.442px 8px; transform-origin: 360.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = hyper(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('hyper.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'interp1') || contains(filetext, 'find') || ...\r\n          contains(filetext, 'str2num') || contains(filetext, 'switch') || ...\r\n          contains(filetext, '26977') || contains(filetext, '1403221')|| ...\r\n          contains(filetext, '1570153') || contains(filetext, '4304341'); \r\nassert(~illegal)\r\n\r\n\r\n%%\r\nx = 1;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,6)\u0026isequal(k,1))\r\n\r\n%%\r\nx = 2;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,21)\u0026isequal(k,2))\r\n\r\n%%\r\nx = 4;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,6)\u0026isequal(n,301))\r\n\r\n%%\r\nx = 7;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,697)\u0026isequal(k,12))\r\n\r\n%%\r\nx = 11;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,2)\u0026isequal(n,2133))\r\n\r\n%%\r\nx = 17;\r\n[n,k]=hyper(x);\r\nassert(isequal(60,k)\u0026isequal(24601,n))\r\n\r\n%%\r\nx = 18;\r\n[n,k]=hyper(x);\r\nassert(isequal(26977,n)\u0026isequal(48,k))\r\n\r\n%%\r\nx = 20;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,132)\u0026isequal(96361,n))\r\n\r\n%%\r\nx = 21;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,130153)\u0026isequal(k,132))\r\n\r\n%%\r\nx = 25;\r\n[n,k]=hyper(x);\r\nassert(isequal(214273,n)\u0026isequal(k,31))\r\n\r\n%%\r\nx = 31;\r\n[n,k]=hyper(x);\r\nassert(isequal(78,k)\u0026isequal(n,486877))\r\n\r\n%%\r\nx = 37;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,1055833)\u0026isequal(k,348))\r\n\r\n%%\r\nx = 39;\r\n[n,k]=hyper(x);\r\nassert(isequal(1232053,n)\u0026isequal(498,k))\r\n\r\n%%\r\nx = 43;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,12)\u0026isequal(1570153,n))\r\n\r\n%%\r\nx = 45;\r\n[n,k]=hyper(x);\r\nassert(isequal(1787917,n)\u0026isequal(438,k))\r\n\r\n%%\r\nx = 48;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,336)\u0026isequal(2462881,n))\r\n\r\n%%\r\nx = 52;\r\n[n,k]=hyper(x);\r\nassert(isequal(798,k)\u0026isequal(n,2708413))\r\n\r\n%%\r\nx = 53;\r\n[n,k]=hyper(x);\r\nassert(isequal(810,k)\u0026isequal(2768581,n))\r\n\r\n%%\r\nx = 54;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,2856481)\u0026isequal(k,528))\r\n\r\n%%\r\nx = 60;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,162)\u0026isequal(n,4304341))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-13T06:25:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2025-09-13T06:25:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-07T10:09:14.000Z","updated_at":"2025-12-15T21:31:12.000Z","published_at":"2022-06-08T17:42:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Hyperperfect_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-hyperperfect number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a natural number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for which the equality \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e = 1 + \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eσ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e)  − \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e  − 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e holds, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eσ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Divisor_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edivisor function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., the sum of all positive divisors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Example\\nsigma(6) = 1 + 2 + 3 + 6 = 12\\n%for k=1\\n1 + 1*(12-6-1) = 1 + 5 = 6\\n\\n%Example\\nsigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\\n%for k=3\\n1 + 3*(434-325-1) = 1 + 3*108 = 324  ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eHyperperfect number (serial/order wise) and corresponding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54750,"title":"Find the length of stream affected by a spill","description":"When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration  is often computed as a function of time  and distance  from the spill using the advection-dispersion equation:\r\n\r\nwhere  is the mean velocity of the river and  is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass  mixed over the cross section (with area ) at , the concentration can be shown—using some of the math needed for Cody Problem 51625—to be\r\n\r\nWrite a function to compute the length of stream affected by the spill. In other words, find the position  (say) beyond which the concentration never exceeds a threshold . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 282.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 141.35px; transform-origin: 407px 141.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.317px 8px; transform-origin: 378.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.675px 8px; transform-origin: 123.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is often computed as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.833px 8px; transform-origin: 168.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the spill using the advection-dispersion equation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dC/dt + U dC/dx = K d^2C/dx^2\" style=\"width: 126.5px; height: 36.5px;\" width=\"126.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.158px 8px; transform-origin: 202.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.242px 8px; transform-origin: 125.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e mixed over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 8px; transform-origin: 12.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAC7UlEQVRoQ+2YPU8VQRSG4ReI2lkRPwoqKDQ0WmgBJLYmQPwBaENFTNBSMdFAQ4GY2KsBWiOaSIGFBEK0svCjtFMw/AB9X3MmOTs7s3Puyl1IdjY52Xt3vs48886Zs9vbk68kgd5kjVyhJ0MyiCBDypAMBAxVspIypCiBsyg5I6XvU5zapqQJAHkA24HtwvphfDYLW4X9DAFrE6QlALgNewi7p2BM4fcybB12MwSqLZAciG+AMBwA8RrPRgMA/7FsA6TTmOcX2MkYBNlyz0VdQ7h/0tuuDZCcijjv67BXgbjDQE6V8fK3YyuUtI2JXxQA53D/HoDER79EbYR1vo6S3JH5ObCfL+PZgS/RiCNH8fiPDLqH+6kKB1xcYpUCzKrtNojKlOqINPKlyPI1KaMDXK3YKjnfGB8GDoHUD8NYHIY+fqwBqbAtqyBRPb9FOV8FhjsdTuA/c40nsHFZoapVclyous1DgHQLfTw19KPH60RJhf6tgfsOHHokTlGKL2ELsBcGR3UVrqzrp8OmheqL+BcKwH6fGhJ9ZuIYu/Qca0HSg1FBb2A6IfufCXezrfabyeJYxWBzKLsr5bUgsa01AHZz0p323eh2o3Mu+lNJlzr19gjrWxdXn26FhNIakzhHxh8GaQbAC7Dgy2ACRtOnG91xh441cJdOaisknbVy4FjmmhJM06cb/XEvtvxdeuVQDjvFlXaKBZLLNXiqRVP3FB0pb/p047B6YSZlR/ju6nyqlF6kIHF7bMGmYTxyQ3GJKzUPSyWSRo5dqeb8jp1w7mQLfiUIQeLW4vUB9gy2Anssz/x8aQbPuYePezrAxJjbiF8C/C2nvxJcQXnpS6UPyY8ZfgKmZUluqQStK7Ko2Sl935C2V3Hn5xDC4xz4ShWNsz4kUr0vjd8pBWm/qKZrsFh5zTk00ozzuwEjpD7YvoB7i3s0XKRiUiOeH/dBMiTDCmVIGZKBgKFKVlKGZCBgqJKVlCEZCBiqZCUZIP0F1sSXJS9IuzgAAAAASUVORK5CYII=\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration can be shown—using some of the math needed for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51625\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51625\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5583px 8px; transform-origin: 22.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—to be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.05px; text-align: left; transform-origin: 384px 20.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\" style=\"width: 204.5px; height: 40px;\" width=\"204.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.617px 8px; transform-origin: 313.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = L_a\" style=\"width: 42.5px; height: 20px;\" width=\"42.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3417px 8px; transform-origin: 44.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) beyond which the concentration never exceeds a threshold \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = C_t\" style=\"width: 46px; height: 20px;\" width=\"46\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function La = affectedReach(U,K,M,A,Ct)\r\n% La = length of affected reach of stream [L]\r\n% U  = mean velocity [L/T]\r\n% K  = dispersion coefficient [L^2/T]\r\n% M  = mass of contaminant [M]\r\n% A  = cross-sectional area (L^2)\r\n% Ct = threshold concentration (M/L^3)\r\n\r\n  La = M/(Ct*A);\r\nend","test_suite":"%%\r\nM = 100;                    %  Mass (kg)\r\nA = 30;                     %  Cross-sectional area (m2)\r\nU = 0.3;                    %  Mean velocity (m/s)\r\nK = 2;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 50;                     %  Mass (kg)\r\nA = 15;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 8.4;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.001;                 %  Target concentration (kg/m3)\r\nLa_correct = 26332.1;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 0.003;                 %  Target concentration (kg/m3)\r\nLa_correct = 91.59;         %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 3e-4;                  %  Target concentration (kg/m3)\r\nLa_correct = 7256.28;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 70;                     %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.15;                   %  Mean velocity (m/s)\r\nK = 1;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 280;                    %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.54;                   %  Mean velocity (m/s)\r\nK = 3.7;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.007;                 %  Target concentration (kg/m3)\r\nLa_correct = 42140.42;      %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%% Approximately plug flow\r\nM = 5*rand;                 %  Mass (kg)\r\nA = 40;                     %  Cross-sectional area (m2)\r\nU = 0.3*(1+rand);           %  Mean velocity (m/s)\r\nK = rand*1e-3;              %  Dispersion coefficient (m2/s)\r\nCt = 0.02*rand;             %  Target concentration (kg/m3)\r\nLa_approx = (U/(4*pi*K))*(M/(Ct*A))^2;\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_approx)/La_approx\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('affectedReach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'if'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-14T05:04:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-06-14T05:04:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-14T04:57:20.000Z","updated_at":"2022-06-14T05:04:44.000Z","published_at":"2022-06-14T04:59:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is often computed as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the spill using the advection-dispersion equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + U dC/dx = K d^2C/dx^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t} + U \\\\frac{\\\\partial C}{\\\\partial x} = K \\\\frac{\\\\partial^2 C}{\\\\partial x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e mixed over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the concentration can be shown—using some of the math needed for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51625\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51625\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—to be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L_a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L_a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) beyond which the concentration never exceeds a threshold \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = C_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = C_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61010,"title":"q-dimensional Cartesian product","description":"Your mission, should you choose to accept it, is to compute a q-dimensional Cartesian product, as follows. Let the input G be an 1×q cell array of vectors of size 1×n_i each (here and in the following, 1≤i≤q). The output V should be a q-dimensional cell array of size n_1×n_2×…×n_q such that for 1≤k_i≤n_i, V{k_1,k_2,…,k_q} is equal to the vector [ G{1}(k_1), G{2}(k_2), …, G{q}(k_q) ]. In other words, the indices into V are the Cartesian product of the indices into the vectors in G, and each element of V is the combination of values from those vectors at those indices.\r\n\r\nAn example: if G = { 1:2, 3:4 }, then V = { [1 3], [1 4] ; [2 3], [2 4] }; if G = { 1:2, 3:4, 5:6 }, then V(:, :, 1) = { [1 3 5], [1 4 5] ; [2 3 5], [2 4 5] } and V(:, :, 2) = { [1 3 6], [1 4 6] ; [2 3 6], [2 4 6] }; and so on.\r\n\r\nNote: due to the way MATLAB handles trailing singleton dimensions, ndims(V) will report a number less than q if n_j = … = n_q = 1 for some j≤q. This is alright since indexing V along q dimensions will still work. \r\n\r\nNote 2: cheating isn't banned by the test suite, but don't do it. It's not sportsmanlike.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 348px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 174px; transform-origin: 408px 174px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.5px; text-align: left; transform-origin: 385px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour mission, should you choose to accept it, is to compute a q-dimensional Cartesian product, as follows. Let the input \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eG\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be an 1×q cell array of vectors of size 1×n_i each (here and in the following, 1≤i≤q). The output \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should be a q-dimensional cell array of size n_1×n_2×…×n_q such that for 1≤k_i≤n_i, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV{k_1,k_2,…,k_q}\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is equal to the vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[ G{1}(k_1), G{2}(k_2), …, G{q}(k_q) ]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In other words, the indices into \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the Cartesian product of the indices into the vectors in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eG\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and each element of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the combination of values from those vectors at those indices.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn example: if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eG = { 1:2, 3:4 }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV = { [1 3], [1 4] ; [2 3], [2 4] }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eG = { 1:2, 3:4, 5:6 }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV(:, :, 1) = { [1 3 5], [1 4 5] ; [2 3 5], [2 4 5] }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV(:, :, 2) = { [1 3 6], [1 4 6] ; [2 3 6], [2 4 6] }\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote: due to the way MATLAB handles trailing singleton dimensions, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003endims(V)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will report a number less than q if n_j = … = n_q = 1 for some j≤q. This is alright since indexing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eV\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e along q dimensions will still work. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNote 2: cheating isn't banned by the test suite, but don't do it. It's not sportsmanlike.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function V = grid2vectors(G)\r\n    \r\nend\r\n","test_suite":"%%\r\nassert(isequal(grid2vectors({1:10}), num2cell(1:10).'))\r\n\r\n%% \r\nassert(isequal(grid2vectors({1:2, 3:4}), {[1 3], [1 4] ; [2 3], [2 4]}))\r\n\r\n%%\r\nV = grid2vectors({1:2, 3:4, 5:6});\r\nassert(isequal(V(:, :, 1), { [1 3 5], [1 4 5] ; [2 3 5], [2 4 5] }));\r\nassert(isequal(V(:, :, 2), { [1 3 6], [1 4 6] ; [2 3 6], [2 4 6] }));\r\n\r\n%%\r\nassert(isequal(grid2vectors({1, 2, 3, 4, 5}), {[1 2 3 4 5]}))\r\n\r\n%%\r\nV = grid2vectors({1:2 3 4:5 6 7});\r\nassert(isequal(V(:, :, 1), { [1 3 4 6 7] ; [2 3 4 6 7] }));\r\nassert(isequal(V(:, :, 2), { [1 3 5 6 7] ; [2 3 5 6 7] }));\r\n\r\n%%\r\nV(:,:,1,1) = [\r\n    {[-1 2 -1 1]}    {[-1 2.2500 -1 1]}    {[-1 2.5000 -1 1]}    {[-1 2.7500 -1 1]}    {[-1 3 -1 1]};\r\n    {[ 0 2 -1 1]}    {[ 0 2.2500 -1 1]}    {[ 0 2.5000 -1 1]}    {[ 0 2.7500 -1 1]}    {[ 0 3 -1 1]};\r\n    {[ 1 2 -1 1]}    {[ 1 2.2500 -1 1]}    {[ 1 2.5000 -1 1]}    {[ 1 2.7500 -1 1]}    {[ 1 3 -1 1]}\r\n];\r\n\r\nV(:,:,2,1) = [\r\n    {[-1 2 1 1]}    {[-1 2.2500 1 1]}    {[-1 2.5000 1 1]}    {[-1 2.7500 1 1]}    {[-1 3 1 1]};\r\n    {[ 0 2 1 1]}    {[ 0 2.2500 1 1]}    {[ 0 2.5000 1 1]}    {[ 0 2.7500 1 1]}    {[ 0 3 1 1]};\r\n    {[ 1 2 1 1]}    {[ 1 2.2500 1 1]}    {[ 1 2.5000 1 1]}    {[ 1 2.7500 1 1]}    {[ 1 3 1 1]}\r\n];\r\n\r\nV(:,:,1,2) = [\r\n    {[-1 2 -1 1.2500]}    {[-1 2.2500 -1 1.2500]}    {[-1 2.5000 -1 1.2500]}    {[-1 2.7500 -1 1.2500]}    {[-1 3 -1 1.2500]};\r\n    {[ 0 2 -1 1.2500]}    {[ 0 2.2500 -1 1.2500]}    {[ 0 2.5000 -1 1.2500]}    {[ 0 2.7500 -1 1.2500]}    {[ 0 3 -1 1.2500]};\r\n    {[ 1 2 -1 1.2500]}    {[ 1 2.2500 -1 1.2500]}    {[ 1 2.5000 -1 1.2500]}    {[ 1 2.7500 -1 1.2500]}    {[ 1 3 -1 1.2500]}\r\n];\r\n\r\nV(:,:,2,2) = [\r\n    {[-1 2 1 1.2500]}    {[-1 2.2500 1 1.2500]}    {[-1 2.5000 1 1.2500]}    {[-1 2.7500 1 1.2500]}    {[-1 3 1 1.2500]};\r\n    {[ 0 2 1 1.2500]}    {[ 0 2.2500 1 1.2500]}    {[ 0 2.5000 1 1.2500]}    {[ 0 2.7500 1 1.2500]}    {[ 0 3 1 1.2500]};\r\n    {[ 1 2 1 1.2500]}    {[ 1 2.2500 1 1.2500]}    {[ 1 2.5000 1 1.2500]}    {[ 1 2.7500 1 1.2500]}    {[ 1 3 1 1.2500]}\r\n];\r\n\r\nV(:,:,1,3) = [\r\n    {[-1 2 -1 1.5000]}    {[-1 2.2500 -1 1.5000]}    {[-1 2.5000 -1 1.5000]}    {[-1 2.7500 -1 1.5000]}    {[-1 3 -1 1.5000]};\r\n    {[ 0 2 -1 1.5000]}    {[ 0 2.2500 -1 1.5000]}    {[ 0 2.5000 -1 1.5000]}    {[ 0 2.7500 -1 1.5000]}    {[ 0 3 -1 1.5000]};\r\n    {[ 1 2 -1 1.5000]}    {[ 1 2.2500 -1 1.5000]}    {[ 1 2.5000 -1 1.5000]}    {[ 1 2.7500 -1 1.5000]}    {[ 1 3 -1 1.5000]}\r\n];\r\n\r\nV(:,:,2,3) = [\r\n    {[-1 2 1 1.5000]}    {[-1 2.2500 1 1.5000]}    {[-1 2.5000 1 1.5000]}    {[-1 2.7500 1 1.5000]}    {[-1 3 1 1.5000]};\r\n    {[ 0 2 1 1.5000]}    {[ 0 2.2500 1 1.5000]}    {[ 0 2.5000 1 1.5000]}    {[ 0 2.7500 1 1.5000]}    {[ 0 3 1 1.5000]};\r\n    {[ 1 2 1 1.5000]}    {[ 1 2.2500 1 1.5000]}    {[ 1 2.5000 1 1.5000]}    {[ 1 2.7500 1 1.5000]}    {[ 1 3 1 1.5000]}\r\n];\r\n\r\nV(:,:,1,4) = [\r\n    {[-1 2 -1 1.7500]}    {[-1 2.2500 -1 1.7500]}    {[-1 2.5000 -1 1.7500]}    {[-1 2.7500 -1 1.7500]}    {[-1 3 -1 1.7500]};\r\n    {[ 0 2 -1 1.7500]}    {[ 0 2.2500 -1 1.7500]}    {[ 0 2.5000 -1 1.7500]}    {[ 0 2.7500 -1 1.7500]}    {[ 0 3 -1 1.7500]};\r\n    {[ 1 2 -1 1.7500]}    {[ 1 2.2500 -1 1.7500]}    {[ 1 2.5000 -1 1.7500]}    {[ 1 2.7500 -1 1.7500]}    {[ 1 3 -1 1.7500]}\r\n];\r\n\r\nV(:,:,2,4) = [\r\n    {[-1 2 1 1.7500]}    {[-1 2.2500 1 1.7500]}    {[-1 2.5000 1 1.7500]}    {[-1 2.7500 1 1.7500]}    {[-1 3 1 1.7500]};\r\n    {[ 0 2 1 1.7500]}    {[ 0 2.2500 1 1.7500]}    {[ 0 2.5000 1 1.7500]}    {[ 0 2.7500 1 1.7500]}    {[ 0 3 1 1.7500]};\r\n    {[ 1 2 1 1.7500]}    {[ 1 2.2500 1 1.7500]}    {[ 1 2.5000 1 1.7500]}    {[ 1 2.7500 1 1.7500]}    {[ 1 3 1 1.7500]}\r\n];\r\n\r\nV(:,:,1,5) = [\r\n    {[-1 2 -1 2]}    {[-1 2.2500 -1 2]}    {[-1 2.5000 -1 2]}    {[-1 2.7500 -1 2]}    {[-1 3 -1 2]};\r\n    {[ 0 2 -1 2]}    {[ 0 2.2500 -1 2]}    {[ 0 2.5000 -1 2]}    {[ 0 2.7500 -1 2]}    {[ 0 3 -1 2]};\r\n    {[ 1 2 -1 2]}    {[ 1 2.2500 -1 2]}    {[ 1 2.5000 -1 2]}    {[ 1 2.7500 -1 2]}    {[ 1 3 -1 2]}\r\n];\r\n\r\nV(:,:,2,5) = [\r\n    {[-1 2 1 2]}    {[-1 2.2500 1 2]}    {[-1 2.5000 1 2]}    {[-1 2.7500 1 2]}    {[-1 3 1 2]};\r\n    {[ 0 2 1 2]}    {[ 0 2.2500 1 2]}    {[ 0 2.5000 1 2]}    {[ 0 2.7500 1 2]}    {[ 0 3 1 2]};\r\n    {[ 1 2 1 2]}    {[ 1 2.2500 1 2]}    {[ 1 2.5000 1 2]}    {[ 1 2.7500 1 2]}    {[ 1 3 1 2]}\r\n];\r\n\r\nassert(isequal(grid2vectors({[-1 0 1], 2:0.25:3, [-1 1], 1:0.25:2}), V))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":332395,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-10-02T09:35:39.000Z","updated_at":"2026-03-03T15:00:19.000Z","published_at":"2025-10-02T09:35:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYour mission, should you choose to accept it, is to compute a q-dimensional Cartesian product, as follows. Let the input \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e be an 1×q cell array of vectors of size 1×n_i each (here and in the following, 1≤i≤q). The output \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e should be a q-dimensional cell array of size n_1×n_2×…×n_q such that for 1≤k_i≤n_i, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV{k_1,k_2,…,k_q}\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e is equal to the vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ G{1}(k_1), G{2}(k_2), …, G{q}(k_q) ]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. In other words, the indices into \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e are the Cartesian product of the indices into the vectors in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, and each element of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e is the combination of values from those vectors at those indices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eAn example: if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG = { 1:2, 3:4 }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV = { [1 3], [1 4] ; [2 3], [2 4] }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e; if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eG = { 1:2, 3:4, 5:6 }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV(:, :, 1) = { [1 3 5], [1 4 5] ; [2 3 5], [2 4 5] }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV(:, :, 2) = { [1 3 6], [1 4 6] ; [2 3 6], [2 4 6] }\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e; and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eNote: due to the way MATLAB handles trailing singleton dimensions, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003endims(V)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e will report a number less than q if n_j = … = n_q = 1 for some j≤q. This is alright since indexing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e along q dimensions will still work. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eNote 2: cheating isn't banned by the test suite, but don't do it. It's not sportsmanlike.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53125,"title":"Easy Sequences 54: Product of Products of Proper Divisors","description":"A divisor of a number that is less than the number is called a \"proper divisor\". \r\nFor a given positive integer , we are asked to evaluate the following summation:\r\n             \r\nThis is equivalent to finding the product of the products of proper divisors of all integers from  to .\r\nFor example for , we have:\r\n                            \r\nPlease present your output modulo .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 413.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.75px; transform-origin: 407px 206.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA divisor of a number that is less than the number is called a \"proper divisor\". \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eor a given positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we are asked to evaluate the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.75px; text-align: left; transform-origin: 384px 22.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 110px; height: 45.5px;\" width=\"110\" height=\"45.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is equivalent to finding \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233px 8px; transform-origin: 233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethe product of the products of proper divisors of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e2\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 209px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.5px; text-align: left; transform-origin: 384px 104.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-99px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 509px; height: 209px;\" width=\"509\" height=\"209\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.5px 8px; transform-origin: 112.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease present your output modulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 55.5px; height: 18px;\" width=\"55.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = pppd(n)\r\n    s = 2 * (n + 2) ^ 2 * n;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 2880;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 20;\r\ns_correct = 178754;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 651627;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 200;\r\ns_correct = 471492;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 132068;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 2000;\r\ns_correct = 192916;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 700691;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 20000;\r\ns_correct = 135567;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 919193;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 200000;\r\ns_correct = 581218;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 811966;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nns = 2000000:2222222;\r\ns = arrayfun(@(n) pppd(n),ns);\r\nss = mod([sum(s) sum(num2str(s))],1000003);\r\nss_correct = [526924 445038];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('pppd.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-12-04T15:11:17.000Z","updated_at":"2026-03-19T13:19:46.000Z","published_at":"2021-12-06T15:33:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA divisor of a number that is less than the number is called a \\\"proper divisor\\\". \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eor a given positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we are asked to evaluate the following summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\prod_{i=2}^{n}\\\\left (\\\\prod_{\\\\ d|i\\\\ \\\\\u0026amp;\\\\  d\u0026lt;i}^{}d\\\\   \\\\right )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is equivalent to finding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe product of the products of proper divisors of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\prod_{i=2}^{10}\\\\prod_{d|i\\\\ \\\\\u0026amp;\\\\  d\u0026lt;i}^{}d\\\\ = \\\\prod_{d|2\\\\ \\\\\u0026amp;\\\\  d\u0026lt;2}^{}d \\\\ \\\\times\\\\prod_{d|3\\\\ \\\\\u0026amp;\\\\  d\u0026lt;3}^{}d \\\\ \\\\times\\\\prod_{d|4\\\\ \\\\\u0026amp;\\\\  d\u0026lt;4}^{}d  \\\\ \\\\times\\\\prod_{d|5\\\\ \\\\\u0026amp;\\\\  d\u0026lt;5}^{}d\\\\ \\\\times\\\\prod_{d|6\\\\ \\\\\u0026amp;\\\\  d\u0026lt;6}^{}d \\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\times\\\\prod_{d|7\\\\ \\\\\u0026amp;\\\\  d\u0026lt;7}^{}d \\\\ \\\\times\\\\prod_{d|8\\\\ \\\\\u0026amp;\\\\  d\u0026lt;8}^{}d \\\\ \\\\times\\\\prod_{d|9\\\\ \\\\\u0026amp;\\\\  d\u0026lt;9}^{}d \\\\ \\\\times\\\\prod_{d|10\\\\ \\\\\u0026amp;\\\\  d\u0026lt;10}^{}d \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =1\\\\times1\\\\times(1\\\\cdot2)\\\\times1\\\\times(1\\\\cdot2\\\\cdot3)\\\\times1\\\\times(1\\\\cdot2\\\\cdot4)\\\\times(1\\\\cdot3)\\\\times(1\\\\cdot2\\\\cdot5) \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =1\\\\times1\\\\times2\\\\times1\\\\times6\\\\times1\\\\times8\\\\times3\\\\times10 \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =2880\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present your output modulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1000003\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61176,"title":"[Master Regular Expression] Reformat Phone Number","description":"You are given a phone number as a string number. number consists of digits, spaces ' ', and/or dashes '-'.\r\nYou would like to reformat the phone number in a certain manner. Firstly, remove all spaces and dashes. Then, group the digits from left to right into blocks of length 3 until there are 4 or fewer digits. The final digits are then grouped as follows:\r\n2 digits: A single block of length 2.\r\n3 digits: A single block of length 3.\r\n4 digits: Two blocks of length 2 each.\r\nThe blocks are then joined by dashes. Notice that the reformatting process should never produce any blocks of length 1 and produce at most two blocks of length 2.\r\nReturn the phone number after formatting.\r\n \r\nExample 1:\r\nInput: number = \"1-23-45 6\"\r\nOutput: \"123-456\"\r\nExplanation: The digits are \"123456\".\r\nStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \"123\".\r\nStep 2: There are 3 digits remaining, so put them in a single block of length 3. The 2nd block is \"456\".\r\nJoining the blocks gives \"123-456\".\r\nExample 2:\r\nInput: number = \"123 4-567\"\r\nOutput: \"123-45-67\"\r\nExplanation: The digits are \"1234567\".\r\nStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \"123\".\r\nStep 2: There are 4 digits left, so split them into two blocks of length 2. The blocks are \"45\" and \"67\".\r\nJoining the blocks gives \"123-45-67\".\r\nExample 3:\r\nInput: number = \"123 4-5678\"\r\nOutput: \"123-456-78\"\r\nExplanation: The digits are \"12345678\".\r\nStep 1: The 1st block is \"123\".\r\nStep 2: The 2nd block is \"456\".\r\nStep 3: There are 2 digits left, so put them in a single block of length 2. The 3rd block is \"78\".\r\nJoining the blocks gives \"123-456-78\".\r\n \r\nConstraints: \r\n2 \u003c= number.length \u003c= 100\r\nnumber consists of digits and the characters '-' and ' '.\r\nThere are at least two digits in number","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1056.62px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 528.312px; transform-origin: 408px 528.312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a phone number as a string number. number consists of digits, spaces ' ', and/or dashes '-'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou would like to reformat the phone number in a certain manner. Firstly, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eremove\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e all spaces and dashes. Then, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003egroup\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the digits from left to right into blocks of length 3 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003euntil\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e there are 4 or fewer digits. The final digits are then grouped as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2 digits: A single block of length 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3 digits: A single block of length 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4 digits: Two blocks of length 2 each.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe blocks are then joined by dashes. Notice that the reformatting process should \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enever\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e produce any blocks of length 1 and produce \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eat most\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e two blocks of length 2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ethe phone number after formatting.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number = \"1-23-45 6\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"123-456\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The digits are \"123456\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \"123\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: There are 3 digits remaining, so put them in a single block of length 3. The 2nd block is \"456\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eJoining the blocks gives \"123-456\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number = \"123 4-567\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"123-45-67\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe digits are \"1234567\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \"123\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: There are 4 digits left, so split them into two blocks of length 2. The blocks are \"45\" and \"67\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eJoining the blocks gives \"123-45-67\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 3:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number = \"123 4-5678\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"123-456-78\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The digits are \"12345678\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: The 1st block is \"123\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: The 2nd block is \"456\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: There are 2 digits left, so put them in a single block of length 2. The 3rd block is \"78\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eJoining the blocks gives \"123-456-78\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2 \u0026lt;= number.length \u0026lt;= 100\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003enumber consists of digits and the characters '-' and ' '.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are at least \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etwo\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits in number\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(number)\r\n\r\nend","test_suite":"%%\r\ncode = fileread('solution.m');\r\nassert(contains(code, 'regexp') || contains(code, 'regexprep'), 'Phải dùng regexp hoặc regexprep');\r\nassert(~contains(code, 'for'), 'Không cho dùng for');\r\nassert(~contains(code, 'while'), 'Không cho dùng while');\r\n%%\r\nnumber = '1-23-45 6';\r\ncorrect_answer = '123-456';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '123 4-567';\r\ncorrect_answer = '123-45-67';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '123 4-5678';\r\ncorrect_answer = '123-456-78';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5048 479  2-57---6-65 323408- 3 0 44 53832506002399320060523835 44 0 3 -804323 56-6---75-2  974 8405';\r\ncorrect_answer = '504-847-925-766-532-340-830-445-383-250-600-239-932-006-052-383-544-038-043-235-667-529-748-405';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '885-2- 703- 33 -307 -2-588';\r\ncorrect_answer = '885-270-333-307-25-88';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '18 61891-7449764808-74-2166  73266237  6612-47-8084679447-19816 81';\r\ncorrect_answer = '186-189-174-497-648-087-421-667-326-623-766-124-780-846-794-471-981-681';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '--4-88- 8056928602564-99-4652068296508 -88-4--';\r\ncorrect_answer = '488-805-692-860-256-499-465-206-829-650-88-84';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '2 950668--55--866059 2';\r\ncorrect_answer = '295-066-855-866-05-92';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '- -99508 9009 80599- -';\r\ncorrect_answer = '995-089-009-805-99';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = ' 7542-528825-2457 ';\r\ncorrect_answer = '754-252-882-524-57';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '85  58';\r\ncorrect_answer = '85-58';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '7817 2 -77- 2 7187';\r\ncorrect_answer = '781-727-727-187';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5--5';\r\ncorrect_answer = '55';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = ' 5486-513315-6845 ';\r\ncorrect_answer = '548-651-331-568-45';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-999841-44-148999-';\r\ncorrect_answer = '999-841-441-489-99';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '7934 -4--- 3--- 7--0 68---5445885445---86 0--7 ---3 ---4- 4397';\r\ncorrect_answer = '793-443-706-854-458-854-458-607-344-397';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-  220985027  --  720589022  -';\r\ncorrect_answer = '220-985-027-720-589-022';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '651831 6 168--55193-5621 -6-92014  2 2 11 2 2  41029-6- 1265-39155--861 6 138156';\r\ncorrect_answer = '651-831-616-855-193-562-169-201-422-112-241-029-612-653-915-586-161-381-56';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-7-4825-5- 07 628--------826 70 -5-5284-7-';\r\ncorrect_answer = '748-255-076-288-267-055-28-47';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-- 2171645---30- 8380624--35  031  130  53--4260838 -03---5461712 --';\r\ncorrect_answer = '217-164-530-838-062-435-031-130-534-260-838-035-461-712';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '4 25-  -494- -  612-08--61724-2 5710-1-5650  0565-1-0175 2-42716--80-216  - -494-  -52 4';\r\ncorrect_answer = '425-494-612-086-172-425-710-156-500-565-101-752-427-168-021-649-45-24';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '9  7-1062-0163-57488475-3610-2601-7  9';\r\ncorrect_answer = '971-062-016-357-488-475-361-026-01-79';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '-9-1609  0 45 1368464-9290  0929-4648631 54 0  9061-9-';\r\ncorrect_answer = '916-090-451-368-464-929-009-294-648-631-540-906-19';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5  5';\r\ncorrect_answer = '55';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '628826';\r\ncorrect_answer = '628-826';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5-0 4-45------54-4 0-5';\r\ncorrect_answer = '504-455-44-05';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '15 9-3430 4041180-0726-9-56 - 2443 4--9-499481  184994-9--4 3442 - 65-9-6270-0811404 0343-9 51';\r\ncorrect_answer = '159-343-040-411-800-726-956-244-349-499-481-184-994-943-442-659-627-008-114-040-343-951';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '90-03562-1 941--256 -- 9-5- -61-9 8-2 2198 00 8912 2-8 9-16- -5-9 -- 652--149 1-26530-09';\r\ncorrect_answer = '900-356-219-412-569-561-982-219-800-891-228-916-596-521-491-265-30-09';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '8 2882 8';\r\ncorrect_answer = '828-828';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '90427 -0--7512 8 6 6-19-48-8 88 8-84-91-6 6 8 2157--0- 72409';\r\ncorrect_answer = '904-270-751-286-619-488-888-849-166-821-570-724-09';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '61-67 05 0045 26 -8--9--5--5 42 9834 8443781221873448 4389 24 5--5--9--8- 62 5400 50 76-16';\r\ncorrect_answer = '616-705-004-526-895-542-983-484-437-812-218-734-484-389-245-598-625-400-507-616';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '87126  98-742368-44932070888807023944-863247-89  62178';\r\ncorrect_answer = '871-269-874-236-844-932-070-888-807-023-944-863-247-896-21-78';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '5 867768 5';\r\ncorrect_answer = '586-776-85';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = '1  89893   20 -804--  --408- 02   39898  1';\r\ncorrect_answer = '189-893-208-044-080-239-89-81';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nnumber = ' 186960670076069681 ';\r\ncorrect_answer = '186-960-670-076-069-681';\r\nresult = solution(number)\r\nassert(isequal(correct_answer, result))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4945898,"edited_by":4945898,"edited_at":"2026-02-01T15:35:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2026-02-01T15:35:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T12:40:48.000Z","updated_at":"2026-04-01T12:48:58.000Z","published_at":"2026-01-31T12:40:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a phone number as a string number. number consists of digits, spaces ' ', and/or dashes '-'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou would like to reformat the phone number in a certain manner. Firstly, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eremove\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e all spaces and dashes. Then, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egroup\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the digits from left to right into blocks of length 3 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003euntil\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e there are 4 or fewer digits. The final digits are then grouped as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2 digits: A single block of length 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3 digits: A single block of length 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4 digits: Two blocks of length 2 each.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe blocks are then joined by dashes. Notice that the reformatting process should \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enever\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e produce any blocks of length 1 and produce \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eat most\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e two blocks of length 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe phone number after formatting.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number = \\\"1-23-45 6\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"123-456\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The digits are \\\"123456\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \\\"123\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: There are 3 digits remaining, so put them in a single block of length 3. The 2nd block is \\\"456\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJoining the blocks gives \\\"123-456\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number = \\\"123 4-567\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"123-45-67\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe digits are \\\"1234567\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: There are more than 4 digits, so group the next 3 digits. The 1st block is \\\"123\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: There are 4 digits left, so split them into two blocks of length 2. The blocks are \\\"45\\\" and \\\"67\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJoining the blocks gives \\\"123-45-67\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 3:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number = \\\"123 4-5678\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"123-456-78\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e The digits are \\\"12345678\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: The 1st block is \\\"123\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: The 2nd block is \\\"456\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: There are 2 digits left, so put them in a single block of length 2. The 3rd block is \\\"78\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eJoining the blocks gives \\\"123-456-78\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2 \u0026lt;= number.length \u0026lt;= 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003enumber consists of digits and the characters '-' and ' '.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are at least \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etwo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e digits in number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60411,"title":"Compute a sequence with the whyphi sieve","description":"A few problems on Cody involve sieving. For example, Cody Problem 45367 involves the famous Sieve of Eratosthenes. CP 50811 uses the sieve of Flavius Josephus, and CP 50913 uses the golden sieve. \r\nThis problem uses a process that I will call the whyphi sieve: \r\nMake a list x of integers 1, 2, 3,… \r\nRemove the first term. That is, delete x(1).\r\nRenumber the terms. \r\nDelete x(2) and x(2+1)\r\nRenumber the terms. \r\nDelete x(3), x(3+2), and x(3+2+1). \r\nContinue renumbering and deleting terms in this way. \r\nWrite a function to compute the nth term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 266.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 133.017px; transform-origin: 407px 133.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170.375px 7.79167px; transform-origin: 170.375px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA few problems on Cody involve sieving. For example, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45367\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 45367\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.075px 7.79167px; transform-origin: 138.075px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the famous Sieve of Eratosthenes. \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50811\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 50811\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.967px 7.79167px; transform-origin: 127.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uses the sieve of Flavius Josephus, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50913\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 50913\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 7.79167px; transform-origin: 73.5167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uses the golden sieve. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.65px 7.79167px; transform-origin: 188.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem uses a process that I will call the whyphi sieve: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 143.033px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 71.5167px; transform-origin: 391px 71.5167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.775px 7.79167px; transform-origin: 105.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake a list x of integers 1, 2, 3,… \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 130.667px 7.79167px; transform-origin: 130.667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemove the first term. That is, delete x(1).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRenumber the terms. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 69.8333px 7.79167px; transform-origin: 69.8333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDelete x(2) and x(2+1)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRenumber the terms. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 107.567px 7.79167px; transform-origin: 107.567px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDelete x(3), x(3+2), and x(3+2+1). \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 166.758px 7.79167px; transform-origin: 166.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eContinue renumbering and deleting terms in this way. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 181.108px 7.79167px; transform-origin: 181.108px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the nth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = whyphiSieve(n)\r\n  c = 100*[0.000057513128234 0.093378634167431 -2.856145294974328]\r\n  y = polyval(c,n);\r\nend","test_suite":"%%\r\nassert(isequal(whyphiSieve(1),2))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(5),14))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(19),79))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(54),305))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(89),594))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(135),1032))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(336),3443))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(689),8948))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(1000),14685))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(4509),109040))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(whyphiSieve(428)),116991))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(whyphiSieve(620)),225368))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(10000),315192))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(20000),793960))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-04T15:38:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-28T02:46:53.000Z","updated_at":"2026-03-30T07:39:19.000Z","published_at":"2024-05-28T02:47:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few problems on Cody involve sieving. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45367\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45367\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the famous Sieve of Eratosthenes. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50811\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 50811\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e uses the sieve of Flavius Josephus, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50913\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 50913\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e uses the golden sieve. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem uses a process that I will call the whyphi sieve: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a list x of integers 1, 2, 3,… \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemove the first term. That is, delete x(1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRenumber the terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDelete x(2) and x(2+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRenumber the terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDelete x(3), x(3+2), and x(3+2+1). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eContinue renumbering and deleting terms in this way. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the nth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61277,"title":"The Optimal 2D Guillotine Cutting Stock Problem","description":"You are working in a factory that produces rectangular glass sheets. You have a large stock plate of size W x H. Customers have placed order for N differents types of smaller rectangular pieces. Each piece type  has dimensions  and a specific market value .\r\nThe Challenge:\r\nYou need to cut the stock plate to maximize the total value of the pieces obtained. However, you must follow the Guillotine Cut constraint:\r\nEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\r\nYou can rotate the pieces 90 degrees if it helps.\r\nThis is a \"2nd-stage\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). Or, to make it harder, we allow recursive guillotine cuts to any depth.\r\nInput:\r\nStockSize: A 1x2 vector [W, H] ( The dimensions of the large plate ).\r\nItems: An N x 3 matrix. Each row is [width, height, value].\r\nOutput:\r\nmaxValue: The maximum total value you can extract from the stock plate","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 440.367px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 333.5px 220.183px; transform-origin: 333.5px 220.183px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 31.7333px; text-align: left; transform-origin: 309.5px 31.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are working in a factory that produces rectangular glass sheets. You have a large stock plate of size \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eH\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Customers have placed order for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e differents types of smaller rectangular pieces. Each piece type \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"20\" style=\"width: 42.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a specific market value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12.5\" height=\"20\" style=\"width: 12.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eThe Challenge:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 21px; text-align: left; transform-origin: 309.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou need to cut the stock plate to maximize the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etotal value\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the pieces obtained. However, you must follow the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGuillotine Cut constraint:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 122.6px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 61.3px; transform-origin: 316.5px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 20.4333px; text-align: left; transform-origin: 288.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou can rotate the pieces 90 degrees if it helps.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 30.65px; text-align: left; transform-origin: 288.5px 30.65px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is a \"2nd-stage\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOr, to make it harder, we allow recursive guillotine cuts to any depth.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 20.4333px; transform-origin: 316.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eStockSize: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA 1x2 vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[W, H]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ( The dimensions of the large plate ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eItems:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e An \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex 3 matrix. Each row is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e[width, height, value].\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 309.5px 10.5px; text-align: left; transform-origin: 309.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4333px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 316.5px 10.2167px; transform-origin: 316.5px 10.2167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 288.5px 10.2167px; text-align: left; transform-origin: 288.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emaxValue:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e The maximum total value you can extract from the stock plate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function maxValue = solve_guillotine(StockSize,Item)\r\n\r\nend","test_suite":"%% Test Case 1: \r\nassert(isequal(solve_guillotine([10, 10], [5, 5, 100]), 400))\r\n\r\n%% Test Case 2: \r\nItems2 = [3, 3, 10; 4, 2, 8; 1, 10, 12];\r\nassert(isequal(solve_guillotine([10, 10], Items2), 120)) % Giá trị giả định\r\n\r\n%% Test Case 3: \r\nrand_w = randi([15, 20]);\r\nrand_h = randi([15, 20]);\r\nval1 = randi([50, 100]);\r\nval2 = randi([50, 100]);\r\nitems_rand = [rand_w, floor(rand_h/2), val1; rand_w, ceil(rand_h/2), val2];\r\nexpected = val1 + val2;\r\nactual = solve_guillotine([rand_w, rand_h], items_rand);\r\nassert(actual \u003e= expected);\r\n\r\n%% Test Case 4: \r\nassert(isequal(solve_guillotine([5, 5], [10, 10, 100; 6, 2, 50]), 0))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945722,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-17T14:07:03.000Z","updated_at":"2026-04-05T12:47:10.000Z","published_at":"2026-03-17T14:07:03.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are working in a factory that produces rectangular glass sheets. You have a large stock plate of size \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e x \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. Customers have placed order for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e differents types of smaller rectangular pieces. Each piece type \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e has dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew_{i} \\\\times h_{i}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e and a specific market value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_{i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe Challenge:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYou need to cut the stock plate to maximize the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etotal value\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e of the pieces obtained. However, you must follow the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGuillotine Cut constraint:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eEvery cut must go from one edge of the current plate to the opposite edge in a straight line (horizontal or vertical), splitting the plate into two smaller rectangles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eYou can rotate the pieces 90 degrees if it helps.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eThis is a \\\"2nd-stage\\\" guillotine problem, meaning you first cut the stock plate into several strips (first stage), and then each strip is cut into individual pieces (second stage). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOr, to make it harder, we allow recursive guillotine cuts to any depth.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStockSize: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eA 1x2 vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[W, H]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e ( The dimensions of the large plate ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eItems:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e An \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003ex 3 matrix. Each row is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[width, height, value].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaxValue:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e The maximum total value you can extract from the stock plate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55,"title":"Counting Sequence","description":"Given a vector x, find the \"counting sequence\" y.\r\n\r\nA counting sequence is formed by \"counting\" the entries in a given sequence.\r\n\r\nFor example, the sequence\r\n\r\n x = 5, 5, 2, 1, 1, 1, 1, 3\r\n\r\ncan be read as\r\n\r\n Two 5's, one 2, four 1's, one 3\r\n\r\nwhich translates to\r\n\r\n y = 2, 5, 1, 2, 4, 1, 1, 3\r\n\r\nSo y is the counting sequence for x.\r\n\r\nFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\r\n","description_html":"\u003cp\u003eGiven a vector x, find the \"counting sequence\" y.\u003c/p\u003e\u003cp\u003eA counting sequence is formed by \"counting\" the entries in a given sequence.\u003c/p\u003e\u003cp\u003eFor example, the sequence\u003c/p\u003e\u003cpre\u003e x = 5, 5, 2, 1, 1, 1, 1, 3\u003c/pre\u003e\u003cp\u003ecan be read as\u003c/p\u003e\u003cpre\u003e Two 5's, one 2, four 1's, one 3\u003c/pre\u003e\u003cp\u003ewhich translates to\u003c/p\u003e\u003cpre\u003e y = 2, 5, 1, 2, 4, 1, 1, 3\u003c/pre\u003e\u003cp\u003eSo y is the counting sequence for x.\u003c/p\u003e\u003cp\u003eFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\u003c/p\u003e","function_template":"function y = CountSeq(x)\r\ny = x;\r\nend","test_suite":"%%\r\nx = [5 5 2 1 1 1 1 3];\r\ncorrect = [2 5 1 2 4 1 1 3];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = [9];\r\ncorrect = [1 9];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = ones(1,9);\r\ncorrect = [9 1];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = 1:9;\r\ncorrect = [1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n%%\r\nx = [1 2 2 1];\r\ncorrect = [1 1 2 2 1 1];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n","published":true,"deleted":false,"likes_count":30,"comments_count":13,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2181,"test_suite_updated_at":"2013-03-14T15:22:01.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:25.000Z","updated_at":"2026-04-14T15:14:41.000Z","published_at":"2012-01-18T01:00:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector x, find the \\\"counting sequence\\\" y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA counting sequence is formed by \\\"counting\\\" the entries in a given sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = 5, 5, 2, 1, 1, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ecan be read as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Two 5's, one 2, four 1's, one 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich translates to\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = 2, 5, 1, 2, 4, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo y is the counting sequence for x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":803,"title":"Twist 'n' Match","description":"Given n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places. \r\n\r\nThe number of matches m is calculated as follows: \r\n \r\n m = nnz(rot90(a)==a)\r\n\r\nYour answer a is clearly not unique. It must only meet the criteria stated above.\r\n\r\nExamples:\r\n\r\n Input n = 2, m = 1\r\n One possible output: a = [ 1 2 \r\n                            1 3 ]\r\n\r\n Input n = 3, m = 7\r\n One possible output: a = [ 0 1 1\r\n                            1 1 1\r\n                            1 1 1 ]","description_html":"\u003cp\u003eGiven n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places.\u003c/p\u003e\u003cp\u003eThe number of matches m is calculated as follows:\u003c/p\u003e\u003cpre\u003e m = nnz(rot90(a)==a)\u003c/pre\u003e\u003cp\u003eYour answer a is clearly not unique. It must only meet the criteria stated above.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input n = 2, m = 1\r\n One possible output: a = [ 1 2 \r\n                            1 3 ]\u003c/pre\u003e\u003cpre\u003e Input n = 3, m = 7\r\n One possible output: a = [ 0 1 1\r\n                            1 1 1\r\n                            1 1 1 ]\u003c/pre\u003e","function_template":"function a = twist_n_match(n,m)\r\n  a = 0;\r\nend","test_suite":"%%\r\nn = 2; \r\nm = 1;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 3; \r\nm = 7;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 6; \r\nm = 6;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 10; \r\nm = 11;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 10; \r\nm = 14;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 20; \r\nm = 83;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 21; \r\nm = 1;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));","published":true,"deleted":false,"likes_count":9,"comments_count":9,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":85,"test_suite_updated_at":"2012-07-03T15:06:05.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-06-28T15:15:32.000Z","updated_at":"2025-12-16T03:15:00.000Z","published_at":"2012-06-29T19:04:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number of matches m is calculated as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ m = nnz(rot90(a)==a)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour answer a is clearly not unique. It must only meet the criteria stated above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input n = 2, m = 1\\n One possible output: a = [ 1 2 \\n                            1 3 ]\\n\\n Input n = 3, m = 7\\n One possible output: a = [ 0 1 1\\n                            1 1 1\\n                            1 1 1 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1286,"title":"MatCAT - Reconstruct X from Its X-rays","description":"Consider a matrix x\r\n\r\n x = [ 1 2 0\r\n       0 5 0 \r\n       3 0 8 ]\r\n\r\nIf we sum x along the rows we get\r\n\r\n row_sums = [3 5 11]\r\n\r\nSumming along the columns gives \r\n\r\n col_sums = [4 7 8]\r\n\r\nMetaphorically, we might call these sums \"x-rays\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a \u003chttp://en.wikipedia.org/wiki/X-ray_computed_tomography CAT scan\u003e. Can you put all the bones in the right place?\r\n\r\nAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\r\n\r\nBonus question: Under what circumstances does the answer become unique? Discuss.","description_html":"\u003cp\u003eConsider a matrix x\u003c/p\u003e\u003cpre\u003e x = [ 1 2 0\r\n       0 5 0 \r\n       3 0 8 ]\u003c/pre\u003e\u003cp\u003eIf we sum x along the rows we get\u003c/p\u003e\u003cpre\u003e row_sums = [3 5 11]\u003c/pre\u003e\u003cp\u003eSumming along the columns gives\u003c/p\u003e\u003cpre\u003e col_sums = [4 7 8]\u003c/pre\u003e\u003cp\u003eMetaphorically, we might call these sums \"x-rays\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a \u003ca href = \"http://en.wikipedia.org/wiki/X-ray_computed_tomography\"\u003eCAT scan\u003c/a\u003e. Can you put all the bones in the right place?\u003c/p\u003e\u003cp\u003eAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\u003c/p\u003e\u003cp\u003eBonus question: Under what circumstances does the answer become unique? Discuss.\u003c/p\u003e","function_template":"function x = matcat(row_sums,col_sums)\r\n  x = 0;\r\nend","test_suite":"%%\r\nrow_sums = [3 5 11];\r\ncol_sums = [4 7 8];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [2 2 2 2 2 6];\r\ncol_sums = [2 3 3 3 3 2];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [65 65 65 65 65];\r\ncol_sums = [65 65 65 65 65];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [22 34 33];\r\ncol_sums = [15 23 18 21 12];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = 55;\r\ncol_sums = [1 2 3 4 5 6 7 8 9 10];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":4,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":147,"test_suite_updated_at":"2013-02-21T17:46:45.000Z","rescore_all_solutions":false,"group_id":23,"created_at":"2013-02-21T17:25:12.000Z","updated_at":"2026-04-02T21:49:21.000Z","published_at":"2013-02-21T17:46:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a matrix x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 1 2 0\\n       0 5 0 \\n       3 0 8 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf we sum x along the rows we get\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ row_sums = [3 5 11]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSumming along the columns gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ col_sums = [4 7 8]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMetaphorically, we might call these sums \\\"x-rays\\\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/X-ray_computed_tomography\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCAT scan\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Can you put all the bones in the right place?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBonus question: Under what circumstances does the answer become unique? Discuss.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1499,"title":"Kryptos - CIA Cypher Sculpture: Vigenere Encryption","description":"The \u003chttp://en.wikipedia.org/wiki/Kryptos Kryptos Sculpture\u003e contains four encypted messages.\r\n\r\nThis Challenge is to Encrypt two of the original messages for the sculptor.\r\n\r\nThe method employed is \u003chttp://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher Vigenere Encryption\u003e. One clarification is that \"?\" are removed from the coding sequence and then re-inserted in the final encoded message.\r\n\r\nOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\r\n\r\nFor coding purposes spaces and punctuation are removed, except \"?\".\r\n\r\nPhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\r\n\r\n*Input:* Encode Phrase, Vigenere alphabet word, Vigenere shift word\r\n\r\nVigenere alphabet word ='KRYPTOS';\r\n\r\nVigenere shift word ='PALIMPSEST';\r\n\r\n*Output:* EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\r\n\r\nThe encryption matrix for this case:\r\n\r\n  KRYPTOSABCDEFGHIJLMNQUVWXZ\r\n\r\n  PTOSABCDEFGHIJLMNQUVWXZKRY\r\n  ABCDEFGHIJLMNQUVWXZKRYPTOS\r\n  LMNQUVWXZKRYPTOSABCDEFGHIJ\r\n  IJLMNQUVWXZKRYPTOSABCDEFGH\r\n  MNQUVWXZKRYPTOSABCDEFGHIJL\r\n  PTOSABCDEFGHIJLMNQUVWXZKRY\r\n  SABCDEFGHIJLMNQUVWXZKRYPTO\r\n  EFGHIJLMNQUVWXZKRYPTOSABCD\r\n  SABCDEFGHIJLMNQUVWXZKRYPTO\r\n  TOSABCDEFGHIJLMNQUVWXZKRYP\r\n\r\nFollow Up Challenges:\r\n\r\n1) \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption Vigenere Decryption\u003e\r\n\r\n2) Dictionary search\r\n\r\n3) KRYPTOS Part IV\r\n\r\n\u003chttp://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1 KRYPTOS Solutions\u003e\r\n\r\n  \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eThe \u003ca href = \"http://en.wikipedia.org/wiki/Kryptos\"\u003eKryptos Sculpture\u003c/a\u003e contains four encypted messages.\u003c/p\u003e\u003cp\u003eThis Challenge is to Encrypt two of the original messages for the sculptor.\u003c/p\u003e\u003cp\u003eThe method employed is \u003ca href = \"http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher\"\u003eVigenere Encryption\u003c/a\u003e. One clarification is that \"?\" are removed from the coding sequence and then re-inserted in the final encoded message.\u003c/p\u003e\u003cp\u003eOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\u003c/p\u003e\u003cp\u003eFor coding purposes spaces and punctuation are removed, except \"?\".\u003c/p\u003e\u003cp\u003ePhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Encode Phrase, Vigenere alphabet word, Vigenere shift word\u003c/p\u003e\u003cp\u003eVigenere alphabet word ='KRYPTOS';\u003c/p\u003e\u003cp\u003eVigenere shift word ='PALIMPSEST';\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\u003c/p\u003e\u003cp\u003eThe encryption matrix for this case:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eKRYPTOSABCDEFGHIJLMNQUVWXZ\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ePTOSABCDEFGHIJLMNQUVWXZKRY\r\nABCDEFGHIJLMNQUVWXZKRYPTOS\r\nLMNQUVWXZKRYPTOSABCDEFGHIJ\r\nIJLMNQUVWXZKRYPTOSABCDEFGH\r\nMNQUVWXZKRYPTOSABCDEFGHIJL\r\nPTOSABCDEFGHIJLMNQUVWXZKRY\r\nSABCDEFGHIJLMNQUVWXZKRYPTO\r\nEFGHIJLMNQUVWXZKRYPTOSABCD\r\nSABCDEFGHIJLMNQUVWXZKRYPTO\r\nTOSABCDEFGHIJLMNQUVWXZKRYP\r\n\u003c/pre\u003e\u003cp\u003eFollow Up Challenges:\u003c/p\u003e\u003cp\u003e1) \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption\"\u003eVigenere Decryption\u003c/a\u003e\u003c/p\u003e\u003cp\u003e2) Dictionary search\u003c/p\u003e\u003cp\u003e3) KRYPTOS Part IV\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1\"\u003eKRYPTOS Solutions\u003c/a\u003e\u003c/p\u003e","function_template":"function encoded=encode_vigenere(phrase,word1,word2)\r\n encoded=phrase;\r\nend","test_suite":"phrase=upper('Between subtle shading and the absence of light lies the nuance of iqlusion.');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\nencoded_exp='EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD';\r\nword1='KRYPTOS';\r\nword2='PALIMPSEST';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n%%\r\n\r\nphrase=upper('It was totally invisible Hows that possible? They used the Earths magnetic field X The information was gathered and transmitted undergruund to an unknown location X Does Langley know about this? They should Its buried out there somewhere X Who knows the exact location? Only WW This was his last message X Thirty eight degrees fifty seven minutes six point five seconds north Seventy seven degrees eight minutes forty four seconds west ID by rows');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\n\r\nencoded_exp='VFPJUDEEHZWETZYVGWHKKQETGFQJNCEGGWHKK?DQMCPFQZDQMMIAGPFXHQRLGTIMVMZJANQLVKQEDAGDVFRPJUNGEUNAQZGZLECGYUXUEENJTBJLBQCRTBJDFHRRYIZETKZEMVDUFKSJHKFWHKUWQLSZFTIHHDDDUVH?DWKBFUFPWNTDFIYCUQZEREEVLDKFEZMOQQJLTTUGSYQPFEUNLAVIDXFLGGTEZ?FKZBSFDQVGOGIPUFXHHDRKFFHQNTGPUAECNUVPDJMQCLQUMUNEDFQELZZVRRGKFFVOEEXBDMVPNFQXEZLGREDNQFMPNZGLFLPMRJQYALMGNUVPDXVKPDQUMEBEDMHDAFMJGZNUPLGEWJLLAETG';\r\n\r\nword1='KRYPTOS';\r\nword2='ABSCISSA';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n%%\r\nphrase=upper('The fox jumped over the moon');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\nencoded_exp='VUIPFSBYVQMMWPIMEVPZCVK';\r\nword1='KRYPTOS';\r\nword2='MATLAB';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n\r\n%%\r\nphrase=upper('Between the Devil and the deep blue sea');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\n\r\nword1='AWEIGH';\r\nword2='MATLAB';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\nencoded_exp='SENMEDWTZNDDFIBLNNCHVTEDIBBCEZOA';\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":28,"created_at":"2013-05-11T20:36:34.000Z","updated_at":"2026-03-07T04:46:20.000Z","published_at":"2013-05-11T21:19:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Kryptos\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKryptos Sculpture\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contains four encypted messages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to Encrypt two of the original messages for the sculptor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe method employed is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere Encryption\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. One clarification is that \\\"?\\\" are removed from the coding sequence and then re-inserted in the final encoded message.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor coding purposes spaces and punctuation are removed, except \\\"?\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Encode Phrase, Vigenere alphabet word, Vigenere shift word\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere alphabet word ='KRYPTOS';\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere shift word ='PALIMPSEST';\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe encryption matrix for this case:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[KRYPTOSABCDEFGHIJLMNQUVWXZ\\n\\nPTOSABCDEFGHIJLMNQUVWXZKRY\\nABCDEFGHIJLMNQUVWXZKRYPTOS\\nLMNQUVWXZKRYPTOSABCDEFGHIJ\\nIJLMNQUVWXZKRYPTOSABCDEFGH\\nMNQUVWXZKRYPTOSABCDEFGHIJL\\nPTOSABCDEFGHIJLMNQUVWXZKRY\\nSABCDEFGHIJLMNQUVWXZKRYPTO\\nEFGHIJLMNQUVWXZKRYPTOSABCD\\nSABCDEFGHIJLMNQUVWXZKRYPTO\\nTOSABCDEFGHIJLMNQUVWXZKRYP]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow Up Challenges:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere Decryption\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Dictionary search\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) KRYPTOS Part IV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKRYPTOS Solutions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45426,"title":"The Tortoise and the Hare - 02","description":"Previous problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\u003e\r\n\r\nSuppose in an infinitely long line, the tortoise is standing in position 0.\r\n\r\nFrom that place, it can move in both +ve and -ve direction. The condition is that, in i-th jump, it can move i step forward or backward. \r\n\r\nSo one possible scenario can be -\r\n\r\n 0 [i=1] --- 1 step forward\r\n 1 [i=2] --- 2 step forward\r\n 3 [i=3] --- 3 step forward\r\n 6 [i=4] --- 4 step backward\r\n 2 [i=5] --- 5 step forward\r\n 7 [i=6] --- 6 step backward\r\n 1 [i=7] --- 7 step forward\r\n 8\r\n\r\nIf you look carefully, you'll find that -- If the tortoise moves this way, it'll always be able to reach any destination (x). \r\n\r\nThe question is what is the minimum number of moves it'll take to reach destination x.\r\n\r\nFor example -- \r\n\r\n if x=8\r\n  \u003e\u003e in the above example, it takes 7 steps\r\n  \u003e\u003e but if it moves this way  -- [0,-1,1,4,8] -- steps required = 4.\r\n\r\nSo 4 is the optimum way.\r\n","description_html":"\u003cp\u003ePrevious problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\"\u003ehttps://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSuppose in an infinitely long line, the tortoise is standing in position 0.\u003c/p\u003e\u003cp\u003eFrom that place, it can move in both +ve and -ve direction. The condition is that, in i-th jump, it can move i step forward or backward.\u003c/p\u003e\u003cp\u003eSo one possible scenario can be -\u003c/p\u003e\u003cpre\u003e 0 [i=1] --- 1 step forward\r\n 1 [i=2] --- 2 step forward\r\n 3 [i=3] --- 3 step forward\r\n 6 [i=4] --- 4 step backward\r\n 2 [i=5] --- 5 step forward\r\n 7 [i=6] --- 6 step backward\r\n 1 [i=7] --- 7 step forward\r\n 8\u003c/pre\u003e\u003cp\u003eIf you look carefully, you'll find that -- If the tortoise moves this way, it'll always be able to reach any destination (x).\u003c/p\u003e\u003cp\u003eThe question is what is the minimum number of moves it'll take to reach destination x.\u003c/p\u003e\u003cp\u003eFor example --\u003c/p\u003e\u003cpre\u003e if x=8\r\n  \u0026gt;\u0026gt; in the above example, it takes 7 steps\r\n  \u0026gt;\u0026gt; but if it moves this way  -- [0,-1,1,4,8] -- steps required = 4.\u003c/pre\u003e\u003cp\u003eSo 4 is the optimum way.\u003c/p\u003e","function_template":"function y = rabbit(n)","test_suite":"%%\r\nassert(isequal(rabbit(8),4))\r\n%%\r\nassert(isequal(rabbit(18),7))\r\n%%\r\nassert(isequal(rabbit(-600),35))\r\n%%\r\nassert(isequal(rabbit(6600),115))\r\n%%\r\nassert(isequal(rabbit(99999),449))\r\n%%\r\nassert(isequal(rabbit(-16),7))\r\n%%\r\nassert(isequal(rabbit(45237929),9513))\r\n%%\r\nassert(isequal(rabbit(46),11))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-04-07T05:20:53.000Z","updated_at":"2026-03-30T18:12:01.000Z","published_at":"2020-04-07T05:20:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.mathworks.com/matlabcentral/cody/problems/45425-the-tortoise-and-the-hare-01\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSuppose in an infinitely long line, the tortoise is standing in position 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFrom that place, it can move in both +ve and -ve direction. The condition is that, in i-th jump, it can move i step forward or backward.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo one possible scenario can be -\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 0 [i=1] --- 1 step forward\\n 1 [i=2] --- 2 step forward\\n 3 [i=3] --- 3 step forward\\n 6 [i=4] --- 4 step backward\\n 2 [i=5] --- 5 step forward\\n 7 [i=6] --- 6 step backward\\n 1 [i=7] --- 7 step forward\\n 8]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you look carefully, you'll find that -- If the tortoise moves this way, it'll always be able to reach any destination (x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe question is what is the minimum number of moves it'll take to reach destination x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example --\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ if x=8\\n  \u003e\u003e in the above example, it takes 7 steps\\n  \u003e\u003e but if it moves this way  -- [0,-1,1,4,8] -- steps required = 4.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo 4 is the optimum way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":520,"title":"Choose the best fitting dominoes","description":"You will be given a cell array of nx2 matrices. Choose one row from each matrix. These are the ordered pairs that will be placed in a line like this.\r\n{[1 2  [4 5 [0 4\r\n  3 5   2 4  3 2\r\n  1 5]  5 1] 5 3]}\r\nChoices might be: [1 2 3]\r\nyields: [1 2][2 4][5 3]\r\n    or: abs(2-2) + abs(4-5)\r\n    or:        0 + 1\r\n    or: 1\r\nYou are trying to minimize the score, the absolute difference of the sum of the difference at the intersections.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 267.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 133.517px; transform-origin: 407px 133.517px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou will be given a cell array of nx2 matrices. Choose one row from each matrix. These are the ordered pairs that will be placed in a line like this.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e{[1 2  [4 5 [0 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 64px 8.5px; tab-size: 4; transform-origin: 64px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  3 5   2 4  3 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 72px 8.5px; tab-size: 4; transform-origin: 72px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  1 5]  5 1] 5 3]}\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5px 8px; transform-origin: 78.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eChoices might be: [1 2 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eyields: [1 2][2 4][5 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    or: abs(2-2) + abs(4-5)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; tab-size: 4; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    or:        0 + 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    or: 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 341px 8px; transform-origin: 341px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are trying to minimize the score, the absolute difference of the sum of the difference at the intersections.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function order = ChooseBestFittingDominoes(list)\r\n  order = 1;\r\nend","test_suite":"%%\r\nlist = {[1 3; 2 4; 5 6],[4 6; 2 5;6 7],[3 4; 6 1; 4 6]}\r\n\r\nselections = [2 1 2];\r\n\r\nassert(isequal(ChooseBestFittingDominoes(list),selections))\r\n\r\n\r\n%%\r\nlist = {[1 5; 2 3; 2 2; 3 4; 0 3], \r\n        [0 4; 1 5; 2 2; 4 5; 4 6],\r\n        [7 7; 3 8; 4 7; 5 9; 0 4]};\r\n    \r\nselections = [4 4 4];\r\n\r\nassert(isequal(ChooseBestFittingDominoes(list),selections))\r\n\r\n%%\r\nlist = {[1 4; 2 2; 1 1; 3 3],[1 2; 2 3],[2 2]};\r\n\r\nselections = [3 1 1];\r\n\r\nassert(isequal(ChooseBestFittingDominoes(list),selections))\r\n\r\n%%\r\nlist = {[3 4; 1 2; 5 6],[5 7; 11 13; 17 19; 29 31; 2 3]};\r\n    \r\nselections = [2 5];\r\n\r\nassert(isequal(ChooseBestFittingDominoes(list),selections))","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":240,"edited_by":223089,"edited_at":"2022-12-28T15:22:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":243,"test_suite_updated_at":"2022-12-28T15:22:04.000Z","rescore_all_solutions":false,"group_id":5,"created_at":"2012-03-22T17:38:21.000Z","updated_at":"2026-02-19T11:48:16.000Z","published_at":"2012-04-03T18:00:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will be given a cell array of nx2 matrices. Choose one row from each matrix. These are the ordered pairs that will be placed in a line like this.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[{[1 2  [4 5 [0 4\\n  3 5   2 4  3 2\\n  1 5]  5 1] 5 3]}]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eChoices might be: [1 2 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[yields: [1 2][2 4][5 3]\\n    or: abs(2-2) + abs(4-5)\\n    or:        0 + 1\\n    or: 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are trying to minimize the score, the absolute difference of the sum of the difference at the intersections.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":733,"title":"Extract Built In Functions and Toolbox Functions from String or Function Handle","description":"Find the Built-In functions and Toolbox functions in either a string or a function handle.\r\n\r\nGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\r\n\r\n*Inputs:*\r\n\r\nfh=@(x)log10(x)+log2(x)+abs(x)\r\n\r\nstr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\r\n\r\n*Outputs:*\r\n\r\n'abs log2 log10'\r\n\r\n'abs filter numel sin filter2 smooth3'\r\n\r\nRelated to \r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer Cody_464\u003e","description_html":"\u003cp\u003eFind the Built-In functions and Toolbox functions in either a string or a function handle.\u003c/p\u003e\u003cp\u003eGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003efh=@(x)log10(x)+log2(x)+abs(x)\u003c/p\u003e\u003cp\u003estr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e'abs log2 log10'\u003c/p\u003e\u003cp\u003e'abs filter numel sin filter2 smooth3'\u003c/p\u003e\u003cp\u003eRelated to  \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer\"\u003eCody_464\u003c/a\u003e\u003c/p\u003e","function_template":"function functions = find_functions(fh_str)\r\n  functions = '';\r\nend","test_suite":"%%\r\nfh_str='log2(x)+smooth3(x,y)+abs(2)+log10(5)';\r\nexp_str='abs log10 log2 smooth3';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='for k=log10(x):log2(x)+abs(x)';\r\nexp_str='abs for log10 log2';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str=@(x)x^2+sin(x)-cos(x);\r\nexp_str='cos sin';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='@(x)x^2+sin(x)-cos(x)';\r\nexp_str='cos sin';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='filter2(x,A)+filter(x)-cos(x) expm(z)';\r\nexp_str='cos filter expm filter2';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)';\r\nexp_str='abs filter numel sin filter2 smooth3';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":"2012-07-18T13:18:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-01T23:09:01.000Z","updated_at":"2026-03-31T20:12:36.000Z","published_at":"2012-06-02T00:17:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the Built-In functions and Toolbox functions in either a string or a function handle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efh=@(x)log10(x)+log2(x)+abs(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003estr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'abs log2 log10'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'abs filter numel sin filter2 smooth3'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody_464\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":875,"title":"Return a list sorted by number of consecutive occurrences","description":"Inspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\r\n y = [2 3 7 1 93]\r\nBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\r\n y = [2 1 3 7 1 93]\r\nUpdate - Test case added 22-8-22","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 185.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 92.9333px; transform-origin: 407px 92.9333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365px 8px; transform-origin: 365px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e y = [2 3 7 1 93]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e y = [2 1 3 7 1 93]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUpdate - Test case added 22-8-22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = popularity_bis(x)\r\n  y = unique(x);\r\nend","test_suite":"%%\r\nx = [1 2 2 2 3 3 7 7 93]\r\ny_correct1 = [2 3 7 1 93] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [1 1 2 2 2 3 3 7 7 1 93];\r\ny_correct2 = [2 1 3 7 1 93] ;\r\nassert(isequal(popularity_bis(x),y_correct2))\r\n%%\r\nx = [1 0 0 2 2 -5 9 9 2 1 1 1 0 11];\r\ny_correct1 = [1 0 2 9 -5 0 1 2 11] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [1 0 1 1 0 0];\r\ny_correct0 = [0 1 0 1] ;\r\nassert(isequal(popularity_bis(x),y_correct0))\r\n%%\r\nx = [0 1 0 0 1 1];\r\ny_correct1 = [0 1 0 1] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [-2 -2 3 3 3 -7 -7 0 0 0];\r\ny_correct1 = [0 3 -7 -2] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":5,"created_by":5390,"edited_by":223089,"edited_at":"2022-08-22T17:30:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":432,"test_suite_updated_at":"2022-08-22T17:30:08.000Z","rescore_all_solutions":false,"group_id":12,"created_at":"2012-08-03T00:17:38.000Z","updated_at":"2026-04-16T10:17:24.000Z","published_at":"2012-08-03T00:32:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 3 7 1 93]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 1 3 7 1 93]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUpdate - Test case added 22-8-22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2237,"title":"Mmm! Multi-dimensional Matrix Multiplication ","description":"You have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions.\r\nYou may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar.\r\nIn the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u003e2, or either ndims(A)\u003cn or ndims(B)\u003cn, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\r\n\r\nWrite a function |mtimesm| that does this, and ask Mathworks to include it in the |elmat| toolbox of the Next Release.","description_html":"\u003cp\u003eYou have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions.\r\nYou may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar.\r\nIn the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u0026gt;2, or either ndims(A)\u0026lt;n or ndims(B)\u0026lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003emtimesm\u003c/tt\u003e that does this, and ask Mathworks to include it in the \u003ctt\u003eelmat\u003c/tt\u003e toolbox of the Next Release.\u003c/p\u003e","function_template":"function C = mtimesm(A,B)\r\n  C = A*B;\r\nend","test_suite":"%% case 1\r\nA = 1;\r\nB = 2;\r\nC = mtimesm(A,B);\r\nC_correct = 2;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 2\r\nA = rand(2,3);\r\nB = rand(3,4);\r\nC = mtimesm(A,B);\r\nC_correct = A*B;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 3\r\nA = rand(2,3);\r\nB = 2;\r\nC = mtimesm(A,B);\r\nC_correct = 2*A;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 4\r\nA = rand(2,3,2);\r\nB = rand(3,4,2);\r\nC = mtimesm(A,B);\r\nC_correct = cat(3,A(:,:,1)*B(:,:,1),A(:,:,2)*B(:,:,2));\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 5\r\nA = rand(2,3,3);\r\nB = rand(3,4);\r\nC = mtimesm(A,B);\r\nC_correct = cat(3,A(:,:,1)*B,A(:,:,2)*B,A(:,:,3)*B); \r\nassert(isequal(C,C_correct))\r\n\r\n%% case 6\r\nA = rand(4,3,1,2);\r\nB = rand(3,2,2);\r\nC = mtimesm(A,B);\r\nC_correct(:,:,1,1) = A(:,:,1,1)*B(:,:,1);\r\nC_correct(:,:,1,2) = A(:,:,1,2)*B(:,:,1);\r\nC_correct(:,:,2,1) = A(:,:,1,1)*B(:,:,2);\r\nC_correct(:,:,2,2) = A(:,:,1,2)*B(:,:,2);\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 7\r\nA = rand(4,3,1,2);\r\nB = rand(3,2,1,1,2);\r\nC = mtimesm(A,B);\r\nC_correct(:,:,1,1,1) = A(:,:,1,1)*B(:,:,1,1,1);\r\nC_correct(:,:,1,1,2) = A(:,:,1,1)*B(:,:,1,1,2);\r\nC_correct(:,:,1,2,1) = A(:,:,1,2)*B(:,:,1,1,1);\r\nC_correct(:,:,1,2,2) = A(:,:,1,2)*B(:,:,1,1,2);\r\nassert(isequal(C,C_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":5,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":"2014-03-07T06:22:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-06T11:17:42.000Z","updated_at":"2026-04-03T03:22:22.000Z","published_at":"2014-03-06T11:17:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions. You may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar. In the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u0026gt;2, or either ndims(A)\u0026lt;n or ndims(B)\u0026lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emtimesm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that does this, and ask Mathworks to include it in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eelmat\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e toolbox of the Next Release.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44080,"title":"Construct a \"diagAdiag\" matrix","description":"Construct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\r\n\r\nFor:\r\n\r\n  n = 4\r\n\r\noutput\r\n\r\n  M = \r\n[1   2   6   7;\r\n 3   5   8   13;\r\n 4   9   12  14;\r\n 10  11  15  16]\r\n\r\nNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\r\n","description_html":"\u003cp\u003eConstruct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\u003c/p\u003e\u003cp\u003eFor:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003en = 4\r\n\u003c/pre\u003e\u003cp\u003eoutput\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eM = \r\n[1   2   6   7;\r\n3   5   8   13;\r\n4   9   12  14;\r\n10  11  15  16]\r\n\u003c/pre\u003e\u003cp\u003eNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\u003c/p\u003e","function_template":"function y = diagAdiag(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [1 2 6; 3 5 7;4 8 9];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = [1   2   6   7; 3   5   8   13;4   9   12  14;10  11  15  16];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = [1 2 6 7 15;3 5 8 14 16;4 9 13 17 22;10 12 18 21 23;11 19 20 24 25];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = [ 1  2  6  7 15 16;\r\n              3  5  8 14 17 26;\r\n              4  9 13 18 25 27;\r\n             10 12 19 24 28 33;\r\n             11 20 23 29 32 34;\r\n             21 22 30 31 35 36];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [ 1  2  6  7 15 16 28;\r\n              3  5  8 14 17 27 29;\r\n              4  9 13 18 26 30 39;\r\n             10 12 19 25 31 38 40;\r\n             11 20 24 32 37 41 46;\r\n             21 23 33 36 42 45 47;\r\n             22 34 35 43 44 48 49];\r\nassert(isequal(diagAdiag(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":98103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":"2017-04-19T17:09:18.000Z","rescore_all_solutions":false,"group_id":24,"created_at":"2017-03-04T19:12:05.000Z","updated_at":"2026-04-02T22:13:25.000Z","published_at":"2017-03-04T19:15:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConstruct a matrix whose elements begin from 1 and end at n^2 with the order of arrangement as shown below:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[n = 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M = \\n[1   2   6   7;\\n3   5   8   13;\\n4   9   12  14;\\n10  11  15  16]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote the elements increase and decrease along alternating diagonals with the last element being always n^2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42829,"title":"Number construction III","description":"Given a positive integer, n, return a, b and c, such that\r\n\r\n1. n = a^1.5+b^2.5+c^3.5\r\n\r\n2. a, b and c are all positive integers greater than 1\r\n\r\nIf a solution does not exist, set all three output variables to zero.\r\n\r\nExample 1:\r\n\r\nn = 168\r\n\r\na = 4\r\n\r\nb = 4\r\n\r\nc = 4\r\n\r\nExample 2:\r\n\r\nn = 100\r\n\r\na = 0\r\n\r\nb = 0\r\n\r\nc = 0","description_html":"\u003cp\u003eGiven a positive integer, n, return a, b and c, such that\u003c/p\u003e\u003cp\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/p\u003e\u003cp\u003e2. a, b and c are all positive integers greater than 1\u003c/p\u003e\u003cp\u003eIf a solution does not exist, set all three output variables to zero.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003en = 168\u003c/p\u003e\u003cp\u003ea = 4\u003c/p\u003e\u003cp\u003eb = 4\u003c/p\u003e\u003cp\u003ec = 4\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003en = 100\u003c/p\u003e\u003cp\u003ea = 0\u003c/p\u003e\u003cp\u003eb = 0\u003c/p\u003e\u003cp\u003ec = 0\u003c/p\u003e","function_template":"function [a b c] = numcons(n)\r\n  a = n;\r\n  b = n;\r\n  c = n;\r\nend","test_suite":"%%\r\nn = 100;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 888;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 19666;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 314159;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 1100;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 116600;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 16999;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 10000040;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 94940;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 9990;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2016-04-28T18:19:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-25T11:29:04.000Z","updated_at":"2026-04-09T07:25:23.000Z","published_at":"2016-04-25T11:29:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, n, return a, b and c, such that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. a, b and c are all positive integers greater than 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a solution does not exist, set all three output variables to zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 168\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":375,"title":"N-Dimensional Array Slice","description":"Given an N-dimensional array, _A_, an index, _I_, and a dimension, _d_, return the _I_ th elements of _A_ in the _d_ dimension.\r\n\r\nFor Example,\r\n\r\n    array_slice( A, 5, 3 )\r\n\r\nis equivalent to\r\n\r\n    A(:,:,5)\r\n\r\nNote: |eval| and |str2func| cannot be used. This is a Cody restriction.","description_html":"\u003cp\u003eGiven an N-dimensional array, \u003ci\u003eA\u003c/i\u003e, an index, \u003ci\u003eI\u003c/i\u003e, and a dimension, \u003ci\u003ed\u003c/i\u003e, return the \u003ci\u003eI\u003c/i\u003e th elements of \u003ci\u003eA\u003c/i\u003e in the \u003ci\u003ed\u003c/i\u003e dimension.\u003c/p\u003e\u003cp\u003eFor Example,\u003c/p\u003e\u003cpre\u003e    array_slice( A, 5, 3 )\u003c/pre\u003e\u003cp\u003eis equivalent to\u003c/p\u003e\u003cpre\u003e    A(:,:,5)\u003c/pre\u003e\u003cp\u003eNote: \u003ctt\u003eeval\u003c/tt\u003e and \u003ctt\u003estr2func\u003c/tt\u003e cannot be used. This is a Cody restriction.\u003c/p\u003e","function_template":"function S = arraySlice(A,I,d)\r\n  S = A(:,I);\r\nend","test_suite":"%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,4,2),A(:,4)))\r\n\r\n%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,4,1),A(4,:)))\r\n\r\n%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,1,10),A))\r\n\r\n%%\r\nA = randn(5,5,5,3);\r\nassert(isequal(arraySlice(A,3,4),A(:,:,:,3)))\r\n\r\n%%\r\nA = randn(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2);\r\nassert(isequal(arraySlice(A,2,18),A(:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,2)))","published":true,"deleted":false,"likes_count":13,"comments_count":7,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":285,"test_suite_updated_at":"2012-02-21T16:23:06.000Z","rescore_all_solutions":false,"group_id":19,"created_at":"2012-02-21T16:23:06.000Z","updated_at":"2026-04-12T19:36:51.000Z","published_at":"2012-02-21T16:23:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an N-dimensional array,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, an index,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and a dimension,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e th elements of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e dimension.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor Example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    array_slice( A, 5, 3 )]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis equivalent to\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    A(:,:,5)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeval\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2func\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cannot be used. This is a Cody restriction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":579,"title":"Spiral In","description":"Create an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\r\nFor example:\r\n\u003e\u003e spiralIn(4,5)\r\nans =\r\n   1    14    13    12    11\r\n   2    15    20    19    10\r\n   3    16    17    18     9\r\n   4     5     6     7     8","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"baseline-shift: 0px; block-size: 190px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 95px; transform-origin: 468.5px 95px; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 434.5px 8px; transform-origin: 434.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8417px 8px; transform-origin: 40.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 108px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 464.5px 54px; transform-origin: 464.5px 54px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; spiralIn(4,5)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1    14    13    12    11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   2    15    20    19    10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   3    16    17    18     9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   4     5     6     7     8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = spiralIn(m,n)\r\n  s = zeros(m,n);\r\nend","test_suite":"%%\r\nm = 3;\r\nn = 5;\r\ns_correct = [1 12 11 10 9; 2 13 14 15 8; 3 4 5 6 7];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 3;\r\ns_correct = [1 12 11; 2 13 10; 3 14 9; 4 15 8; 5 6 7];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n\r\n%%\r\nm = 1;\r\nn = 1;\r\ns_correct = 1;\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 0;\r\ns_correct = zeros(5,0);\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 2;\r\nn = 2;\r\ns_correct = [1 4; 2 3];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n\r\n%%\r\n%Test case added on 4/4/26\r\nm = 2*randi(10)+1;\r\ns_correct = m^2+1-rot90(spiral(m));\r\nassert(isequal(spiralIn(m,m),s_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":3117,"edited_by":223089,"edited_at":"2026-04-04T09:55:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":120,"test_suite_updated_at":"2026-04-04T09:55:47.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-04-13T13:50:35.000Z","updated_at":"2026-04-04T09:56:24.000Z","published_at":"2012-04-13T13:50:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e spiralIn(4,5)\\nans =\\n   1    14    13    12    11\\n   2    15    20    19    10\\n   3    16    17    18     9\\n   4     5     6     7     8]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46938,"title":"Numerical computation of the optimal shooting angle of a catapult","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 879.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 439.833px; transform-origin: 406.5px 439.833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 32.1667px; text-align: left; transform-origin: 383.5px 32.1667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"109\" height=\"21\" style=\"width: 109px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and an initial velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the optimal shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"18.5\" style=\"width: 16px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21.25px; text-align: left; transform-origin: 383.5px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Consider the states \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAoCAYAAAACJPERAAABwElEQVRYR+3VS6hNcRTH8c9VKDKSiTKRiYzlGUaSYsRAMbkD14SSooiUt4nEwMDUoxhI6d6ukRtKMWBmrESUwkheLa20O23249zTGdy964zO/7++a/1+a63/iCF8I0Ng6qADVb2Tt5N3WhToGmlaZPxXkJkt7ywswVZsxzrcx3584s8jsQbnsQL7cKeJH2XyzsVSvMV63MICbMZDbMRBfMMWHMXVfqHF+4txA5sy+D0cwjG8bwIqnq1qpDkpY1T2IKs7iVdtgXGvChpnxnAtIXtxHb8GDV2NSXzFNryoAC7KRCOxM2Vn61QaTXUbK7E7PS6LNR978kx0/AmcagONTo5so3niO4fj+FESbHbKvgqP20JDhV1Yiw+IBprIaj7+R+KosjV0OY7kbxnG8Q47snvDu1gOU/hZSKIRNMYjfPmChbiMK3iC4ryGrzGv4ddNPO+pujY0gBHkMF5n5qdzG0UXhrcXcQAv8Sb/i23VOz61oeHfzgz8Of2Laoqyxb69hHk4i7v4XuJtbWg/s957t4P+VaTORmoq/VDk3YBHbTdS0wrjoY8qR3MSnuECnva+vYOQtzLZDlopUT8HZo68vwGa/l8pXtmErgAAAABJRU5ErkJggg==\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-position of the projectile, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45\" height=\"22\" style=\"width: 45px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,     \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45.5\" height=\"22\" style=\"width: 45.5px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"22\" style=\"width: 63px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e    \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"22\" style=\"width: 87.5px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.   \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.1667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 31.5833px; text-align: left; transform-origin: 383.5px 31.5833px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"97.5\" height=\"19.5\" style=\"width: 97.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"17.5\" style=\"width: 47.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"231.5\" height=\"20\" style=\"width: 231.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Plotting \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e vs. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 2: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse the following update law, to incrementally update the shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATMAAAAoCAYAAACSPh2yAAAR5UlEQVR4Xu3dB7A1S1UF4IUZIwgGzFYRFDFizmIExEgyoJhFzDlHzBkDKiKYURCzICbAgKAIiqKoZc4551Tfq97PZpg5M+eeOeem6aq//vf+O6Fnd/faa6+9u+9NsrXNApsFNgtcAQvc5Ap8w/YJmwU2C2wWyAZm2yTYLLBZ4EpYYAOzKzGM20dsFtgssIHZNgc2C2wWuBIW2MDsSgzj9hGX3AIvmuQ1k/xUkv+5wN/yskleOsmTkvzvRevnBmYXbUS2/lw3C9wmyYcl+dwkf37BP/45krx7kudO8q1J/usi9XdfMHuuJK+W5PWTvFCSX03yuCT/fJE+6pL25aZJXivJ6yZ5ziS/mOSJSf79kn7P1u15C9wuyUcn+fQ9gezF2xp85ST/mOQnkvzmidgSzLh3kue7aIC2FMxc9wZJviLJ45N8cZI7JPmmJE9L8kF7Dsb8MF+fK3i7d0nymUkeluTrk7xjkq9tk+Xjr5CzeLHGQN4+yRcm+eok/73yUD9vko9L8iFJPqXZ9MKFREnY4ivbeFtTSxoC8YlJ7pzkE5I8OcnnJ3nPJB+c5DtPBGgcLyb5Q0l+cknHT3HNEjBzzTsn+bIkP5ykFhfDfk2S+yT5yCQPPJEhT2GXU70D0zUJP69Nji9t1P2lknx7kjs2+37/qTp0xPcAGQvAXMI8/y7JvZI8c+V3YjvfleTVk/xokvdI8tcrv+PQx/l+jIxNvmBhuAb8zI83TfLejVTox1sneWySn22g9nuHdm7h/ezMIVn7p3rnzq4tAbM3S/LNSX6nLaw/7p74aUk+O8kjk7x/kr9faIjtstxQ4/duSb4uyfc23eQfmmF4vi9vjNffvPF/XHKjAWYM3re8TJKHJ/mIJD+28nddBmb2Kkm+Ksn9FoL5CyT5osY2PzDJN3bEoQdvjP4HVrbn1OPM349KcrMkn3UEhr33Z8yBGXGS0Hf7CYZQYPZzTRj8/b17cH1veKPGvljg7k0jK2v0YHYKRwFosENhC/b0b0cYlg9tz/eOF2kL8vs6GxzhlRfykVjZZyTByq2fuTC7WBwwe0RzCH/bfVkPZtge53eqRj9/UBIA+2uneukudJ36We8NxozovgKzXz5SyHDe9jnW+1+i08aEDrSdXujvwewUoRJg/ZnWJ972X4/14QPm+dPXEMxePsl3NI10CSutyEj5BklnKDn0YCaR8DlHHrv+8SU10c2B6Llqk7uYGcqKlWljRnyeFu+b/BuYLZ9BbP7hLZmCyQ5ZmScVc/GzDcyW2/YyXPkOLXspI/jbMx2+eXMw95hgZW7Hqn8wya3ac08JZt7/SS0Lf+4y0xSYSf0+OAnD03PeL0lPbX1Ezx6UZxBa/+QyzKZz7mPvSSVNJFSG5Re3aIzlbZtDuX9LwR+r6+fFzDCUJyz4KPYgehP1abe3TvJXTW9SwPnUkWeYn2QSCYax8hZZ5NdoutUrJMGWf72J6RJdar6GTIMDdw8g8nMCuHvVid21lSs8qrGUPxzpk5AR2OjXksVvTX1be867JvHsYaux8++SSbLhp2ww4gFJ7pnkN0754uG7psBMqcD3tIun4nDZFZPxrVqWE3sbAt55fttFfHeJpkJLbUqwfaUk353kVVuJxsccSccqG50azNRHKSMA0rJwu5p5ZoH+Upf5Y8e3a3qNBV/PoEOppPdv5uMvTGQzK4uMIX9AywwKmYATUb5vFXUoTVICoQ7QtXQvdZbGRuX+LZNgUMLBKVmmwjJAPJfUwcoe0rK/uzTp92oJOn0GsjK5p2zFDDmbJWFz3zfjKOxm11dM8k9JOHBz40v2LUkaAzNamfqf+zZPZYDGxL1TL7i1B6j3eoc8+40XLMh6vlDgW5oD+PEkJuKfjrxc+r1qjz651RId0se5e08JZi/cMnlKNN4myc/PdK7GaWhngCSL9ozGYrEmACeqkGzYVZrhvRIr5nkvwltQFtLrNRlADdd/Nlas2r0P//+iJTGUVihctZb0lTTj/32fYta+FQHARufCwbdsUREAdO1YxtA7gao/3rnEnnNzYd+fV6ShdMvcXtrYgiNAnEhVj27MVu0d1rp3ZnYMzGQoDHRlMqdCHPSyxMhTZ1GWGmzXdecBZlUTpF8WylQ2y+CaHNreg3oG45wKzACQCQwAluqslWQaliT4TAseeAGgav0CH9MblW7IDGJlQ0dRYSAdSKg5jDZ6aUXBuBorIFKtxP03bHVkw8xiLXwZwF3hYN8PzwZSY6ynB9fzqigQ8iuzgQVzAF12YgesU4lOXzPXs9Gpb56c3mNgtu8in/JCZ1hTV/oWtpa1XDrgjEHDmWLGaxrrVGBWmTmLfimY0WvVVUmWcKw8eG3Gxlowvb72kV0KAMfArNcjx7J/Nf/H+teDGTAaZn7nnl1gZgeNouipJmTF8DDNpc3uEYz01FsL65uF+kvmdgGZOUcv5rSVp/R1l6IWNYl/ufTjXTcEsz5DCaRsmxjTNHqPsCtc2qcvV/3a3ma7FnLv3deaoH3S4RA7H5L672sW6YEv2bzyXHW+Uxos7LdoHRfKCKt2VZ0vBbMxdlzA/pSmQfUZx1OBWZ+hHAPNGsM+OhKaYTunbvuAWV/uRWfEfDkiOGR8sd0/akC2d93aEMz6BbcrQ0kEVfBIAxI2VI2JweYpCbwWkEwobeEYTTaKpxd+2Ne49raYtfvcg5TFORW+98mXPoP1gq3a2p5Y250IvUu98HmDWT+JZckll7CapVuNLG5b52hZ2t+0DNo3TNhgF5j12/DGMvUFZmPFymuB2VyY2YPUVIayD5dldO0m+d0DJi0JgG3MU/bmcB12MNdqbpmPnMOuVuVe3lO4QTt7n7Yb5KFNq+wZmXUOlzg/yR1j/5ixlwzBrM9QTnmEqmA2YYZhkMG2W4CHkKa1YOc875yxhj/XZ+KurJM6LCnwY+zx27dfc9f3CZMphtMnX4aMF5gRwXkvzMZG47VO1DhmmGm8sAbAY4FYdFgar7ykPKHsajLbOidjZzFo9iQKrX5rYPxdYObSvobSHPKcasIbW8xk2Iah4KFgtjQB0GcopxJMtkTJmiIOUwmCuTnZ/xyY6R8bIwn6MJeccf/S0Lmf2wiOSgisW/kLvc18HyM+wIyWBkskQTh7TujZ2hDMllQT9xkfAioxtd+SUYsWc1u6Z6vQV+ZIenZX02deyd8YoeOIzgJm+2qDU31ams3s64HGForn94x37JrKcq4dUhwTzHqdDIABCGdivcmI5jS3+Iw572xeOXlDM7GH+socmFm4xp9eAwgJ+co4HMFkTkko0OmGzuJQMFtamjG3s6Yv8VmqPc7Z1s+fv53koXZuKtM+fE7NHeO8q2awEgVYn8hEacqfLTyMspI6atkmNeR9wQwrI9rZx9fHvP0HVsZuEkFHrLpP3F2318S6KmDWLxS6kELM2njeswb0fKnXXDKBXXMsMOu3bQkvhZZCY/2X8SsBHbiYi5zZsCkRUuLQF6FyZuQF+0gBxDDzNQdm3uGdnkFspw/Ti0Ua2MiUNHIomFUSSGSxi5XOgVlPOsayvEvHfXhdndYCIJcyf0TCkUtzOxqsUwzYeO2rvZYTMEaT0d4QzOpj3nziha/dyjYYoU+pllFqsFD3fdjSeYDZWQf8rPf1JS9jrKtCH3VTNAQLq2+1kOiUCj3X1CKPAWb6i7ULAyu8rG+yWF+u6SRYPS8t2TF2UMGntkMqhzVbdBQ6GoY1LBadAzNgiI39StNflu4pPBTMjCdnL5u5a31UqDvGuuooJU7NmXdrnndnHsgWk3B2ZVtrXlYJiTk5l0ntkxqYtT9Du4vQRDrE/16e6nW5YSR44xoZglkvKqLZjmj5l3Z1eVnhAXQk+A07UwkE96g9g8Zieo3HI1SOed/rAGZ9Dc1wMNmI+Ok4FZ52jK5XAkFiRqW67TPOZBcKKbB9+oITGKaAeG0w69PsvGqFlzVfgI3+08/IFqq+/dvYMUf+HXsabvuqkEjfh6HHLjDTNzVmkiv6tc9JL2uAWRVOSwKMbU8yRr3c0IdvvV2J4Nj71FHbgEHCxM4FjgM4CKt3JY0wZY6Sc9BkGJ0oK7GgzGV4xFeVkEiWzGVS+4LxsaiOXvexbZuaUL8/kltCxLYuJIkWf7ckNGRhqvq7G7ZRjtWZFfvqD88jvkJE7IJHcLrkmDcr9mFhul4HUVD/D22nPOB1ADP2LvZlMItd0RhVPWuovRMIxlqF78XqAOD7tmr6PzgrXWz3rQ1m5oFCSn3sw8vqZjEPoSPHp5ZsalsTYKqTY4nGVWNmkXu2UNNEL912Lssn2y4ZgRlp9nVW9kymjFMAqmPHlvcOaSwj3YvyU/tuS+/inMb25epTz75Kl7Z2ADBWR/iXOdTfsWa9sot5YR2+TnN4uwpRK5RDSMxNz0Zm7IX9kYlkk6Jl40MKmDugcejgaJSYtVIMmAOwgBiA73+pS7G/u7Qxczw4J2gcjcGN4DwGZiWyov4+EAgxPKFV1mEXsqP8PA4ENUm8FGrPbUC/LmDGW96phVUmi61MAJ9GBuCmspMVvhPOeU0AANws7jUOxFwTzHqdbBhe1sJzjcMJMQa7AcyrKUcH+HhpLJQMgklhc8BLZtf5aO4FAGxLqwVUlfHEKGR/AUBtO8IEHQEvfNnV3FPsByBY5P5oniU6kSwAxIBCxOLZmvGVFeXIh6djENhVCyiinip/kP2jqwF6cwNrt6dTxISdTNmr7G+fNOJBdxUJiKholVOgU6GcnQ82jgNOjMzOgrF3ldOwP7U/LHKXPWv+65c5Z4xEFTCCHccqH4r9kVUwamGoZlyf5ReqjIHZWZ18FdwSdqWKyysPF9u+NU9TJSKHJgDO+p3ncV+F7yaVQTfA2Mha546d4nDG87Db1DttBregHJ3D8wtZ1e+Zw5q/hXrmsoW99oGHxVJkZmmCa5XYVIIOAGPwQJZs4TAIgIZgTIFg1bZh+4BT+AaopprMut+z4F17VervORFKaxO9iBbVkwLAZ/uONcFsuAWDV+PFhmAGjWVzZJOq+TdeiiCLbfTNB4zpQdcJzIYOgPaBOY/pj3vOlWt3uSjDBnNsYu53K2B6NowLB9dyHGVw85f2ifkIyddoNU+EyaQg60qIOPcb1IZb7YT/79ROKhnrF/YHXJxssaSw9pBvG5ZQTe5VXhPMegQFbMS8pZtFr0uYedZBLa8p7KAVSawI5YH/1pZboE7sEK4K2ecYBe3PoqY/zR1vvbwX/38lhkgnpf3sYkFLn13zRPJNGL/091r2zF+Y6d7hiSI9CMsES+YJf5dmgpd+Q39dH+1x4Hb6AM/R3TNrghltw545mo4z5BXNMgwRUUbEZJjSdzYwmx7qoQBKZLYdqDKixF7sdW3mcJbJd9HvKYdLf6HnDstf+v7TrMglIoVjso8KeQnf9oMe0orFDLdAWV/0qgJv/+37FKgDoz5xh7GSdhS5KlKlmyEn9lBik8JKOuVoqHdI50furVIxoaWTTIAZ3YxDF0LbQYBF3gCoa4FZhXy3beluQiVvJl4XuxM8/daYKfHxLGBWqXnC7D41bSvb++iP6wVQEwm4mWw0HpqFTBAhfCqzdfQOXqIX9LtXZNM4BL/7oJws6YNzUJJgTmEnhOZjsg/mI6YrXZDcOORdTsFFIsgyasUk3oTKkkVCQmAGxGiAJCBJENlSSZNK3Clsray772cfOCFctU71dXhKybGmQNW90TeBLGckWQBI1SUCMyH6DQx0LTCrGigTpCqH/RujWYwQdRcl3RfMJBccj4L1eY80NbYie7aUWh9rANZ+brGJ/pfm2nYj9Y9h2Es3Vc6xdl8u+/PMd6K+kgC67ViTpfSrFZ0GPFducNHs4fsAkTnhlGKhIJACAFWFgHjYwSNUxATV2gE2dqnN6q4BIIq3zTOlLOfB/NW9AeXa8VLb0DBmobkxutGJrwVmhw6qAjgMDmUUmm5ts8AxLWCxKlWQkcNmNA7hiU2Qvw7HvysJkklFNK7E914UMDvmxN2evVlgs8CzWqAYDuZZx7NfehttYHbph3D7gM0Ce1tANlzhNW3tEI1u7xcf84YNzI5p3e3ZmwU2C5zMAhuYnczU24s2C2wWOKYFNjA7pnW3Z28W2CxwMgv8Hzpz12VmMIZCAAAAAElFTkSuQmCC\" width=\"153.5\" height=\"20\" style=\"width: 153.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21.8333px; text-align: left; transform-origin: 383.5px 21.8333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"20\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"298\" height=\"20\" style=\"width: 298px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis a difference angle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"55.5\" height=\"17.5\" style=\"width: 55.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ean update parameter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample of algorithm's numerical result:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 40px; transform-origin: 403.5px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = catapult(25,3,25)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    0.8431\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 383.5px 132.167px; text-align: left; transform-origin: 383.5px 132.167px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"570\" height=\"259\" style=\"vertical-align: baseline;width: 570px;height: 259px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function theta = catapult(xd,yd,v0) \r\n  \r\n    global g nu;\r\n    \r\n    g   = -9.81;  % grav. acceleration\r\n    nu  = 0.5;    % air friction coeff.\r\n    k   = 0;      % solver increments\r\n    dt  = 1e-2;   % timesteps\r\n    T   = 10;     % simulation time\r\n    TOL = 1e-2;   % absolute tolerance\r\n    \r\n    [~,y] = ode45(@ODECatapult,0:dt:T,[v0,0,0]); \r\n    \r\n    % solver for optimal angle\r\n    while (e \u003e= TOL) \u0026\u0026 (k \u003e 150)        \r\n        \r\n        %theta = theta + beta;\r\n        \r\n        k = k+1;    % add increment\r\n    end\r\n  \r\n    function dx = ODECatapult(t,x)\r\n        global g nu;\r\n        %% fill in ordinary differential equation %%\r\n    end\r\n    \r\n    function e = EuclideanDistance(y,xd,yd)\r\n        %% fill in computation of smallest euclidean distance %%\r\n    end\r\n    \r\n    function beta = UpdateLaw(y,e,lambda)\r\n        %% fill in update law to update the shooting angle %%\r\n    end\r\nend","test_suite":"xd = 8;\r\nyd = 2;\r\nv0 = 35;\r\ny_correct = 1.446;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),3),y_correct))\r\n\r\n%%\r\nxd = 15;\r\nyd = 5;\r\nv0 = 35;\r\ny_correct = 1.33;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),2),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":636373,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-19T12:41:43.000Z","updated_at":"2025-01-02T11:31:42.000Z","published_at":"2020-10-19T13:39:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$z_d = [x_d, y_d] \\\\in \\\\mathbb{R}^2$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and an initial velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, find the optimal shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Consider the states \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-position of the projectile, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x_1} = x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_2 = x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e      \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_3 = -\\\\nu x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_4 = -g - \\\\nu x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.   \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\; (\\\\text{m/s}^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t = 0) = (0,0,v_0 \\\\cos(\\\\theta_k), v_0 \\\\sin(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Plotting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e vs. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 2: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eUse the following update law, to incrementally update the shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{k+1} = \\\\theta_k + \\\\lambda \\\\, \\\\text{sign}(\\\\theta_{e,k})\\\\,e_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee_k \\\\in \\\\mathbb{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{e,k} = \\\\text{atan2}(d_y,d_x) - \\\\text{atan2}(v_0\\\\sin(\\\\theta_k),v_0\\\\cos(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis a difference angle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\lambda = 0.01$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ean update parameter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample of algorithm's numerical result:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[theta = catapult(25,3,25)\\ntheta = \\n    0.8431\\n    ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"570\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57477,"title":"Solve an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there are no solutions, the function should return three empty vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is adapted from one in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.egmo2012.org.uk/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2012 European Girls’ Math Olympiad\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":53064,"title":"Amazing circle of numbers 1 to n","description":"For given natural number n, create amazing circle of numbers 1 to n without a repeat.\r\nThis circle is that the sum of any two adjacent numbers is a perfect square.\r\nFor example, if n = 32,\r\n\r\nSo, output is\r\n                          [1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15]\r\nIf the condition is satisfied, it is the correct answer regardless of the order of the vectors.\r\nIf there is no amazing circle vector, return empty vector [].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 984px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 492px; transform-origin: 407px 492px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor given natural number n, create amazing circle of numbers 1 to n without a repeat.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis circle is that the sum of any two adjacent numbers is a perfect square.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, if n = 32,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 774px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 387px; text-align: left; transform-origin: 384px 387px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"768\" height=\"768\" style=\"vertical-align: baseline;width: 768px;height: 768px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSo, output is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                          [1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf the condition is satisfied, it is the correct answer regardless of the order of the vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIf there is no amazing circle vector, return empty vector [].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = amazing_circle(n)\r\n  v = n;\r\nend","test_suite":"%%\r\nn=32;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=33;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=34;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=35;\r\nv = amazing_circle(n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=36;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=37;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))\r\n\r\n%%\r\nn=38;\r\nv = amazing_circle(n);\r\nv = v(1:n);\r\nflag = false;\r\nif length(unique(v)) == n \u0026 (min(v) == 1) \u0026 (max(v) == n)\r\n    for i = 1:n-1\r\n        lst(i) = mod(sqrt(v(i)+v(i+1)), 1) == 0;\r\n    end\r\n    lst(n) = mod(sqrt(v(n)+v(1)), 1) == 0;\r\n    if sum(lst) == n\r\n        flag = true;\r\n    end\r\nend\r\nassert(isequal(flag,true))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":517609,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2021-11-29T05:26:18.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-11-15T02:36:58.000Z","updated_at":"2025-07-07T00:57:09.000Z","published_at":"2021-11-15T04:44:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor given natural number n, create amazing circle of numbers 1 to n without a repeat.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis circle is that the sum of any two adjacent numbers is a perfect square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if n = 32,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"768\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"768\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo, output is\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                          [1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf the condition is satisfied, it is the correct answer regardless of the order of the vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf there is no amazing circle vector, return empty vector [].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57815,"title":"List numbers such that every sum of consecutive positive integers ending in those numbers is not prime","description":"The sequence in question in this problem involves numbers  such that all sums of consecutive positive integers ending with  are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \r\nWrite a function that returns the th number in this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 46.5px; transform-origin: 469px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 31.5px; text-align: left; transform-origin: 445px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sequence in question in this problem involves numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that all sums of consecutive positive integers ending with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth number in this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = lastInCompositeSum(n)\r\n  y = isprime(sum(n:-1:1));\r\nend","test_suite":"%%\r\nfor n = 1:3:51\r\n    y(ceil(n/3)) = lastInCompositeSum(n);\r\nend\r\ny_correct = [1 18 26 33 39 48 58 63 72 78 85 92 95 104 110 118 123];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 104;\r\ny = lastInCompositeSum(n);\r\ny_correct = 226;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 583;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1028;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1117;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1875;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8513;\r\ny = lastInCompositeSum(n);\r\ny_correct = 12567;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 22698;\r\ny = lastInCompositeSum(n);\r\ny_correct = 32092;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 51734;\r\ny = lastInCompositeSum(n);\r\ny_correct = 71082;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 87777;\r\ny = lastInCompositeSum(n);\r\ny_correct = 118638;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 453867;\r\ny = lastInCompositeSum(n);\r\ny_correct = 588425;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1243598;\r\ny = lastInCompositeSum(n);\r\ny_correct = 1579325;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 890;\r\ny = lastInCompositeSum(lastInCompositeSum(lastInCompositeSum(n)));\r\ny_correct = 3949;\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nfiletext = fileread('lastInCompositeSum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2026-03-11T00:52:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-03-20T03:20:55.000Z","updated_at":"2026-03-11T00:52:46.000Z","published_at":"2023-03-20T03:23:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe sequence in question in this problem involves numbers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that all sums of consecutive positive integers ending with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are not prime. The number 12 is not in the sequence because 11+12 is prime. The number 13 is not in the sequence because 13 is prime. However, 14 is in the sequence because all of the sums 14, 14+13, 14+13+12, etc. through 14+13+12+…+1 are not prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth number in this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60461,"title":"Generate a point cloud on an equilateral triangle 2","description":"The input is the iteration parameter H.\r\nThe output is a point cloud W involving N points.\r\nW is N uniformly distributed points on an equilateral triangle.\r\nThe side length of an equilateral triangle is 2.\r\nThe relationship between H and N is as follows:\r\nH = [1 2 3 4 5 6 7 8 9];\r\nN = [4 10 19 31 46 64 85 109 136];\r\nThe results for cases where H is 1 to 6 are as follows.\r\n\r\n\r\nEx)\r\n[W,N] = lattice2(H=1) -\u003e W = [0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0]; N = 4;\r\n[W,N] = lattice2(H=2) -\u003e W = [0 0; 0.5 sqrt(3)/6; 0.5 sqrt(3)/2; 1 0; 1 sqrt(3)/3; 1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 sqrt(3)/2; 2 0]; N = 10;","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 749.188px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 374.594px; transform-origin: 407px 374.594px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe input is the iteration parameter\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eH\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe output is a point cloud\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003einvolving\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003epoints.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eW\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003euniformly distributed points on an equilateral triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe side length of an equilateral triangle is 2.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe relationship between H and N is as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2188px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH = [1 2 3 4 5 6 7 8 9];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2188px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eN = [4 10 19 31 46 64 85 109 136];\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe results for cases where H is 1 to 6 are as follows.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 197px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 98.5px; text-align: left; transform-origin: 384px 98.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 197px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 98.5px; text-align: left; transform-origin: 384px 98.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cimg class=\"imageNode\" width=\"193\" height=\"191\" style=\"vertical-align: baseline;width: 193px;height: 191px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEx)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 64.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 32.1562px; transform-origin: 391px 32.1562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.7188px; text-align: left; transform-origin: 363px 10.7188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[W,N] = lattice2(H=1) -\u0026gt; W = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; N = 4;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 42.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 21.4375px; text-align: left; transform-origin: 363px 21.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e[W,N] = lattice2(H=2) -\u0026gt; W = [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e0 0; 0.5 sqrt(3)/6; 0.5 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esqrt(3)/2; 1 0; 1 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003esqrt(3)/3; 1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esqrt(3)/2; 2 0]; N = 10;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [W,N] = lattice2(H)\r\n  W = [0 0; 1 sqrt(3); 2 0];\r\n  N = size(W,1);\r\nend","test_suite":"%%\r\nH = 1;\r\nA = [0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0];\r\n\r\n[W,N] = lattice2(H);\r\nassert(isequal(N,4))\r\nassert(sum(abs(sortrows(W)-sortrows(A)),'all') \u003c 1e-6)\r\n\r\n%%\r\nH = 2;\r\nA = [0 0; 0.5 sqrt(3)/6; 0.5 sqrt(3)/2; 1 0; 1 sqrt(3)/3;\r\n    1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 sqrt(3)/2; 2 0];\r\n\r\n[W,N] = lattice2(H);\r\nassert(isequal(N,10))\r\nassert(sum(abs(sortrows(W)-sortrows(A)),'all') \u003c 1e-6)\r\n\r\n%%\r\nH = 3;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,19))\r\n\r\n%%\r\nH = 4;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,31))\r\n\r\n%%\r\nH = 5;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,46))\r\n\r\n%%\r\nH = 10;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,166))\r\n\r\n%%\r\nH = 100;\r\n[~,N] = lattice2(H);\r\nassert(isequal(N,15151))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2217275,"edited_by":2217275,"edited_at":"2024-06-09T21:16:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2024-06-09T21:08:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-09T14:14:29.000Z","updated_at":"2026-03-03T11:47:38.000Z","published_at":"2024-06-09T14:24:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input is the iteration parameter\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output is a point cloud\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003einvolving\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003epoints.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eW\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003euniformly distributed points on an equilateral triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe side length of an equilateral triangle is 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe relationship between H and N is as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH = [1 2 3 4 5 6 7 8 9];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eN = [4 10 19 31 46 64 85 109 136];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe results for cases where H is 1 to 6 are as follows.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"191\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"193\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEx)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[W,N] = lattice2(H=1) -\u0026gt; W = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e; N = 4;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[W,N] = lattice2(H=2) -\u0026gt; W = [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0 0; 0.5 sqrt(3)/6; 0.5 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esqrt(3)/2; 1 0; 1 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esqrt(3)/3; 1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esqrt(3)/2; 2 0]; N = 10;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image2.png\",\"relationshipId\":\"rId2\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image3.png\",\"relationshipId\":\"rId3\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image4.png\",\"relationshipId\":\"rId4\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image5.png\",\"relationshipId\":\"rId5\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image6.png\",\"relationshipId\":\"rId6\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAwMAAAL9CAIAAAD4ry2pAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6AYJFDgY21emZAAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAxMC1KdW4tMjAyNCAwNTo1NjoyNDd0e8EAACAASURBVHic7N1/cFTV/f/xt0igiTQoyWgRUhZHEuwUxX4tHVLtbEqtjAN12hGtSNndMjpqaz8WbItMyu7Saj+WwowdgWbE7rX+pIq1DTodR8zNgGESfwDlY2tShOsEUSSLiBgiuJvvH2dZQ35usvfu/fV8/BV3k5PjL/LKOed1z1nd3d0CAADgS6PsngAAAIBtRts9gYyqqiq7pwAAAHyktbVVnJOE5PSELFJVVWXp+HAU/nX7Cv+6fYV/3b5i6b/u7BIMu2MAAMC/SEIAAMC/SEIAAMC/SEIAAMC/SEIAAMC/SEIAAMC/znLIM6YpRgIAgILJBg/WhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+RhAAAgH+NNnGsdDq9e/fuTz755NJLLy0tLTVxZAAAACuYloTq6urq6uo++eQT9ZezZs36zW9+EwgEzBofAADAdObsjq1atWrt2rXjx48PBoPl5eUi0tLSsmDBgtbWVlPGBwAAsIIJSWjnzp3//Oc/N27c2NDQUFdX98orr0SjURE5duzY8uXL8x8fAADAIiYkoc2bN2/YsOGqq67KvrJw4cI77rhDRP7973/v27cv/28BAABgBROS0IwZMy677LJeL958883qg/b29vy/BQAAgBVMSEI33nhj3xfLy8tHjx4tIpMmTcr/WwAAAFjBqucJpVKpzz777Etf+tLFF19s0bcAAADIk5nPE+qpublZRBYvXpz7l1RVVfV9kfYZAADIU78ZQ7EqCT377LOTJk1atGhR7l9C6AEAAFbomzGy2ciSJLR37976+vpHH3107NixVowPAABgCvPPCaXT6Xvuueeuu+6aNWuW6YMDAACYyPwkdP/990+bNu322283fWQAAABzmbw7tnnzZsMw6urqzB0WAADACmYmocbGxr/97W8PP/ywiWMCAABYx7QktH379vXr1z/88MO9Tkl3dHSkUqkLLrjArG8EAABgFnPOCW3btu2BBx6oq6sbN25cz9d379596623fvGLXzTluwAAAJjLhDWhl19++c477xSRnpewisjJkydFZP78+SUlJfl/FwAAANPlm4RaWloGr4ldd911eX4LAAAAi+SbhGbNmsWzoQEAgEtZdQMrAACA85GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAf5GEAACAfw2YhFpbW0cw3OHDh7dv375z5850Op3HrAAAAAphdN+X3njjjbVr1+7evXvPnj25D9TS0nLvvfdOmDBhypQpJ0+eXLp06dy5c++6666xY8eaN1sAAAAznZGEWlpaNmzY0NzcnEqlxowZk/soLS0tkUiktrb2pptuUq8cPXr0+uuvf+uttxKJhJnzBQAAMM8Zu2MXXXRRIpGora0d7igrV6686KKLsjFIRM4999wf//jHTU1NL730kgnTBAAAsMAZSai8vFxEJk2aNKwhjh8/vn///nPPPbfX6+eff76INDc35zdDAAAAq/RzYrqoqGgEA73++uuHDh3q+cr7778vIl/96ldHNjMAAACrmdCiHzdu3JQpU1Kp1LJlyz799FP1Yjqd3rRpU0VFxdy5c/P/FgAAAFYw53lCy5cvF5FXX331pptuOnz4sIjU1tYeP348kUjQHQMAAI7VT4t+BL797W+vWLHivvvue/PNN6+77rqvfe1ro0aN+vvf/15aWpr7IFVVVX1fHNljjQAAALL6zRiKOUlIREKh0DnnnLNy5cpkMvnyyy/fe++9w4pBQugBAADW6JsxstnIzNs2Pv7446997WtlZWWpVGr58uWrV682cXAAAADTmbYmtHLlyv/7v//btGlTR0fHLbfc8t///nfjxo2fffbZPffcY9a3AAAAMJc5a0J1dXWbNm36/e9/X1RUNHHixCeeeGLmzJkiomnatm3bTPkWAAAApjMhCR09evTBBx+cPn36xRdfrF4pLS196KGHpk6dKiJ/+ctf8v8WAAAAVjAhCb322msnT54MBAI9XywtLVXnhHbu3Jn/twAAALCCaeeEuru7e70yY8aMMWPG9L2FAwDykUwm29rakslkR0dHMplMJpNlZWVlZWXl5eVlZWWzZ8+2e4IA3GQkSWj37t0vvvji4sWLL7jgAhH55je/ec4557z22mvpdHrUqM8XmVKpVCqVuvrqq02bLAB/SyaTO3bsqK+vLykpqaioEJHy8vKKiooTJ050dnbu2rVLROrr6ysrK6urqysrK+2eLwAX6CcJdXZ2ikgqlTp16lTfO8jS6fTixYu7urreeuuthx9+WESKi4t//etfL1++fO3atXfffXf2Mx988MELL7zw9ttvt3L+AHwhmUxqmnbgwIGKioo5c+aUlJT0fLekpKSsrExlo87OzgMHDqxZs6asrGzZsmVlZWU2TRmAO5yRhJqbm59//vnGxkYRSaVSCxcuvOKKK8LhsFr7ySotLe3q6powYUL2le9///tjx469//7733zzze9973sismXLlvHjx//1r38d7vMVAaCXtra2NWvWVFVVzZkzZ8hPLikpqaysnDx5sspD8+fPZ78MwCDO6nu+xxZVVVU8YxpAX1u2bNm6devMmTNHsLqTTCZbW1urq6vnzZtnxdwAuFc2eJh2YhoATKdi0OzZs3tth+WorKxs5syZW7duFRHCEIB+mXnbBgCYqK2trb6+fubMmSOLQUpJScns2bObmpra2tpMnBsAzyAJAXAoTdOqq6vzP/KsimaapiWTSVMmBsBLSEIAnEjTNPV8IFNGq6ioKCkpqa+vN2U0AF5CEgLgRDt27Jg8ebKJA1ZWVrJBBqAvkhAAx9mxY4daxTFxTDXajh07TBwTgAeQhAA4Tn19vXpMormqqqrYIAPQC0kIgLNkrxIzfeSysrITJ06wRwagJ5IQAGdpa2uz7oqM4uJii0YG4FIkIQCOY+4JoV4jsyYEoCeSEABnaW1ttTQJWTQyAJciCQHwkeLi4o6ODrtnAcBBSEIAnKW8vNy6wZPJpKXjA3AdkhAAZ6msrLR02ca649gA3IgkBMBxTpw4YdHIyWSysrLSosEBuBFJCICzWLpm09nZad3gANyIJATAWcrKyiZPnmxF1729vX327NnsjgHoiSQEwHHmz5/f3t5u+rBtbW3V1dWmDwvA1UhCABynsrJy8uTJyWTSxDHb29snT57MISEAvZCEADhRdXX1rl27TDzW09bWNn/+fLNGA+AZJCEATjR79uw5c+bs2rXLlNGampouu+wyFoQA9EUSAuBQ6nRz/ken1ZWu4XDYjEkB8BqSEACHUvGlo6MjnzDU1tbW0dFBDAIwEJIQAOcqKytbtmzZhAkTtm7dOtwzQ52dnU1NTd3d3ffddx/NeQADGW33BABgMGVlZfPnzy8vL9+6dWtFRUUuZ306OzsPHDjQ2to6f/78efPmFWCSANyLNSEATldWVjavo6N261a1OLRr166BCvadnZ1tbW1bt27t7u5etmfPvHHjCjxVAK7DmhAAN4jHyxKJcDCYTCZ37NjR2tra1NRUUlJSXFxcUlLS2dmpslFZWVl1dfXSpUtFRP7f/5NIRPbvt3nmAJztrO7ubrvnICJSVVXV2tpq9ywAOFI8LrouDQ09X1PRJ5lMJpPJstN6f2FNjQSDEo0WbKYA3CIbPFgTAuB4sVivGCSnL2od4ih0IiE1NRIKSSBg2eQAuBvnhAA4W02NhMMSDI7kawMBCQYlHjd5SgA8hDUhAA6m66Lrks8mfjQqNTWi6yPMUgC8jjUhAA4Wj0sikdcIgYBEoxKJmDQhAF5DEgLgVJomIpL/46GDQQkEMqMBwJlIQgCcKh43p/alloU4LQSgPyQhAI4Uj0swaNrhHrUsxB4ZgD44MQ3AeQxDYjGTH4qoGvWGQaMeQE+sCQFwnkhEYjGTI0sgIOEwy0IAeiEJAXAY1Zy34sHQoZAYhui6+SMDcC2SEACHyb85PxAa9QD6IAkBcBKzmvMDCYdp1APoiRPTAJwkEul7xZjJ1NFp68IWAFdhTQiAY0QiI79iLHfqMjL2yACICGtCAJzCMETTTG7OD4TLyACcxpoQAGewojk/EJ46DeA0khAAB9B1MQxLmvMDCQZp1AMQkhAAR4hErGrODyQQkESC00IABkxCra2teQ6dTqf/85//bNu2LZVK5TkUAC/TtMwp5gJTl5GxRwb4Wz8npt944421a9fu3r17z549Ixu0oaHhiSee6OjomDNnzvTp0/ObIQCvK0BzfiCqUR8KcRkZ4FtnJKGWlpYNGzY0NzenUqkxY8aMYLgjR4786le/ev3111etWjVv3jyTJgnAuwrTnB+IWouy7qnWABzvjN2xiy66KJFI1NbWjmys99577/rrr3/zzTc3bdpEDAIwNF0XTbM5hUSjmZvOAPjSGUmovLxcRCZNmjSCgY4cOfLDH/7w/fffX7du3bRp08yZHQBvc8JiDI16wN/6OTFdVFQ0goF+9rOfvf/++7fccsvll1+e96wA+ICmiWE44tYLtTfHZWSAL5nTon/mmWdeffXV4uLiW265xZQBAXifExaEFJaFAB8zJwmtW7dORH7wgx+MGzfu+PHj27Zta2lpSafTpgwOwIPicXua8wOhUQ/4lQn3jjU3Nx88eFBEJk2atGTJkn/9619dXV0nT54sKyurra299tprcxynqqqq74v5P9YIgOMYhsRitjXnB0KjHvCufjOGYkISeumll9QH77zzzm9/+9uJEyeeOnXqd7/73eOPP/7zn/989OjR3/3ud3MZh9AD+IW9zfmBBAISDjtozw6AefpmjGw2MmF37MCBAyIybdq0VatWTZw4UUSKiopWrlx56aWXikg8HmebDMDnVGXdmWkjFKJRD/iNCUnoyJEjIvLlL3+51+uRSEREOjo6tm3blv93AeARTl50UUenuYwM8BMTkpB6GvUXvvCFXq/X1NSoD44dO5b/dwHgBaqp7oTm/EDU0Wka9YBvmJCExo8fLyJ9r1ktLi4uLi7Of3wA3hGPSzRq9yQGRaMe8BkTktBXvvIVEXn77bf7GX3UKBE577zz8v8uAFwvHpdg0HEHpftSk2SPDPAHE5KQ6sn/97//PXz4cK+3Tp06dd5551VXV+f/XQC4m2rOO3xBKIvLyADfGEkS2r179+rVqw8dOqT+MhAILFiwQESeffbZnp+2Z8+ekydP3nLLLWplCICvRSISi7nmUT3ZRj0Ar+sno3R2dopIKpU6depU33fT6fTixYs3bty4YsWK7IsrVqyYPn16XV3dvn371Cuffvrpvffe+61vfWvJkiXWzByAe+i6GIZrFoSUUEgMg2UhwPPOeLJic3Pz888/39jYKCKpVGrhwoVXXHFFOBy+4IILen5aaWlpV1fXhAkTsq+UlJQkEona2tobb7zxRz/60bnnnvvcc8/Nnj176dKlhfnbAOBoTm7ODyTbqN+/3+6pALDQWd3d3XbPQUSkqqqKZ0wD3qRp8sgjjrtbI0fq/g0n1/4BjEg2eJhw2wYADCYScWsMktOXkZGEAO/iLDMAKznzirHcBQI06gFvY00IgGUMQzTN9edsolGpqRFdd3GeAzAw1oQAWMZdzfmB8NRpwNNIQgCs4cbm/EDUahCNesCLSEIArBGJuK85PxDuqAe8iyQEwALxeOassWeoO+rZIwM8hyQEwAIuumIsd4mEaJoYht3zAGAmkhAAs7m9OT8QtcrFshDgLbToAZhK10XTxBkPrzdfNCpTp0oo5MGcB/gVa0IATOXGK8ZyFwhIIsGyEOAlJCEA5lHHaLx9N4VaDdI0e2cBwCwkIQDm8faCkMKDFgFvIQkBMIn3mvMDUY16Hi8EeAInpgGYwTAkFnP9FWO5U3fUG4br7xIBfI81IQBm8MYVY7kLBCQcZo8M8ACSEIC86brougcfpTi4UCjzNw7AzUhCAPLmh4PSfXEZGeAJJCEA+VF9cm835weijk7TqAfcjCQEID/xuO/2xbJo1APuRxICkId4XIJBXzTnB6L+9tkjA1yLFj2AkfJbc34g0ajU1Iiu+zoRAq7FmhCAkfJbc34g7JEBbkYSAjAiui6G4d8TQr0Eg2IYNOoBNyIJARgRfzbnB0KjHnAtkhCA4VO9cY7F9BQO06gH3IgT0wCGLxKRhga7J+E86jIyfz5aCXAt1oQADFMkIuEwC0L9CARo1AOuw5oQgOHQddE0mvMDolEPuA1rQgCGIx6nOT8YGvWA25CEAORM02jOD02tBtGoB1yCJAQgZzTnc0GjHnAVkhCA3MTjmRPBGJK6o549MsANSEIAchOLsS82DIlEZjMRgLORhADkgOb8cKn1M5aFAMejRQ9gKKo5391t9zzcJhqVqVMlFCJBAk7GmhCAoXBQemQCAUkkODoNOBxJCMCg1EVa3CAxMuroNJeRAQ5GEgIwqHicg9Ijx4MWAccjCQEYGM35/KllIfbIAKfixDSAARiGxGJcMWYCdUe9YXBLCeBArAkBGEAkwhVj5ggEJBxmjwxwJpIQgP7ouug6J4RMEwpl/pECcBiSEID+0Jw3F5eRAU5FEgLQB815K4TDNOoBByIJAegjEmFfzBI06gHnGTAJtba25jNuR0dHY2PjsWPH8hkEgA24Ysw6waAEg+yRAY7STxJ64403Fi1adP311+cz7k9+8pNbb721ra0tn0EAFJphiKaxIGShaJSj04CjnPE8oZaWlg0bNjQ3N6dSqTFjxox40PXr1+/atSvvuQEoOJrzVss+dZpVN8AZzlgTuuiiixKJRG1tbT4jvvnmm48//nh+swJgB10Xw2BByHLBoBgGy0KAQ5yRhMrLy0Vk0qRJIx7uxIkTy5YtW716db7zAlB4NOcLg0Y94CT9nBMqKioa8XCrV6++6qqrqqur85gSADuodjdbNoWhGvX0yAAHMPPescbGxpaWls2bN5s4JoACiUSkocHuSfiJuowsFOJUFmAv054ndOTIkdra2jVr1owdO9asMQEUCM35wgsEJBhkWQiwnWlrQrW1teFwuKqqasQj9Pu1eT7WCMDQdF00jTvnbRCNSk2N6DoZFLDaIPnEnCT0zDPPfPzxx0uWLMlnEEIPYA91UJo9msKjUQ8USt+Mkc1GJuyOvfPOO+vWrfvDH/6Q/1AACk3TxDC4Ysw2KgPRqAfsk28SSqfTv/zlL3/xi19ccMEFpkwIQEHRnLcXjXrAbvnujiUSibfffrupqampqanvuw899NBzzz339a9//brrrsvzGwEwXzyeObcLGwWDmUY9z7QE7JBvEtq/f//HH3/89NNP9/uufnrJlyQEOFEsRnPeEWjUA/bJNwmFQqGrr7667+u33nqriNx9992VlZUXXnhhnt8FgPlqamjOO0UgIOEwO5WALfJNQtOmTZs2bdpA715++eVXXHFFnt8CgPnUdejd3XbPA6eFQjTqAVuM5MT07t27V69efejQIdNnA6BAWH5wGo5OAzbpJwl1dnaKSCqVOnXqVN930+n04sWLN27cuGLFCstnB8AK6ooxmvNOo45Oq387AArljN2x5ubm559/vrGxUURSqdTChQuvuOKKcDjcqyFfWlra1dU1YcKEgs4UgFlYEHKm7LIQIRUooLO6nXFQoKqqimdMA4UQj4thkIScq6ZGAgH+BQFWywYPM++iB+B0hiGxGFeMOZpq1HN0GigU0+6iB+ACkYjEYjy0xtGyjXoABUESAnxDNed5kLHzhUJiGFxGBhQGSQjwjXicJ0q7A416oIBIQoA/qG42R0/cIhymUQ8UBiemAX+IRFgQchl1dJpGPWAx1oQAH1CPqGFByF0CAQkG2SMDrMaaEOB1hiGaRnPelaJRGvWA1VgTAryO5rx7qaPTNOoBK5GEAE/TdTEMmvMuFgzSqAcsRRICPC0S4d4Gd1M3b3BaCLAMSQjwLk3LnLqFq6k76tkjA6xBEgK8KxJhX8wjEgnRNDEMu+cBeBBJCPAomvNeotb2WBYCLECLHvAiXRdNk+5uu+cB89CoB6zBmhDgRfE4B6W9hkY9YA2SEOA56kAJtzR4j1oN4jIywFQkIcBzWBDyKpaFAAuQhABvicdpznsZjXrAbCQhwEMMQ2IxFoQ8jkY9YCqSEOAhqjnPFWPeFghIOMyyEGAWWvSAV+i66DrNeV8IhWjUA2ZhTQjwCg5K+4c6Os1lZIAZSEKAJ6hmNc15/1BHp2nUA3kjCQGeEI9zxZi/0KgHTEISAtwvHpdgkCMjvqP+pbNHBuSHE9OAy6nm/P79ds8DduAyMiBvrAkBLheJSCxGc96naNQDeSMJAW6m62IYnBDytVBIDEN03e55AG5FEgLcjOY8aNQD+SEJAa6lGtQcEIF6sDiNemBEODENuFYkIg0Ndk8CzpBISE0ND5QCRoA1IcCd1BVjLAhBCQRo1AMjw5oQ4EK6LppGcx5noFEPjAhrQoALxeM059EbT50GRoQkBLgNzXkMRK0G0agHhoMkBLhNJEJzHv2jUQ8MH0kIcJV4PHM2FuiXuqOePTIgZyQhwFViMfbFMIREQjRNDMPueQDuQBIC3IPmPHKhVg1ZFgJyQ4secAnVnO/utnsecINoVKZOlVCI3AwMiTUhwCW4Ygy5CwQkkWBZCMgFSQhwA3Xsg7sUkDu1GsRlZMBQSEKAG7AghOHiQYtAbkhCgOPRnMfIqEY9jxcCBsWJacDZDENiMa4YwwipO+oNg7tZgIEMuCbU2to63LHS6fTOnTu3b99+7Nix/GYF4LRIhCvGMHKBgITD7JEBg+hnTeiNN95Yu3bt7t279+zZk/tAdXV1dXV1n3zyifrLWbNm/eY3vwnwxzeQD10XXZeGBrvnATcLhbijHhjEGWtCLS0tkUhk0aJFr7766rBGWbVq1dq1a8ePHx8MBsvLy9VQCxYsGMHCEoDPcVAa+eMyMmBQZyShiy66KJFI1NbWDmuInTt3/vOf/9y4cWNDQ0NdXd0rr7wSjUZF5NixY8uXLzdzsoCvqP4zzXnkLxyWQIBGPdCvM5KQWs6ZNGnSsIbYvHnzhg0brrrqquwrCxcuvOOOO0Tk3//+9759+8yYJ+A/8ThXjME0NOqBAfRzYrqoqGhYQ8yYMeOyyy7r9eLNN9+sPmhvbx/ZzABfi8clGORgB0yj/nNijwzow4QW/Y033tj3xfLy8tGjR3/22WfDXWECQHMelohGOToN9GXVkxVTqdRnn332pS996eKLL7boWwCeRXMeVuCp00B/rHqyYnNzs4gsXrw49y+pqqrq+yLtM/iOrothcEIIlggGJR5nWQg+1G/GUKxKQs8+++ykSZMWLVqU+5cQegARmvOwUrZRz94rfKZvxshmI0t2x/bu3VtfX/+///u/Y8eOtWJ8wLNUz5nf12EdGvXAmcxfE0qn0/fcc89dd901a9Ys0wcHPC4S4YnSsJy6jEzdzwr4nvlrQvfff/+0adNuv/1200cGPC4SkXCYBSFYLhDIHBgCYPqa0ObNmw3DqKurM3dYwPt0XTSN0xsoEBr1wGlmrgk1Njb+7W9/++Mf/2jimIBfxOM051E4NOqB00xLQtu3b1+/fv2f/vSnXqekOzo6Dh06ZNZ3AbxJ02jOo9DUapCu2zsLwHYjSUK7d+9evXp1z3yzbdu2Bx54oK6ubty4cb0+89Zbb/3iF7+Y7zQBb6M5j8LjjnpARPo9J9TZ2SkiqVTq1KlTfe8gS6fTixcv7urqeuuttx5++GERefnll++8804R6XkJq4icPHlSRObPn19SUmLR7AEviMczJ1iBAlP1Me76hb+dkYSam5uff/75xsZGEUmlUgsXLrziiivC4fAFF1zQ89NKS0u7uromTJggIi0tLYPXxK677joLpg14SCxGcx62UY36UIgzavCts7q7u+2eg4hIVVUVz5iGH6m9CbbGYCP+I4QvZYOHVbdtABiaas4747cR+Fc0KlOnSijEFi38yaq76AEMjYPScIJAQBIJjk7Dt0hCgE3UxU/hsL2zAEROH53mMjL4EkkIsAmFHTgHD1qEj5GEADvQnIfTqGUh9sjgP5yYBgrOMCQW44oxOI5q1BsGjXr4CmtCQMFFIlwxBicKBCQcZo8MfkMSAgpL10XXOSEEhwqFMv+JAr5BEgIKi+Y8nIzLyOA/JCGggGjOw/nCYRr18BVOTAMFFIlwxRhcQB2dJrLDH1gTAgolEpFwmOY8XEA94oE9MvgDa0JAQRiGaBrNebhGNCo1NaLrZHd4HmtCQEHQnIe78NRp+AZJCLCeroth0JyHywSDYhg06uF5JCHAejTn4UY06uEPJCHAYqqNzGELuJFq1LNHBk8jCQEWi0TYF4OLJRKiaWIYds8DsApJCLASzXm4nWrUsywE76JFD1hG10XTpLvb7nkA+aFRD09jTQiwDAel4Q006uFpJCHAGupoBfcVwBvUahCXkcGLSEKANVgQgpewLATvIgkBFojHM+dMAc8IBmnUw5NIQoDZDENiMZrz8CAa9fAikhBgNprz8KpAQMJhloXgMbToAVPpuug6zXl4VihEox4ew5oQYCoOSsPbuIwMnkMSAsyjOsY05+Ft6ug0jXp417DzZwAAIABJREFUBUkIME88zkFpeB+NengLSQgwSTwuwSCHJ+ALalmIPTJ4AiemATOo5vz+/XbPAyiURIKj0/AG1oQAM0QiEotJIGD3PIBCoVEPryAJAXlTzXlOCMFvQiExDNF1u+cB5IUkBOQtHpeGBrsnARQcjXp4AkkIyI/qEnNUAv4UDtOoh9txYhrITyTCghB8TR2d5jFacC3WhIA8cMUYEAhIMMgeGdyLNSFgpAxDNI3mPCDRKI16uBdrQsBI0ZwHFJ46DTcjCQEjoutiGDTngQy1GkSjHi5EEgJGJBLhznngczTq4VokIWD4NC1zShRAlrqMjD0yuA1JCBi+SIR9MaAfiYRomhiG3fMAhoEkBAwTzXlgIGqtlGUhuIolSai1tdWKYQH76bpoGieEgAFFo5mb+ACXMDkJvfHGG4sWLbr++uvNHRZwinicGAQMhkY93Ma0JNTS0hKJRBYtWvTqq6+aNSbgLOoABLcKAINTe8dcRgaXMC0JXXTRRYlEora21qwBAcdhQQjIBctCcBXTklB5ebmITJo0yawBAWeJx2nOA7lSjXoeLwQ3MPnesaKiInMHBBzBMCQW44oxYBjUHfWGwY00cDha9EAOVHOeP9CB3AUCEg6zRwbn4y56YCiqEtzdbfc8ALcJhbijHs7HmhAwFA5KAyPDZWRwAwetCVVVVfV9kYc0wmaqCUxzHhiZYFAeeUQ0jf+JYK9+M4bioCRE6IETsSAE5CO7LEQSgq36ZoxsNmJ3DBhYPC7BIEccgLyo/4nYI4NTOWhNCHAWmvOAWaJRjk7DsVgTAgYQiUgsRnMeMAGNejgYSQjoj66LYUg0avc8AK8IhcQwuKMeDkQSAvrDQWnAXDTq4VQkIaAP1ZznQANgLvWgdu6oh8OYfGK6s7NTRFKp1KlTp7iDDG4ViUhDg92TALxIXUZGox5OYloSam5ufv755xsbG0UklUotXLjwiiuuCIfDF1xwgVnfAigE9eATFoQAKwQCmUY9u89wDNOS0De+8Y1vfOMbZo0G2EPXRdNozgMWolEPh+GcENBDPE5zHrCWOjpNox6OQRICTqM5DxSGWg2iUQ9nIAkBp3F2ASgMGvVwEpIQICIi8XjmLCeAAggGJRBgjwxOQBICREQkFmNfDCioREI0TQzD7nnA70hCAM15wA5qFZZlIdiNu+jhe6o5391t9zwA/4lGZepUCYX4PQQ2Yk0IvscVY4BdAgFJJFgWgr1IQvA3dQUSz/4H7KJWg7iMDPYhCcHf4nEOSgN24kGLsBtJCD5Gcx5wAtWo5/FCsAknpuFXhiGxGFeMAY6g7qg3DO66QeGxJgS/ikS4YgxwikBAwmH2yGALkhB8SddF1zkhBDhIKJT5HxMoLJIQfInmPOA0XEYGm5CE4D805wFnCoclEKBRjwIjCcF/aM4DjkWjHgVHEoLPRCISDNKcBxxK/e/JHhkKiBY9/MQwRNNozgOOFo1KTY3oOr+xoDBYE4Kf0JwHnI+nTqOwSELwDV0Xw+CEEOACwaAYBo16FAZJCL5Bcx5wCxr1KCCSEPxB9XI5dgC4hWrUs0cG65GE4A+RCPtigMskEqJpYhh2zwMeRxKCD0QiEg6zIAS4TCAgwSDLQrAaLXp4na7TnAfcikY9rMeaELwuHqc5D7gVjXpYjyQET1OHDDghBLiXWg2iUQ/LkITgaTTnAbejUQ+LkYTgXfF45sQlAFcLBmnUwzokIXhXLMa+GOARNOphGZIQPIrmPOAlNOphGVr08CLVnO/utnseAMxDox7WYE0IXsRBacB7ODoNa5CE4DnqirFw2N5ZADCfOjqt/h8HTEISgufE4xyUBryJBy3CAiQheEs8LsEgxwgAz1LLQuyRwTycmIaHGIbEYlwxBnhcIiE1NWIY3KIDU7AmBA+JRLhiDPC+QEDCYZaFYBaSELxC10XXOSEE+EIoJIbBZWQwBUkIXkFzHvAPGvUwD0kInkBzHvCbcJhGPUzBiWl4QiQiDQ12TwJAYamj0/wKhPywJgT344oxwJ/UZWTskSE/rAnB5QxDNI3mPOBTXEaGvLEmBJejOQ/4GU+dRt76SUKpVKq5uXnv3r0jGO7w4cPbt2/fuXNnOp3Oe27AUHRdDIPmPOBrwSCNeuSj9+5YXV1dIpGorq4+fPjw0aNH77vvvhkzZuQyUEtLy7333jthwoQpU6acPHly6dKlc+fOveuuu8aOHWvBtAEREYlEaM4Dfpdt1LNLjhE5IwmtXLnyH//4x9NPPz1t2jQReeCBBxYtWqRp2uWXXz74KC0tLZFIpLa29qabblKvHD169Prrr3/rrbcS/KCCRTQtc14SgM+Fw/LII9y+jJH5fHdsy5YtmzZtikQiKgaJyJ133jlu3LilS5eeOHFi8FFWrlx50UUXZWOQiJx77rk//vGPm5qaXnrpJSvmDUgkwp96ADISCdE0MQy75wH3ySShdDq9Zs0aEbn22ms/f2/UqGuuuebgwYOPPfbYIEMcP358//795557bq/Xzz//fBFpbm42ecqA0JwHcCa1QszRaQxfJgk1NjYePHhwzJgx2QUhZdasWSLy5JNPDjnQ66+/fujQoZ6vvP/++yLy1a9+1bTJAoqui6ZxQgjAGaLRzP2DwHBkktCLL74oIhdffHGvt9W6zrvvvrtv376Bhhg3btyUKVNSqdSyZcs+/fRT9WI6nd60aVNFRcXcuXMtmTj8jCvGAPRFox4jkklCra2tIlJRUdHr7UsuuUR90NbWNsgoy5cvF5FXX331pptuOnz4sIjU1tYeP348kUjQHYPJ1FEAnq8PoC+1Y85lZBiOTBJ6++23RaS4uLjX26NHZ8plHR0dg4zy7W9/e8WKFSLy5ptvXnfddT/96U+PHz/+97//vW+0AvLFghCAgbAshOHLBJ2uri4RKSoqGujzBtkdU0Kh0DnnnLNy5cpkMvnyyy/fe++9paWlw5pKVVVV3xfVYhWQEY/TnAcwmGBQAgEa9eil34yh5Hrv2Nlnnz3k53z88cdf+9rX9u3bl0wmly9fvnfv3l/84he5zpHQgyEZhsRi3DkPYAjqjvpQiHt4kNU3Y2SzUWZ3LLsL1kv20ozp06cP/j1WrlxZX1+fSCQ2b96sCmgbN2783e9+N+JJA73RnAeQi0BAwmH2yJCjTBKaOHGiiGSbX1nJZFJ9MH78+EFGqaur27Rp0+9///uioqKJEyc+8cQTM2fOFBFN07Zt22b+rOFDqhzLCSEAuQiFaNQjR5kkdOmll4rI8ePHe72tTlKLSK/nDPV09OjRBx98cPr06dkSfmlp6UMPPTR16lQR+ctf/mL6pOFHHJQGkLvsZWTAUDJJqKamRkR27tzZ6+2PPvpIRCoqKqZMmTLQEK+99trJkycDZ27HlpaWrl69ut8xgWFTnVia8wByp45O06jHUDJJaO7cuaWlpR9++OF7773X8+2mpiYRWbBgwZADdXd393plxowZY8aM6XsLBzBs1EAADBeNeuQmk4SKiopuu+02EXnhhRey76XT6VdeeaW8vPzmm2/u+TW7d+9evXp19m6Nb37zm+ecc85rr72WPV6tpFKpVCp19dVXW/t3AM+LxyUY5KA0gGFTy0LskWFQn99Fv2TJkurqak3Tjhw5ol5Zv359R0fH2rVrx40bl/20dDq9ePHijRs3qkcpikhxcfGvf/3rZDK5du3ankM/+OCDF1544e2332793wW8SzXnWRACMDKJBEenMbgzyvPr1q2LRqM33HDDlVde2d7e/sEHHzz11FMzZszo9TWlpaVdXV0TJkzIvvL9739/7Nix999//5tvvvm9731PRLZs2TJ+/Pi//vWvw32+InCGSERiMR4KAmCEso161pUxgLP6nu+xRVVVFU9WRG+6LpGI7N9v9zwAuJlhSE2NJBKEIfSUDR6jhvxUwDY05wHkj0Y9BkUSglOp7iu/wwHIXzhMox4DyfXeMaDQIhGuGANgGnUZGY8lQx+sCcGRuGIMgLkCAQkG2SNDX6wJwXkMQzSNg9IATBaNSk2N6Dq/ZaEn1oTgPDTnAViBp06jPyQhOIyui2HwKEUAllCrQTxoET2QhOAwkQjNeQBWoVGPPkhCcJJ4PHOqEQAsoi4jY48Mp5GE4CRcMQagABIJ0TQxDLvnAUcgCcExaM4DKAy19syyEESEFj2cQtdF08QZt+AB8D4a9TiNNSE4A1eMASgkGvU4jSQEB1Ab9jwFH0AhqdUgLiPzPZIQHIAFIQCFx7IQRIQkBPvRnAdgF9Wo5/FC/saJadjKMCQW44oxALZRd9QbBjf8+BZrQrCVas7zBxAAuwQCEg6zR+ZnrAnBProuuk5zHoDNQiEa9X7GmhDsw0FpAE7AZWT+RhKCTVRzleY8ACdQR6dp1PsSSQg2ice5YgyAU9Co9zGSEOwQj0swyJY8AAdRfyixR+Y/nJhGwdGcB+BMXEbmS6wJoeAiEYnFaM4DcBz2yHyJJITC0nUxDE4IAXCoYFAMQ3Td7nmgcEhCKCya8wCcjEa9/5CEUECqocoGPAAnUw++p1HvG5yYRgFFItLQYPckAGAo6jIyHnjmD6wJoVDUFWMsCAFwvkCARr1/sCaEgtB10TSa8wBcg0a9b7AmhIKIx2nOA3ATGvW+QRKC9WjOA3AjtRpEo97rSEKwXiRCcx6A+9Co9weSECwWj2fOHgKA66g76tkj8zSSECwWi7EvBsDFEgnRNDEMu+cBq5CEYCWa8wDcTq1qsyzkXbToYRnVnO/utnseAJCfaFSmTpVQiN/rPIk1IViGK8YAeEMgIIkER6e9iiQEa6gre3hWPQBvUEenuYzMi0hCsEY8zkFpAN7Bgxa9iyQEC9CcB+A9almIPTLP4cQ0zGYYEotxxRgAD1J31BsGdwd5CWtCMFskwhVjALwpEJBwmD0yjyEJwVS6LrrOCSEAnhUKZf6gg1eQhGAqmvMAvI3LyDynnySUSqWam5v37t2b59DpdPo///nPtm3bUqlUnkPBHWjOo7CSyWRbW9uOHTva2tqSyaTd04FvhMM06r2k94npurq6RCJRXV19+PDho0eP3nfffTNmzBjuoA0NDU888URHR8ecOXOmT59u0lTheJGINDTYPQl4XDKZ3LFjR2tra1tbW0lJiYgUFxer18vKykSkurp69uzZ6mPAKmpZiF/8POGs7h6XIaxcufIf//jH008/PW3aNBF54IEH/vznP2uadvnll+c43JEjR371q1+9/vrrq1atmjdvXu7zqKqqam1tHdbU4SxqrZitMVhGZaD6+vqqqqqysrK+Waezs1NE2traOjs7Kysrq6urKysr7Zgp/IE/9FwuGzw+T0JbtmxZtmzZHXfc8T//8z/qlXQ6fdVVV40ZM+aFF15Qv3UN7r333rv55pu7uroeeeQRlaVGMCG4kmHI1Kmyfz+VMVhky5YtW7duraioyCXcdHZ2HjhwoLOzc+bMmcP6lQwYBsOQmhpJJHh2mktlg0fmnFA6nV6zZo2IXHvttdlPGjVq1DXXXHPw4MHHHntsyBGPHDnywx/+8P3331+3bt1wYxBcj+Y8LJNMJtesWbN169bZs2fnuMZTUlJSWVlZWVm5devWNWvWcIQIluCp016RSUKNjY0HDx4cM2ZMrxAza9YsEXnyySeHHOhnP/vZ+++/f8stt+S+lQaP0HUxDJrzsIKKQSdOnJgzZ446FZS7kpKS2bNnn3XWWYQhWCUYFMOgUe92mST04osvisjFF1/c6+3zzz9fRN599919+/YNMsozzzzz6quvFhcX33LLLdbMEw5Gcx6W0TStrKxs5syZI/tytThUXl6u1rwBk9Go94RMElJbZRUVFb3evuSSS9QHbW1tg4yybt06EfnBD34wbty448ePb9u2raWlJZ1Omz9fOI3qkbJNDgts2bIlmUxWVVXlOc7kyZNFRKPzDCuoRj17ZG6WadG//fbbcrqMesbbozOf0NHRMdAQzc3NBw8eFJFJkyYtWbLkX//6V1dX18mTJ8vKympra3sePIIH0ZyHNdra2rZu3Tpnzpz8hyopKZk5c+aOHTt27Ngxe/bs/AcEzqAuIwuFOCvpUpmg09XVJSJFRUUDfd4gu2MvvfSS+uCdd9757W9/O3HixFOnTv3ud797/PHHf/7zn48ePfq73/1uLlPp9zc/CmWOph6nwYIQLFBfXz/iTbG+VBiqr68nCcF8gYAEg5wTcLhBVpdzvYv+7LPPHuitAwcOiMi0adNWrVqlXikqKlq5cuWePXv+9a9/xePx73znO6NGDX2tB6HHZXRdNI0752GFtra2tra2/PfFelJr3m1tbTxkCOaLRqWmRnSd3wwdq2/GyP4Jkwko2V2wXrJnfQZ5VPSRI0dE5Mtf/nKv1yORiIh0dHRs27Zt2FOG86lfgFgNhgWamppMXBBSSkpKKioqmpqazB0WEKFR726ZJDRx4kQR+fTTT3u9na2ejh8/fqAhxowZIyJf+MIXer1eU1OjPjh27JgZU4WTaJoYBk+ah0V27NhhxXUZZWVlg5c/gJFTq0E06l0ok4QuvfRSETl+/Hivt9VJahEZ5GGJKiT1vWa1uLg4lydTw5XYEYdl1IViw316UC7UmIQhWIJGvWtlkpBav9m5c2evtz/66CMRqaiomDJlykBDfOUrX5EememM0UeNEpHzzjvPpNnCGeLxzAlBwALZu1QBlwkGadS7USYJzZ07t7S09MMPP3zvvfd6vq321BcsWDDIEKon/9///vfw4cO93jp16tR5551XXV1t5pRhu1iMJ0rDOpY+D7q8vJw1IVgokcgcHoB7ZJJQUVHRbbfdJiIvvPBC9r10Ov3KK6+Ul5fffPPNPb9m9+7dq1evPnTokPrLQCCgotKzzz7b89P27Nlz8uTJW265JZfiGFyjpobmPCzV0dFh6ZrQIE9HA/KVbdTDPT7PKEuWLKmurtY0TXXBRGT9+vUdHR1r164dN25c9tPS6fTixYs3bty4YsWK7IsrVqyYPn16XV1d9rFDn3766b333vutb31ryZIlBfkbQUHouug6J4RgqfLy8hMnTtg9C2CkotHMH5VwiTPK8+vWrYtGozfccMOVV17Z3t7+wQcfPPXUUzNmzOj1NaWlpV1dXRMmTMi+UlJSkkgkamtrb7zxxh/96Efnnnvuc889N3v27KVLlxbibwIFw0FpFERnZ6d1I/NwRVgre3Sax625xBlJqKSkZPXq1YN/wahRo/p9PtCECRPWr1+f/cvFixebMj84iLq2ieY8LFZZWWndU3+sy1jA54JBeeQR0TT+wHQFTvAgZ/E4B6VRAGVlZdbtjp04cYJnTMNyPGjRVUhCyE08LsEgB6VRAGVlZZMnT7aiQdbe3t7Z2UlFH4WgGvU8XsgNSELIgWHQnEchVVdXW3ERYTKZDLNbgYJJJETXadQ7H0kIOYhEJBbjijEUTGVl5YkTJ0w/09Pe3s7WGAonEJBwmGUh5yMJYSiqDsqCEAqorKzssssuM/cRiG1tbbNnz2ZrDAUVColh0Kh3OJIQhkJzHnaYP39+Z2dne3u7KaMlk8mOjg62xlBoXEbmBiQhDIrmPGxSVla2bNmytra2/PfIOjs7m5qaiEGwRzgsgUDmz1I4EkkIg4pE2BeDXcrKyubMmbNjx458wlBnZ+euXbvmz5/PCSHYJpGgUe9kJCEMLBLhijHYa968eSoMjWybLJlMbt26tbq6et68eabPDciVuoyMPTKnGj30p8CfDEM0jafFw3bz5s2rrKzcsGHDcB+K2NbW1tHRsWzZMlaDYL9oVGpqRNf53dKBWBPCAGjOwzEqKytra2u7u7u3bt065Mmhzs7Otra2+vp6YhAchKdOO9hZ3d3dds9BRKSqqsqKB6lhhHSd6wPhQMlksr6+fvfu3aoMX1ZWVlJSUlxcrB4+dOLEiY6OjmQyOX/+fArzcBzDkJoaSSRYFnKIbPAgCaE/U6fyvyscK5lMtrW1qT8xksmkupejsrKyvLxcRDgSBOfil0wnyQYPzgmhD03LnO8DHKmsrGz27NmzZ8+2eyLAMKnLyLjN2mE4J4Q+aM4DgEUSCdE0LiNzFJIQzkRzHgCso1bcOTrtJOyOoQddF00TZxwdAwBvolHvMKwJoQeuGAMAq9GodxiSEE5TW9fczQQAVlOrQVxG5gwkIZzGghAAFAbLQk5CEoKIiMTjNOcBoHCyjXrYjSQEEcOQWIzmPAAUFI16ZyAJgeY8ANghEJBwmGUh29Gi9z1dF12nOQ8ANgiFaNTbjjUh3+OgNADYRR2djkTsnoevkYT8TXU4ac4DgF3U0Wka9fYhCfkbFwECgL1o1NuNJORj8bgEg2xOA4DN1B/F7JHZhBPTfqWa8/v32z0PAACXkdmJNSG/ikQkFpNAwO55AABo1NuJJORLui6GwQkhAHCQUEgMQ3Td7nn4DknIl2jOA4DT0Ki3CUnIf1RXk61oAHCacJhGfeFxYtp/IhFpaLB7EgCA/iQSUlPDY94KiTUhn+GKMQBwskCARn2BsSbkJ4YhmkZzHgAcjUZ9YbEm5Cc05wHA+XjqdGGRhHyD5jwAuIVaDaJRXxAkId+IRGjOA4A70KgvIJKQP8TjmVN4AABXUHfUs0dmPZKQP8Ri7IsBgMskEqJpYhh2z8PjSEI+QHMeANxIreWzLGQxWvRep+uiadLdbfc8AADDF43K1KkSCvHbrHVYE/I6rhgDAPcKBCSRYFnIUiQhT1MbzDy1HQDcS60GcRmZZUhCnsaCEAC4HQ9atFg/SSiVSjU3N+/duzefcTs6OhobG48dO5bPIMgLzXkA8AbVqOfxQtbofWK6rq4ukUhUV1cfPnz46NGj991334wZM0Yw7k9+8pNdu3Y9/vjjV1xxhRnzxDAZhsRiXDEGAB6h7qg3DG5MMt0ZSWjlypX/+Mc/nn766WnTponIAw88sGjRIk3TLr/88mENun79+l27dpk5TQwXV4wBgJcEAhIOc+bBCp/vjm3ZsmXTpk2RSETFIBG58847x40bt3Tp0hMnTuQ+4ptvvvn444+bPE0Mi66LrvMoRQDwlFAo88c7TJVJQul0es2aNSJy7bXXfv7eqFHXXHPNwYMHH3vssRyHO3HixLJly1avXm36RDEM/NIAAN7DZWTWyCShxsbGgwcPjhkzJrsgpMyaNUtEnnzyyRyHW7169VVXXVVdXW3uLDEMqmlJcx4AvEcdnaZRb6pMEnrxxRdF5OKLL+719vnnny8i77777r59+4Ycq7GxsaWl5e677zZ7khiOeJx9MQDwJhr1FsgkodbWVhGpqKjo9fYll1yiPmhraxt8oCNHjtTW1q5Zs2bs2LFmTxI5i8clGKQ5DwCepf6QZ4/MPJnu2Ntvvy0ixcXFvd8enfmEjo6OwQeqra0Nh8NVVVVmzxA5ozkPAH4QjUpNjeg6v/eaIhN0urq6RKSoqGigzxt8d+yZZ575+OOPlyxZks9U+k1RarEKOaE5DwB+kN0jIwnlbJCVmlzvoj/77LMHeuudd95Zt27dU089Nex5nYnQkxddF8PghBAA+EIwKPE4y0K565sxstkoc04ouwvWSzqdVh9Mnz59oE/45S9/+Ytf/OKCCy4wYaYYMZrzAOAfNOrNkwlAEydObG9v//TTT3u9nUwm1Qfjx4/v9+sTicTbb7/d1NTU1NTU992HHnroueee+/rXv37dddeZN2f0oRqV/GYAAP4RDssjj4im8diUPGWS0KWXXtre3n78+PFeb6uT1CLS6zlDWfv37//444+ffvrpft/VTz8KkyRkrUhEGhrsngQAoLDUZWTqIUMYqUwSqqmpef7553fu3Nnr7Y8++khEKioqpkyZ0u/Xh0Khq6++uu/rt956q4jcfffdlZWVF154oZlTRi+RiITDLAgBgO8EApkDQ5yOyEMmCc2dO3fVqlUffvjhe++9N3HixOzbas9rwYIFA339tGnTBlouEpHLL7+cu+itpeuiaTTnAcCnaNTnLXNiuqio6LbbbhORF154IfteOp1+5ZVXysvLb7755p5fs3v37tWrVx86dKiQE0X/4nGa8wDgXzx1Om+f30W/ZMmS6upqTdOOHDmiXlm/fn1HR8fatWvHjRuX/bR0Or148eKNGzeuWLGi0JNFL5pGcx4A/E6tBnFH/UidUZ5ft25dNBq94YYbrrzyyvb29g8++OCpp56aMWNGr68pLS3t6uqaMGFCAeeJ/rA3DADINuo5KTEiZ3V3d9s9BxGRqqoqnqw4POqZWlTGAAAimRIZuwQ5ywaPUUN+KhwqFuO/eABARiKROTKBYSIJuRPNeQBAT9lGPYYp13vH4CCqOe+MbU0AgFNEozJ1qoRC/J48LKwJuRAHpQEAfQUCkkhwGdlwkYTcRl0xxi0zAIC+1M0b6icFckMScpt4nIPSAID+8aDF4SMJuUo8njkTBwBAv9SyEHtkOePEtHsYhsRiPDgLADAEdUe9YXAXUy5YE3KPSIQrxgAAQwsEJBxmjyxHJCGX0HXRdU4IAQByEgplfnBgKCQhl6A5DwDIXfYyMgyFJOQGNOcBAMMVDtOozwVJyA0iEfbFAADDRqM+ByQhx+OKMQDAyASDEgyyRzY4WvTOZhiiaTTnAQAjFI1KTY3oOr9RD4Q1IWejOQ8AyAdPnR4KScjBdF0MgxNCAIC8BINiGDTqB0IScjCa8wCA/NGoHxRJyKlU75FtXQBA/lSjnj2y/pCEnIrmPADARImEaJoYht3zcBySkCPRnAcAmCsQkGCQZaG+aNE7j67TnAcAmI9GfX9YE3IedVCa5jwAwFw06vtDEnIYtYnLFWMAACuo1SAa9T2QhByG5jwAwDo06vsgCTlJPJ450QYAgEWCQRr1PZGEHMMwJBajOQ8AsByN+h5IQo5Bcx4AUBiBgITDLAsptOidQddF16W72+55AAD8IRSiUa+wJuQMHJQGABRfUIzvAAAXUUlEQVQSR6dPIwk5gLpijOY8AKCQ1NFp9TPIx0hCDhCPc1AaAFBoPGhRREhC9ovHJRhkmxYAYAO1LOTvPTJOTNtKNee5YgwAYJdEwudHp1kTslUkIrEYV4wBAGzj+0Y9Scg+qjnPCSEAgL1CITEM315GRhKyD815AIAT+LtRTxKyCc15AIBzhMO+bdRzYtomkYg0NNg9CQAATlNHp/33KzprQnbgijEAgNMEAhIM+nCPjDWhgjMM0TSa8wAAx4lGfdioZ02o4GjOAwCcyZdPnSYJFZaui2HQnAcAOFQw6LdGPUmosCIRmvMAAOcKBCSR8NVpIZJQAWla5jwaAACOpS4j880eGUmogCIR9sUAAC6QSIimiWHYPY9C6CcJpVKp5ubmvXv3DnesdDq9c+fO7du3Hzt2zIy5eQvNeQCAW6gdDH8sC/Vu0dfV1SUSierq6sOHDx89evS+++6bMWNGLgPV1dXV1dV98skn6i9nzZr1m9/8JkBDStF10TTp7rZ7HgAA5MY3jfoz1oRWrly5YcOGRx99dO3atY8++uh3vvOdRYsW7dy5c8hRVq1atXbt2vHjxweDwfLychFpaWlZsGBBa2urVRN3F64YAwC4i28a9Z8noS1btmzatCkSiUybNk29cuedd44bN27p0qUnTpwYZIidO3f+85//3LhxY0NDQ11d3SuvvBKNRkXk2LFjy5cvt3T27qC2Wv33/HIAgLup1SCvX0aWSULpdHrNmjUicu21137+3qhR11xzzcGDBx977LFBhti8efOGDRuuuuqq7CsLFy684447ROTf//73vn37LJm4i7AgBABwI38sC2WSUGNj48GDB8eMGZNdEFJmzZolIk8++eQgQ8yYMeOyyy7r9eLNN9+sPmhvbzdtsm4Uj9OcBwC4lWrUe/rxQpkk9OKLL4rIxRdf3Ovt888/X0TefffdQZZ2brzxxr4vlpeXjx49WkQmTZpk1lzdxzAkFmNBCADgYolE5oIEj8okIXW0uaKiotfbl1xyifqgra1tWOOmUqnPPvvsS1/6Ut905SOqOU+BDgDgXoGAhMMe3iPLtOjffvttESkuLu799ujMJ3R0dAxr3ObmZhFZvHhxvhN0L10XXac5DwBwvVDIw436TNDp6uoSkaKiooE+b7gHn5999tlJkyYtWrQo9y+pqqrq+6KLe/gclAYAeIM6Oh2JyP79dk9lhPrNGErvJysO5Oyzz879++3du7e+vv7RRx8dO3Zs7l/l4tDTl+oc0pwHAHhDMCiPPCKa5tIfbX0zRjYbZc4JZXfBekmn0+qD6dOn5/jN0un0Pffcc9ddd6nemU/F41wxBgDwDu826jNJaOLEiSLy6aef9no7mUyqD8aPH5/jiPfff/+0adNuv/12k2boQvG4BIOe3EwFAPiX+tHmuUZ9Zino0ksvbW9vP378eK+31UlqEen1nKGBbN682TCMuro6E6foMqo579qdVAAABuTFy8gya0I1NTUi0veKsY8++khEKioqpkyZMuRYjY2Nf/vb3/74xz+aPUlXiUQkFqM5DwDwIC826jNJaO7cuaWlpR9++OF7773X8+2mpiYRWbBgwZADbd++ff369X/60596nZLu6Og4dOiQeRN2NvXsKU4IAQC8KhQSwxBdt3sepskkoaKiottuu01EXnjhhex76XT6lVdeKS8vz16doezevXv16tU98822bdseeOCBurq6cePG9frMW2+99Ytf/KKFfweOQnMeAOBt2Ua9V3xeGVuyZMn27ds1Tfv+978/YcIEEVm/fn1HR8ef//znnvkmnU4vXry4q6vrrbfeevjhh0Xk5ZdfvvPOO0Wk5yWsInLy5EkRmT9/fklJSWH+ZmymmvMe2joFAKAf4bCrG/W9nFGeX7duXTQaveGGG6688sr29vYPPvjgqaeemjFjRq+vKS0t7erqUmmppaVl8JrYddddZ/qkHSoSkYYGuycBAID1EgmpqfFGEjqr2xnXQVRVVbn7yYpqnZCtMQCAT7j8B182eOT6jGkMRtdF02jOAwB8xCuN+lF2T8AT4nGa8wAAf/HKU6dJQnmjOQ8A8Ce1GuTyRj1JKG+RiHt3SQEAGDlPNOpJQvmJxyUQcPsWKQAAIxQMSiDg6j0yklB+YjH2xQAAvpZIiKaJYdg9jxEiCeUhEpFwmAUhAICvqb0R1y4L0aIfKdWcd8bTmAAAsFM0KlOnSijkxtUB1oRGiivGAABQAgFJJFy6LEQSGhG1IeqJp4wDAGACtRqkruB0FZLQiLAgBABAT6590CJJaPhozgMA0Jdq1Lvt8UKcmB4mw5BYjCvGAADoh7qj3jBcdAMVa0LDFIlwxRgAAP0LBCQcdtceGUloOHRddJ1HKQIAMKBQKPPj0iVIQsPBQWkAAAbntsvISEI5U81AmvMAAAxOHZ12SaOeJJSzeJx9MQAAhuaqRj1JKDeRiASDNOcBAMiJ+qHphj0yWvQ5MAzRNJrzAAAMQzQqNTWi6w5fR2BNKAc05wEAGC6X7JGRhIai62IYnBACAGDYgkExDIc36klCQ6E5DwDAyLihUU8SGpRqADp7gxMAAOcKhx3eqOfE9KAiEWlosHsSAAC4mbqMTD1kyHlYExpYJCLhMAtCAADkJRCQYNCxR6dZExqArtOcBwDAHA5u1LMmNIB4nOY8AADmcHCjniTUH02jOQ8AgJnUapDzGvUkof7QnAcAwFxObdSThPqIxzNnuwAAgIlUfcxhe2QkoT5iMfbFAACwRCKROYLiGCShM9GcBwDAOs5r1NOi70E157u77Z4HAADeFY3K1KkSCjlk3YE1oR44KA0AgNUCAUkknHN0miR0mroSJRy2dxYAAHifOjrtjMvISEKnxeMclAYAoBCc9KBFkpCI0JwHAKCw1LKQA/bI/HJiOplMlpWV9f+eYUgsxhVjAAAUlLqj3jDsvdvKs0komUzu2LGjo6MjmUy2tbWpF8tOq6qqmj17duZTIxGuGAMAoNACAQmHJRKRhgb1wpYtWwb6wV1eXj5v3jwrZnFWtzNK41VVVa2traYMpTJQfX29+gdXVlZWXFxcUlLS2dkpIidOnOjs7GxvbxeRysrK6gsvrLzmGprzAADYwDCkpib5hz/sGDu2vr6+pKSkoqIi+4NbRDo7O9UP7mQy2dnZWVlZWV1dXVlZmf93zgYPryWhNWvWHDhwoKKiYsh/TJ2dnQcOHGhtbZ0/Y8a8n/40/28NAACGa8vdd29NpSoqKiZPnqzSz0DUD+729vY5c+bkvz7kwSSUTCY1TUsmk9XV1bl/lfrH2tHRsWzZsgEPEgEAALPZ+4M7Gzw80h1ra2tbsWLFWWedNax/miJSUlJSWVlZXl6+Zs2a7K4kAACwlCk/uLds2ZL/TLyQhJLJ5Jo1a/LZOKysrKyqqlLJ1Ny5AQCAXkz5wT1z5sympqb8VzG8kIQ0Tauurs5zb0sdr16zZo1ZswIAAP3SNK2qqirPH9zqeLWW94OqTU5CqVSqubl579695g47iDVr1gz2rKDhUMk0/3+mAABgIGoHxpT+V0VFRXl5eZ4/uM1MQnV1dd/85jc3bdoUj8fnz5+/Z88eEwfv144dO9ra2oa7xTiImf+/vfuPibp+4Dj+ToF2N8SNz2n+4GZrwvlj/KgVdSxqrjYYdW7W0JbkaKzSmqvJX7ll2g/SOWnWBFkWbGLYGrkBMWPRYuHdoC1gVvNuymyXEHqfzCYnFnz4/vFp92UHot7n87mTz+f5+Ot8D9/vt/f2vfeL9/tz78vLU+vUq0IAABCh3nSj48KdkZERCAS0LNy6JaFdu3bV1tYePXq0urr66NGjTz75ZFlZWV9fn171z8jv9+fl5elYod1ud7lcXq9XxzoBAICqtbXV6XTqWKF6Rtba2hpzDfokoba2ti+++OLFF1/MzMxUS7Zv356amrpjx45r167p0sSMfD6f7h99V9OlvnUCAAAhhM/n0+VcbCpJkmRZjvkzTzokIUVR1AeNS0pK/l/vvHlFRUVDQ0ONjY3am5hRW1ub0+mc/RamGKgV+nw+fasFAMDifD6fQQu33W6PeeHWIQl1dXUNDQ2lpKRENoRU+fn5QoimpibtTcwoFAoZdBei0+nkgAwAAH35/X7jFu6Y72fWIQl1dHQIIVauXBlVvnjxYiHEhQsXBgcHtbcyXSAQMOgN1T2uAgAA4y7ts9lsiTwdU1PY9AegVq9erb4w6LEbWZYNiixa3lAAADAjvW690VeS9irOnTsnhLDZbNFVJ/1XeSgU0t5KnMmyLPbsSXQvAAAwD+O2MOx2+7Vr12JLWjokobGxMSFEcnLyjX7gFk/HXC7X9MIbHfsZ926KyOnY+fMG1Q8AgNXIqakJbH3GjKHSIQnd1Pz582/lx27rWSdJksLhcKw9uon/aq6vN6h+AACsRhJC2rkzHA4btJERDodn2RCanjEi2UiH54Qip2BRFEVRX6xatUp7K9Op9wcYUbNet4ADAIAISZIMumVw9hg0Ox2S0NKlS4UQ169fjyqPxJSFCxdqb2U6Q5+6ugMf6QIAYE4z7jxHyxaGDkkoJydHCHH16tWocvVJaiFE1D1DenG5XMFg0Iiag8HgLAeKAAAgBsYt3FrOiHRIQuvWrRNCTP+KsStXrgghnE7nihUrtLcyndvtNu50zO12G1EzAACWlZWVpX7CS/eag8Ggx+OJ7e/qkISKi4vT0tIuX748PDw8tVy9prm0tFR7EzOSJCkjI0P3dBkIBIhBAADoTpKk3Nxc3RfuYDDodrsT+ZxQcnLy1q1bhRDt7e2RQkVRTp065XA4Nm/erL2JG/F4PLpf2xgMBgsKCvStEwAACCE8Ho/ue0KBQEDLwq3Pd9FXVFQUFBQ0NDT8+eefaklNTU0oFKqurk418v6ArKysjIyM/v5+vSr0er0ZGRl8cAwAACNIkvTEE0/ouHAHAgGNC7c+SUgIcejQoUceeWTjxo27d++uqKj45ptvjh8//vDDD+tV/42Ul5eHw2FdttrU7aXKykrtVQEAgBm53W6bzabLkY4sy6FQSOPCfdfk5KT2rmjncrli/hZZWZbfe+89t9ut5bImWZa9Xm9lZSUbQgAAGEpduPPy8rTcWRMOhzs7O2NeuCPBQ7c9oQSSJGnjxo0+ny/mgBkMBolBAADEh7pw9/f3x7xwy7Lc2dlZXl6ufeGOx7dtxIHb7c7Kyjpw4IAQ4nbflP7+/nA4TAwCACButCzcgUBAPRTTZeE2w+lYhCzLPp+vs7PT6XTe9N0Jh8O///57MBjMyMjg2SAAAOIvgQt3JHiYKgmpAoGA1+sdGBiQJMnpdIopX52hXvKtXuvk9/s9Hk9WVhZbQQAAJJAsy62trerCLUmS3W6/0cItSZLH49Hl2j8zJyGVGjP9fr8sy7Is2+129d1U32WXy/X000/r2BwAANDipgu3lusTpzN/EooiyzJfqgoAwFyhXsBo3NodCR4meWL6pohBAADMIXFbuM3wKXoAAIDYkIQAAIB1kYQAAIB1kYQAAIB1kYQAAIB1kYQAAIB1kYQAAIB1WSUJuVyuRHcB8cNwWwrDbSkMt6XEZ7itkoQAAACmIwkBAADrIgkBAADrIgkBAADrIgkBAADrIgkBAADrIgkBAADrumtycjLRfRCCKyIAAEB8+f1+ceckIQAAgPjjdAwAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFgXSQgAAFiXJZLQxMRET0/P2bNnE90R6IMBRRS/35/oLkA3jCYURenr6+vu7v7777/j0FxSHNpIrLq6uvr6+oKCgkuXLv31119VVVXZ2dmJ7hRip3FAn3nmmaGhoaklFRUVL730kt7dRJz89NNP1dXVAwMDp0+fTnRfoJWW0WRqm0ZdXV1dXd3o6Kj6x/z8/Hfffffee+81rkWTJ6Fdu3a1tLR8+eWXmZmZQoiDBw+WlZU1NDTcf//9ie4aYqFxQNva2n755ZepJUlJSRs2bDCkrzBYb29vbW1tT0/PxMRESkpKorsDTTSOJlPbNN55551jx44tW7bsoYce+vnnn0OhUG9vb2lpaWNjo8vlMqjRuyYnJw2qOuHa2toqKytfffXV119/XS1RFKWwsDAlJaW9vd1msyW2e7hd2ge0pKTkueeeczgckRKHw5Gfn29Uj2GkUCjkcDg+//zzPXv2pKSksCc0p2kcTaa2OfT19b322mv79u0rLCxUS9T/EkKINWvWnDhxwqB2TbsnpCjKgQMHhBAlJSWRwnnz5hUVFR07dqyxsZFd07lF+4CePHkyPT19y5YtxnYU8aIue8uXL090R6ADLaPJ1DaN5ubm2tra3NzcSMnzzz9/6dKlmpqaX3/9dXBw8L777jOiXdM+Md3V1TU0NJSSkqIeo0SovyU0NTUlqF+IkfYBPXToELvl5pOcnJzoLkA3sY0mU9s0srOzp8Yg1ebNm9UXwWDQoHZNm4Q6OjqEECtXrowqX7x4sRDiwoULg4ODCegWYqVxQL/99ttAILBz584HHnhg586dfDgFMAemtpls2rRpeqHD4UhKShJGbgCbNgmp88HpdEaVr169Wn0RCATi3SdooHFAP/74Y/XF6Ohoc3Pz+vXrd+/eff36dQN6CiB+mNqmNzExMT4+vmTJkum/CevFtM8JnTt3Tggx/SlaNVoKIUKhULz7BA00Dujx48cDgcDw8HBXV1dLS8v4+HhTU9Nvv/125MiR+fPnG9RnAEZjapteT0+PEMLQ58BMuyc0NjYmZj115nRsbtE4oDabLTc3t7i4+IMPPvj+++8fe+wxIYTX6/3www917yqAuGFqm95XX321fPnysrIy45owbRK6KX5dMJlbH9BFixZ98sknTz31lBCivr4+PneYAjAaU9t8zp4929raunfv3rvvvtu4VkybhCKHJlEURVFfrFq1Ko7dgVa6D+j777+/bNmy8fHx3t5erZ0DcMdgapuGoihvvvnmG2+8YfTVUKZNQkuXLhVCTH9uTpZl9cXChQvj3SdooPuA2my2Z599VggRudMdgAkwtU1j3759mZmZ27ZtM7oh0yahnJwcIcTVq1ejytUHb4UQUdfS4A5nxICuWbNGCGHopiuA+GNqm0Bzc/P58+erqqri0JZpk9C6deuEEH19fVHlV65cEUI4nc4VK1YkoFuIlREDqp6sTb/IC8CcxtSe67q6uk6cOPHRRx/FpznTJqHi4uK0tLTLly8PDw9PLfd6vUKI0tLSBPULMTJiQH/88ceioiL13A2AaTC157Tu7u6amprDhw9H7eqFQqGRkREjWjRtEkpOTt66dasQor29PVKoKMqpU6ccDkfk9m7MFbc1oAMDA/v374/MmVAo1NHREQ6Ho37m5MmTb731lvF9B6APprbp/fDDDwcPHqyrq0tNTZ1aPjAw8PLLLy9YsMCIRk17s6IQoqKioru7u6GhYcOGDenp6UKImpqaUCj02WefRb3FmBNucUAVRdmyZcvY2NiZM2c+/fRTIcTevXtbW1uXLFmyY8eOkpKS0dHRlpaWxsbGw4cPL1q0KGH/HuhBXQUnJib+/fdfvoNsrpt9NJnapvfdd99t375dCBH5LnrVP//8I4TweDx2u92Idu+anJw0ot47RDgcfvvtt/v6+h599NFgMHjx4sWqqqrs7OxE9wsxupUBVRTl8ccfv3jx4vr16/fv3y+E6Onp2bZtW+SDJAsWLNi0adMrr7ySlpaWgH8DdNLT0/P11193dXX98ccfQoicnJwHH3ywvLz8nnvuSXTXcNtuZTSZ2ubW29v7wgsvzPIDR44ciUpIejF5ElKNjIycOXPG4XCsXbs20X2BDm46oCMjI6dPny4sLIwcM09MTHi9XkVR0tPT165dO2+eac+FARNjasMIlkhCAAAAMyI+AwAA6/ofWkooI1Uii9QAAAAASUVORK5CYII=\",\"relationship\":null},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image4.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image5.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image6.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAwMAAAL9CAIAAAD4ry2pAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6AYJFDgeMjQDUQAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAxMC1KdW4tMjAyNCAwNTo1NjozMCkCjpkAACAASURBVHic7N1/kBvlfT/wjyk21UJNwqMpIWiLzMCKpiFWfkGllM5d1GSYzqlMO0ACoT6pDLQkTUsj2oLr+CwozhB/xUwygOMJVEsy0EJC0lTKj0kjfIzJ7tgQ0JWSRpsEK7OaBAY9lAJZEcPdff94bOV8v6zbffa0q32//mCwfHru8ePz7fs+z68N8/PzBAAAABBJJw27AwAAAABDc/KwO3BUKpUadhcAAAAgQlqtFgUnCdGxDvkklUr52j4ECv66IwV/3ZGCv+5I8fWvu1+CwewYAAAARBeSEAAAAEQXkhAAAABEF5IQAAAARBeSEAAAAEQXkhAAAABE14aAnDGNjZEAAACwbvrBAzUhAAAAiC4kIQAAAIguJCEAAACILiQhAAAAiC4kIQAAAIguJCEAAACILiQhAAAAiC4kIQAAAIguJCEAAACILiQhAAAAiC4kIQAAAIguJCEAAACILiQhAAAAiC4kIQAAAIguJCEAAACIrpMltjU3NzczM/PLX/7yXe961+bNmyW2DAAAAOAHaUlo3759+/bt++Uvfyl+edFFF912223JZFJW+wAAAADSyZkdu/XWW++8887TTz99bGwsHo8T0aFDh6644opWqyWlfQAAAAA/SEhCTz/99He+85177713//79+/bt+/73vz81NUVEr7zyys033+y9fQAAAACfSEhCjzzyyN69ey+55JL+K1dfffXHP/5xIvrhD3/43HPPef8UAAAAAH6QkIQuvPDCrVu3LnrxYx/7mPgf27a9fwoAAAAAP0hIQh/5yEeWvhiPx08++WQiOvvss71/CgAAAAA/+HWe0Ozs7Jtvvvm2t73tvPPO8+lTAAAAAHgk8zyhhQ4ePEhE27ZtG/wtqVRq6YvYfQYAAAAeLZsxBL+S0Ne+9rWzzz77mmuuGfwtCD0AAADgh6UZo5+NfElCP/nJT2q12pe//OVTTjnFj/YBAAAApJC/Tmhubu6WW2658cYbL7roIumNAwAAAEgkPwndcccd559//g033CC9ZQAAAAC5JM+OPfLII+12e9++fXKbBQAAAPCDzCT02GOPff3rX7/vvvsktgkAAADgH2lJ6PHHH7/nnnvuu+++Rauku93u7OzsmWeeKesTAQAAAMgiZ53QgQMHPve5z+3bt++0005b+PrMzMz111//W7/1W1I+CwAAAIBcEmpCjz766Cc/+UkiWngJKxEdOXKEiPL5vKIo3j8LAAAAgHRek9ChQ4dW3yZ22WWXefwUAAAAAD7xmoQuuuginA0NAAAAIeXXDawAAAAAwYckBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0YUkBAAAANGFJAQAAADRhSQEAAAA0bViEmq1Wi6ae/HFFx9//PGnn356bm7OQ68AAAAA1sPJS1966qmn7rzzzpmZmWeeeWbwhg4dOnT77befccYZ55xzzpEjRz71qU9deumlN9544ymnnCKvtwAAAAAyHZeEDh06tHfv3oMHD87Ozm7atGnwVg4dOlQsFnfs2HHVVVeJV15++eXLL7/8Rz/6UbValdlfAAAAAHmOmx0799xzq9Xqjh071trKzp07zz333H4MIqK3vOUtf/EXf2EYxve+9z0J3QQAAADwwXFJKB6PE9HZZ5+9piZee+21w4cPv+Utb1n0+m//9m8T0cGDB731EAAAAMAvy6yY3rhxo4uGfvCDH7zwwgsLX3n++eeJ6J3vfKe7ngEAAAD4TcIu+tNOO+2cc86ZnZ0tlUq/+tWvxItzc3MPPfSQqqqXXnqp908BAAAA4Ac55wndfPPNRPTEE09cddVVL774IhHt2LHjtddeq1ar2DsGAAAAgbXMLnoXPvjBD27fvn337t3PPvvsZZdd9p73vOekk076xje+sXnz5sEbSaVSS190d6wRAAAAQN+yGUOQk4SIaHJy8tRTT925cyfn/NFHH7399tvXFIMIoQcAAAD8sTRj9LORzNs2Xn311fe85z2MsdnZ2ZtvvnnPnj0SGwcAAACQTlpNaOfOnf/93//90EMPdbvd66677sc//vG999775ptv3nLLLbI+BQAAAIBccmpC+/bte+ihhz772c9u3LjxrLPOevDBB9PpNBHpun7gwAEpnwIAAABAOglJ6OWXX77rrrsuuOCC8847T7yyefPmL37xi1u2bCGiL33pS94/BQAAAIAfJCShJ5988siRI8lkcuGLmzdvFuuEnn76ae+fAgAAAMAP0tYJzc/PL3rlwgsv3LRp09JbOAAAvOCcW5bFOe92u5xzzjljjDEWj8cZY5lMZtgdBIAwcZOEZmZmvvvd727btu3MM88kog984AOnnnrqk08+OTc3d9JJvy4yzc7Ozs7OfuhDH5LWWQCINs65aZq1Wk1RFFVViSgej6uq2uv1HMdpNptEVKvVNE3LZrOapg27vwAQAsskIcdxiGh2dvaNN95YegfZ3Nzctm3bXn/99R/96Ef33XcfEcVisU9/+tM333zznXfeedNNN/U/8q677nr7299+ww03+Nl/AIgEzrmu651OR1XVXC6nKMrC31UUhTEmspHjOJ1Op1KpMMZKpRJjbEhdBoBwOC4JHTx48Jvf/OZjjz1GRLOzs1dfffX73ve+QqEgaj99mzdvfv31188444z+K3/6p396yimn3HHHHc8+++yf/MmfEFG9Xj/99NMffvjhtZ6vCACwiGVZlUollUrlcrkTfrCiKJqmJRIJkYfy+TzmywBgFRuWru8ZilQqhTOmAWCper3eaDTS6bSL6g7nvNVqZbPZiYkJP/oGAOHVDx7SVkwDAEgnYlAmk1k0HTYgxlg6nW40GkSEMAQAy5J52wYAgESWZdVqtXQ67S4GCYqiZDIZwzAsy5LYNwAYGUhCABBQuq5ns1nvS57FRjNd1znnUjoGAKMESQgAgkjXdXE+kJTWVFVVFKVWq0lpDQBGCZIQAASRaZqJREJig5qmYYIMAJZCEgKAwDFNU1RxJLYpWjNNU2KbADACkIQAIHBqtZo4JlGuVCqFCTIAWARJCACCpX+VmPSWGWO9Xg9zZACwEJIQAASLZVn+XZERi8V8ahkAQgpJCAACR+4KoUUtoyYEAAshCQFAsLRaLV+TkE8tA0BIIQkBQITEYrFutzvsXgBAgCAJAUCwxONx/xrnnPvaPgCEDpIQAASLpmm+lm38W44NAGGEJAQAgdPr9XxqmXOuaZpPjQNAGCEJAUCw+FqzcRzHv8YBIIyQhAAgWBhjiUTCj73utm1nMhnMjgHAQkhCABA4+Xzetm3pzVqWlc1mpTcLAKGGJAQAgaNpWiKR4JxLbNO27UQigUVCALAIkhAABFE2m202mxKX9ViWlc/nZbUGACMDSQgAgiiTyeRyuWazKaU1wzC2bt2KghAALIUkBAABJVY3e186La50LRQKMjoFAKMGSQgAAkrEl2636yUMWZbV7XYRgwBgJUhCABBcjLFSqXTGGWc0Go21rhlyHMcwjPn5+d27d2PnPACs5ORhdwAAYDWMsXw+H4/HG42GqqqDrPVxHKfT6bRarXw+PzExsQ6dBIDwQk0IAIKOMTbR7e5oNERxqNlsrrTB3nEcy7Iajcb8/HzpmWcmTjttnbsKAKGDmhAAhEG5zKrVwtgY59w0zVarZRiGoiixWExRFMdxRDZijGWz2U996lNERO99LxWLdPjwkHsOAMG2YX5+fth9ICJKpVKtVmvYvQCAQCqXaXqa9u9f+JqIPpxzzjk7ZvEbx8dpbIymptatpwAQFv3ggZoQAATerl2LYhAdu6j1BEuhq1UaH6fJSUomfescAIQb1gkBQLCNj1OhQGNjbt6bTNLYGJXLkrsEACMENSEACLDpaZqeJi+T+FNTND5O09MusxQAjDrUhAAgwMplqlY9tZBM0tQUFYuSOgQAowZJCACCSteJiLwfDz02Rsnk0dYAAI6HJAQAQVUuy9n2JcpCWC0EAMtBEgKAQCqXaWxM2uIeURbCHBkALIEV0wAQPO027dol+VBEsaO+3caOegBYCDUhAAieYpF27ZIcWZJJKhRQFgKARZCEACBgxM55Pw6Gnpykdpump+W3DAChhSQEAAHjfef8SrCjHgCWQBICgCCRtXN+JYUCdtQDwEJYMQ0AQVIsLr1iTDKxdNq/sAUAoYKaEAAERrHo/oqxwYnLyDBHBgBEhJoQAARFu026Lnnn/EpwGRkAHIOaEAAEgx8751eCU6cB4BgkIQAIgOlpard92Tm/krEx7KgHAEISAoBAKBb92jm/kmSSqlWsFgKAFZNQq9Xy2PTc3Nz//M//HDhwYHZ21mNTADDKdP3oKuZ1Ji4jwxwZQLQts2L6qaeeuvPOO2dmZp555hl3je7fv//BBx/sdru5XO6CCy7w1kMAGHXrsHN+JWJH/eQkLiMDiKzjktChQ4f27t178ODB2dnZTZs2uWjupZde+sd//Mcf/OAHt95668TEhKROAsDoWp+d8ysRtSj/TrUGgMA7bnbs3HPPrVarO3bscNfWL37xi8svv/zZZ5996KGHEIMA4MSmp0nXh5xCpqaO3nQGAJF0XBKKx+NEdPbZZ7to6KWXXvroRz/6/PPP33333eeff76c3gHAaAtCMQY76gGibZkV0xs3bnTR0N/8zd88//zz11133bvf/W7PvQKACNB1arcDceuFmJvDZWQAkSRnF/1Xv/rVJ554IhaLXXfddVIaBIDRF4SCkICyEECEyUlCd999NxH92Z/92Wmnnfbaa68dOHDg0KFDc3NzUhoHgBFULg9n5/xKsKMeIKok3Dt28ODBn//850R09tlnX3vttf/1X//1+uuvHzlyhDG2Y8eOP/7jPx6wnVQqtfRF78caAUDgtNu0a9fQds6vBDvqAUbXshlDkJCEvve974n/+dnPfvbP//zPZ5111htvvPGZz3zmgQce+Lu/+7uTTz75wx/+8CDtIPQARMVwd86vJJmkQiFAc3YAIM/SjNHPRhJmxzqdDhGdf/75t95661lnnUVEGzdu3Llz57ve9S4iKpfLmCYDgF8TW9aDmTYmJ7GjHiBqJCShl156iYh+53d+Z9HrxWKRiLrd7oEDB7x/FgAYEUEuuoil07iMDCBKJMyOidOof/M3f3PR6+Pj4+J/XnnlFe+fBQBGgdipLmPnPOeciCzLEr9kjGma5r1ZGhuj++8nXQ/E9n4A8J+EJHT66acT0dJrVmOxWCwW6/V63j8FAIwIzwUhzrlpmrVajYgURYnFYoqiOI4jfkvkoWw26z4V9ctCSEIA0SAhCb3jHe/4z//8z5/+9KdLf+ukk04iore+9a3ePwsAhF65TGNjrhdKW5ZVq9U6nY6qqrlcTlGUpR/jOE6n06lUKoyxfD6fyWTcfCbRyWIxuLN4ACCPhHVCYp/8j3/84xdffHHRb73xxhtvfetbs9ms988CAOEmds5PTbl7d71e37t374YNG3K5nKZpy8YgIlIURdO0XC6nqurDDz9cr9dd9haXkQFEhpskNDMzs2fPnhdeeEH8MplMXnHFFUT0ta99beGHPfPMM0eOHLnuuutEZQgAIq1YpF27XBzVwzmvVCqGYYgMNMhbFEVRVTWTyViWtX37drGiaG36O+oBYNQtk1HEjPvs7Owbb7yx9Hfn5ua2bdt27733bt++vf/i9u3bL7jggn379j333HPilV/96le33377H/7hH1577bX+9BwAwmN6mtptFwUhzvn27ds3bNjgorQs6kPxeLxSqbgJQ5OT1G6jLAQw8o5LQgcPHty5c+dtt91GRLOzs1dfffUdd9zRr/30bd68mYjOOOOM/iuKolSr1d///d//yEc+8vnPf/5LX/rSVVdd9d73vvcLX/iC/38EAAg8twuldV3XNM3LpjBN01RVrVQqa34ndtQDRMOG+fn5YfeBiCiVSuGMaYDRpOt0//0u7tYQtRwpCw2bzWYikSi42A4m7t/APjKAkdMPHljBAwA+KxZdzIuZptnpdGTtt9A0bWZmxjTNNb+zWsVqIYDRhiQEAH5ye8VYrVZLp9OyeqEoSjqdFqcQrU0yeXRHPQCMKCQhAPBNu0267q4g1Ov1GGMS+yJa659JvQbYUQ8w0pCEAMA3bnfOt1otOVdnHE9VVZdloakpzJEBjCokIQDwh9ud80RkmqaqqtJ7xBjjnLvZUS9m91AWAhhFSEIA4A+3t1VYliV3XqxPnEzt8qBF7KgHGFFIQgDgg3L56FrjteOcr3SZhhRukhARjY1RMok5MoDRgyQEAD7wcMWYy6QymHg87r79apV0ndptmR0CgGFDEgIA2dzunBe63a5Ps2P99l2+U1S5UBYCGC0nD7sDADBapqdJ18nD4fXxeNzNXve1tO/+zVNTtGULTU66znkAEDSoCQGAVG6vGOtjjLkv25yI4zieCk7JJE6dBhgxSEIAII9YRuPtli5fp8Ycx/HahKgG6brXdgAgGJCEAEAezwUhImKM9Xo9Kd1ZqtfreT2zEQctAowWJCEAkMTDzvmFGGOJRMKPHWS2bScSCQk1J7GjHscLAYwEJCEAkKHdpl27vBeEhGw222q1pDS1kG3bsi63p2r16CHaABBySEIAIIPbK8aWpWlar9eTXhbinGcyGTltJZNUKGCODGAEIAkBgGfiqna3RykuxRjbunWrbduyGiQiwzCkxSBhchJ31AOMACQhAPBMxkLpRfL5vOM4sg4WEuWlgrdNbYvhMjKAkYAkBADeiP3kckMGEWOsVCrZtu19joxzbhiG5BgkiKXT2FEPEGZIQgDgTbkscV5sIcbYlVde2Ww2vRwC5DhOs9kslUpeN88vCzvqAcIPSQgAPCiXaWzMv6snMplMLpczTdPdNBnnvNFo5HI5X2KQIP74mCMDCK0N8x6uB5IolUr5sWkWAHzUbtOWLXT4sKwtYyvhnFcqlXg8PnigcRyn0+l0u91CoeBjDBLabRofp2oVl5EBhEg/eCAJAYBb4+M0NubT1NginHPTNBuNBmNMVdVVTkcUGajVammaViqV1qFvRES6TvffT/v3r9OnAwDPkIQAwJvpaSoW6fDh9fycIg8ZhtHr9RhjiqLEYjFFURzHERd02LYdi8Wy2ezExMR6dgxlIYDQQRICgOVxzi3LEju2Wq0WYywejzPGGGPHTTONj9PU1FAe/PwY8U1DdDWVShGRpmm+z4WtRNepXF4YDfsj2e12OecrjiQADAOSEAAcZ2G5JRaLxeNxImKMOY4joobYwJXNZjOZDKvVMBm0jPFxmpzk+bxpmrVaTVEUUbii40eScz6cwhUALIAkBAC/Vq/XxZNb0zRVVVf6MHHUoeM4mmkWhlQQCjL+gx+Yn/lMjbFUKpVIJEQGWv4jObdt23Ec5CGAYUESAgAiIs65ruuc83Q6vcqTe6H+tqxSqSThXvdRITa4KYqSTqcHfAtGEmCIkIQAgCzLqlQqqVTKxbIVy7K63S5KGoJpmrquZ7NZF4EGIwkwFP3gcfKwewIAwyFikLuHNxFpmpZIJBqNBhFF/BFuWdbDDz/scSQNwxjmcm+ACMMZ0wBRJKZyXD+8BUVRMpmMYRiy7kkNIxEo0+m0x5FMpVJimlJi3wBgEEhCAFGk63oqlfK+NkVRFFVV9QhfQep6UmwRsce+UqlI6RUADA5JCCByTNPknMuaiBEnPkczDOm6LrbKS2ktkUgQkWmaUloDgAEhCQFETq1WE+cQernjfSFVVaM5QWaapsSVPWKOrFaryWoQAAaBJAQQLaLkIMoYA26bPyHRTr1el9JaWJimqaqqrDEUxN9LNGMlwLAgCQFEi2EYq5yd6FoqlTIMQ3qzQVar1fwYSVVVURYCWE9IQgDRYlmWH8/vqBUzxIVifhyHyBiLzjACBAGSEECEWJYldzYnsjjnfgRKIhJLsBGGANYNkhBAhPhUxhDi8Xh0nt84+AdgZCAJAYA03W532F1YJ91u179MqShKdDIlwNAhCQFECOfcv9mxWCzmU8sB5GtNCDOYAOsJSQggWmSdIbRUr9fzqeUASqVS/v15HcfB1fQA6wZJCCBCNE3zLwk5jiMObIwIX0fSp5YBYCkkIYAIYYz5WsnwqeUA8jVT9no9XEoPsG6QhACixXEcnx7hkXp++50pMTsGsG6QhAAihDGWyWQ6nY70lm3bTiQS0Xl+M8YSiYQf66Zt285kMtKbBYCVrJiEWq2Wl3a73e5jjz32yiuveGkEAKTLZrO2bUtv1rbtbDYrvdkgy2azHr9PLsuyrKiNJMBwLZOEnnrqqWuuuebyyy/30u4nPvGJ66+/HkdiAASNpmnSixmO43DOo1bJ0DSNcy53JEVpLTqTjABBcFwSOnToULFYvOaaa5544gkvjd5zzz3NZtNbxwDAL9lsVu6/0Gazmc/nJTYYCoyxQqEgdyRt247gSAIM13FJ6Nxzz61Wqzt27PDS4rPPPvvAAw946xUA+CiTyeRyOVmPcMuyGGMTExNSWgsXUWCTVfw2DIMxhoIQwDo7LgnF43EiOvvss1031+v1SqXSnj17vPYLAPyUyWRisZj3RzjnvNvtlkolKb0KHVEW6na73pdeiUAZ2ZEEGKJl1glt3LjRdXN79uy55JJLsNwPIODEI9y2bS9hiHNuGEahUJDXr/AR8cWyLC8jaVlWt9vFvBjAUMjcRf/YY48dOnTopptuktgmAPiEMbZjx45ut2sYhou3W5bVarVKpRJmc/oj6SIMOY5jGIaoq2EkAYZCWhJ66aWXduzYUalUTjnlFFltAoCvRD0jm802Go3B53fEw3t+fn737t14eAtiJDVNazQag+8ms23bNE1N03bv3h2do5gAguZkWQ3t2LGjUCh4uXVo2ff6cVwHAPQxxiZOO41961tGItFoNFRVTSQSy96F7jhOp9OxbTsWi2Wz2WgukV6FWDbOGDMMo9lsqqq6UkwUI9lqtRhjV/7wh5nLLlvnrgJE0Cr5RE4S+upXv/rqq69ee+21XhpB6AEYjnI5c8stmUKBc26aZq1WUxQlFov185A4LoiIMscMtbuBJsaHc16r1RaOpKIo4p4TMZL5fH5ycpIxRrpO5TKNjQ274wAjbmnG6GcjCUnoZz/72d133/1v//Zv3psCgPWm69RuU6FAx6oaExMTfAEi0jSNMRac6RuR2LrdLudcLM1hxxBRNpsd+pydWJAuVkCfYCTHxuj++2l6GmEIYFi8JqG5ubl/+Id/+Pu///szzzxTSocAYF2Vy1StLnotULlnIdM0W63WzMyMqqpEFI/HVVUV5ZZerycqLpVKhTGWz+eHXrsSY3iCkUwmaWqKikU6fHidugUAx/OahKrV6k9/+lPDMJbdfvLFL37x3//939///vdfholwgAAqlymZDEU1QkScXq+nqmoul1v0u2L6iTEmVuf0J6dKpVIwI91xxsYomaRymaamht0VgCjymoQOHz786quvfuUrX1n2d6enp8X/IAkBBNGuXbR//7A7cWKmaeq6nk6nRSlodSIVqapqWValUgnH4u5qlcbHaXKSkslhdwUgcrwmocnJyQ996ENLX7/++uuJ6KabbtI07e1vf7vHzwIA8o2PU6EQ/IJQpVLpdDrZbHat1R1xFUaj0SCioIehZJIKhWVnKgHAb16T0Pnnn3/++eev9Lvvfve73/e+93n8FAAg3/Q0TU/T/Pyw+3EC9Xqdc750OmxAiqJkMhkxdx/0MDQ5SePjWDoNsP7cnKw4MzOzZ8+eF154QXpvAGCdhKH8YFlWo9HweHuPoijpdLrRaJimKatjvugvnQaA9bVMEnIch4hmZ2ffeOONpb87Nze3bdu2e++9d/v27b73DgD8oOtERMG+L0wskU6n096bEpWhWq02+OnPwyGWTou/HQBYL8cloYMHD+7cufO2224jotnZ2auvvvqOO+5YWvvZvHkzEZ1xxhnr1ksAkCkM25RqtVoqlZK180tRlHg8rgc8ZIiyULk87H4ARMuG+WAsFEilUjhjGmA9lMvUbgd/auwv//Iv5d7N7jhOs9ksFApDP3fxBMbHKZkM/l8QQNj1g4fMu+gBIOjabdq1K/gFoXq9PsiG+TURu+uXPfksWKrVo+vZAWBdIAkBREmxSLt2Bf/QGsMwpCchItI0TdzOEWj9HfUAsC6QhAAiQ1QaAl8QErd0+XE2tKIovV4vBGFocpLabZSFANYHkhBAZJTLoThR2rIsPwpCQiwW86llmbCjHmAdIQkBRIPYNhX5U/sURQlBTYiICgXsqAdYH17PmAaAcCgWQ1EQIqJWq6Uoik+N+9eyfOIysmAf+wQwAlATAoiAYjEUV4z1+Xe6RywW63a7PjUuWTJJY2OYIwPwG5IQwKhrt0nXg79Qui8ej2/YsMGnxjnnqVTKp8blm5rCjnoAvyEJAYy6kOyc79M0LTRlG7/h1GkA/yEJAYy06Wlqt0NUEBJ6vZ5PLXPOg37G9CJjY9hRD+ArJCGAkVYshu7eBnGSkE+3pTqO48dJRT4SN29gtRCAb5CEAEaXrh9ddRsqjLGtW7fati295WazmclkpDfrO3FHPebIAPyBJAQwuorF0M2LCfl83o+aEOdc7q2u66daJV2ndnvY92ZPzwAAIABJREFU/QAYQUhCACMqbDvnF2KMJRIJuWUh27YTiUTIpsb6RG0PZSEAHyAJAYyi6WnS9dCtEFqoUChYluU4jpTWHMdpNpthLQgJ2FEP4A8kIYBRVC6HOgYREWMsl8uZpimlNRGDQrZrbBHsqAfwB5IQwMgRC0rCf0vDxMTE1q1bm82mx3YMw2CMTUxMSOnVMIm5TlxGBiAVkhDAyAl/Qagvn887jmMYhru3999bKpWk9mtIUBYC8AGSEMBoKZfDuHN+JYyxUqmUzWYbjcZa1ww5jmOapqZpu3fv9ql7Q4Ad9QCy4S56gBHSbtOuXXT48LD7IVN/YqvRaDDGVFU94f4vx3E6nU6r1SoUCqE8QGh14o76yckQ3aACEGQb/LvzeU1SqVSr1Rp2LwBCbnz86JHEo4hzbpqmYRi9Xk/TNEVRFkYiUTHqdDq2bcdisWw2m8lkwrpn/oTKZWq3R/UvGmB99IMHkhDAqJiepvFxkvQvWhxsaFkWYyxQW64455ZlidU/lmUpikLHYhBjjDGWSqUCtTjal5Fst2l8nKrVkZkGBVh//eCB2TGAUeF5obQourRaLcuyiEhRlFgsJl4XxZUgFFoYY5lMpj/nxTkP4KWqC0dSZLWlI+kproml08XiiM2EAgwFakIAI0HX6f77af9+d+8WT+5araYoiqZpqqou+gDHcXq9nm3bjuNompbNZoMWPgKiP5KpVErUqBZ9gOM4Ir2Jkczn8y6TZbtNxSJNTo7AcQkAQ4HZMYDRsmWL67kS0zR1XU+lUolEQhQwViEWI9u2ncvlAjUJFQT1er3RaKiqOkhMFCPZ7Xbd14emp1EWAnANSQhghHhYP6vr+szMTDqdXlNlQlxeQUSlUmlkVyWvBedc13XOeTabXdMbxVZ/97GyWCQiLJ0GcAFJCGBUtNu0ZQsdPuxiT3WlUnHx8Bb6JQ2EIc759u3bU6mUuxnD/ki6OfcIS6cB3OoHD5ysCBByxSLt2rXOMYiIxIqieDxeqVTctTAydF3XNM31wqn+SOourtFIJqlQwEGLAF4gCQGE2fQ0tds0NbXW99XrdS8xqE+c6+PmET4qRKBMpVIe20kkEpZl1ev1Nb9zcpLabdxRD+AakhBAmLnaOW9ZltjcJKULmqbNzMzIujQ+XCzL6nQ63gMlESmKkk6nDcMQRxisQX9HPQC4giQEEFqiErP2BSK1Wm2tS6RXIR7htVpNSmvhout6Op2W1ZqiKKqquhnJQoGSSdxRD+AOkhBAaBWLLubFxBnNS08M8kKEqjUXM0JOlMHkrhZnjFmW5WYkq1WsFgJwB0kIIJyKRSoU3BWEZMWghZfDuyxmhJlhGHIDJR0rC4m7RNYmmaSxMcyRAbiAJAQQQtPTpOsuCkJEZJqmrOOhFx7DyBgT1SYpLYeC9NKaoGmay2GcmqLpaSydBlgrJCGAECqX3e2cF7eBnvAgaRf8aDPITNP06RQlRVF6vZ74m1obsXQac2QAa4QkBBA2bnfO07Eb0aX3SFAUJVI1If/CXywWc5OE6NjyeZSFANYCSQggbIpFL7cr+Pf8jlRZqNVq+TqSLpMQdtQDrB2SEEColMtH18a6wjn3tZIRqTtzYrGYTy27T0JENDZGySTmyAAGhyQEECq7drmbF1sfEb+ATJaFm/LcqFZJ16ndltMbgFGHJAQQHm53zvdpmtbtduV16Dic83g87lPjQROPx3u9nn/te8qUomqIshDAYJCEAEJC7Jz3sEJICO7zO1T8zpReTzqYmiJdx9JpgEEgCQGEhKsrxhbxNalwzqOThMjPTOl1doyIkkmcOg0wICQhgDAQyz4KBY/NMMYSiYT71bgrcxzHcRxZZzYGH2PMcRw/RtK2bU3TJGRKMYuKy8gATgRJCCAMZBSEhGw268cOL8uyMpmM9GYDizGWz+dt25besm3bUi63x0GLAANCEgIIPG875xfRNI1zLr2YYdt2Pp+X22bAZTIZ6cMo6kzSMqXYUY/jhQBWhSQEEGztNu3aJasgRESMsUwmI7eYIQpCkVokRMemGuUeq91sNiWX1qrVo4eSA8AKVkxCLurnc3NzTz/99OOPP/7KK6946xUAHFMsurtibBX5fN5xHFmPcM55q9WSM6ETNoVCwbZtWZUh0U7B82qw4ySTVChgjgxgFcskoaeeeuqaa665/PLL19TQvn373ve+9330ox+99tpr3//+9//5n/95Gz+FAHgkrhaXfZQiY6xUKkl5hDuO02w2S6VSdNZKL8QYu/LKK5vNpvfdXo7jGIYhOQYJk5O4ox5gFccloUOHDhWLxWuuueaJJ55YUyu33nrrnXfeefrpp4+NjYmj1Q4dOnTFFVdE6uh9APnkLZReRMojXMSgXC4XzRgkZDKZXC5nmqaXRvwNlLiMDGBVxyWhc889t1qt7tixY01NPP3009/5znfuvffe/fv379u37/vf//7U1BQRvfLKKzfffLPMzgJEitj/7EeRgIgWPMLdTZM5jmOapqZpExMT0vsWLmIkG42Gu1jJOW80Gtls1sdAWShQMokd9QDLOnnhL0Q55+yzz15TE4888sjevXu3bt3af+Xqq69+8cUX77nnnh/+8IfPPffcueeeK6WvANHiW0Gob2JiIpPJVCoVIlrTY9i27WazWSgUIrVzfiWMMREHG42GqqprGknLsrrd7npML4qykG/BGiC8llkntHHjxjU1ceGFFy6MQcLHPvYx8T9+nLcBMPrKZRobk7VzfhVizdD8/Hyj0bAsa/Wqhlhn3Wg0bNsulUqIQQtNTEzs2LGjP5Krf7AYyVqtNj8/v3v37vWYXhRfTpgjA1hiw/z8/KKXDMMoFoubNm165plnvDT9e7/3e2+++eY3v/nN884774QfnEqlsKgI4Kh2m7ZsocOH5W4ZWx3nvFarzczMMMYURYnFYuK/4rfEzRKtViuTyaRSKWSgVViWZRiGGElxssCikex2u5zzfD6/3kcPtNs0Pk7V6jokbIDg6wePk0/4oe7Mzs6++eabb3vb2waJQQARIfZqWZYl/qfb7aZSKXbMrz/Oh53zJ8QYKxQKnHPLssR3h263a1mW6FsqlSKiT33qU+vZpVXwBbrdbjweZwsMt2+aponjK8VIcs7793KIkRza4qr+qdMLktCikRR/0YyxKK+Ch6jxKwkdPHiQiLZt2zb4W8S/wEVQKILRICoupmmK8oBYk+c4TqfTEY9Jxlg2m52YmDh6Dp7snfMDEucuBrnkY5pmq9WamZkhIlG+IqJOp0PHDmgW92AM/Y8Q0JEcG6NymaanaWysXq8bhiGqff2RXLjuW9M0f9dxA6yjZTOG4Nfs2E033fTUU099+9vfPuWUUwbsIkIPjCTTNGu1Wq/XW2UtrXiEi0V1Wcua+Ou/xvzFUvV6vVarKYoy6EiKZAmL6Hq9Xq8xpiiKpmmqqi77USKmd7tdwkjCiPJ3duwnP/lJrVb78pe/PGAMAhhVuq7PzMys8rwRFEURD3jHcax4fPt3v1u68MKhz/IEB+dc13XOeS6XE6WLlSwcScMwDMMolUoYyT7Ouc4517RcOn3CkexP8zUaDSJCGIJRJf/esbm5uVtuueXGG2+86KKLpDcOEBac80qlYllWLpdbPQYtJB4/8Xi8UqnU63VfexgWlmVt3759w4YN2Wx29Yf3QoqipNNpMZJyrwYLL3cjKab5xHul3zgLEATyk9Add9xx/vnn33DDDdJbBggLznn/kePi7ZqmpdPpRqOBMGRZVqVScbdaRcTKVCql6zrCkGVZe/fu9TKSIlYiDMHokZyEHnnkkXa7vXv3brnNAoSLrutii5DrFhRFyWQyhmFE+REu6mrZbNbL9BZjTFVVMbkmsW/hIgJlOp32MpL9MCSxYwBBIDMJPfbYY1//+tc///nPS2wTIHTEz83ed9yI9S56hG9IEIHS+yofVVXj8XiUR7JWq3kMlIKmaYqiRHkkYSRJS0KPP/74Pffc84UvfGHRKulut/vCCy/I+iwAAWdZVqfTcTcptlSUH+H1el1KoBQSiQTnPJqzjaIeJmvZuKZpMzMzUS5Vwuhxk4RmZmb27NmzMN8cOHDgc5/73L59+0477bRFH3n99df/1m/9ltduAoRErVaTe/5KIpHon8QYKYZhrHL+x1qJBdSGYchqMERM00yn04N//Oo3roiRrNVqnvsFEBTL7KIX/wxmZ2ffeOONpXeQzc3Nbdu27fXXX//Rj3503333EdGjjz76yU9+koguueSShR955MgRIsrn84NvUgAINcuyLMvK5/MS2xTbwk3TjNQeZtM0iUju7nfxjciyrEgdFWiapqqqa/omfMIPjsVinU4naiMJI+y4mtDBgwd37tx52223EdHs7OzVV199xx13LJ3b2rx5MxGdccYZRHTo0KEbbrjhzTfffPPNN48cT3zwZZddth5/DoAAMAxj8A3zg1NVNWrFDP9GMmrFjFqtJn0kxQq2qH1Nwgg7riZ08cUXX3zxxau/4aSTTjpw4ED/lxdddBHOhgYQTNPM5XLSmxWlkUj9CC69tCYwxprNpsRFMwFnmmav1/PjD5tIJJrNpvRmAYZC/nlCAFHm01ywoijRWSokrn31o2VFURhj0RlJkj3D2Ce+ICM1kjDCkIQA5PDv+U0RS0Kcc18XF2IkpYhapoQRhiQEIIevT51YLBadaWhfRzIej0fn+d3tdmOxmH/tR2ckYbQhCQHI4etTIVIbMH19fsdiMXG/ehT4mikjVaeE0YYkBCCHpmmrH8TiheM4EVnkS0TxeLzX6/nUeK/Xi8fjPjUeQP59TZJvi5AA1hmSEIA0eH5LwRjzr2wTqUyZSqWkfE0uG6eiswUPRh6SEIAcvj4VIvX89vVPGqnnt6xMudIUW3RGEkYbkhCAHIwxx3F8WjkRqQUZjDH/qmsUpee3ryMZqXQOow1JCECaTCbjR2ThnDuOk8lkpLccTIwxcWGq9JZt204kEtF5fjPGYrGYHyNpWVZ0viBh5CEJAUiTz+dt25berG3bfhy4HGT5fN6PUwNs285ms9KbDSzGWDab9elrMlIjCaMNSQhAGp+KGbZtR+3nb1G2kTuS4kzkqI2kH3VKUVqLzt0vMPKQhABkymazcu9jMgwjk8lEZ0JHYIxJLwu1Wq2oldaIiDG2detWuV+TESxSwmhDEgKQKZPJ5HI5WQ8e8dN8oVCQ0lq4aJrGGLMsS0pr4i6UiYkJKa2FSz6fdxxH1kgahsEYQ0EIRgmSEIBkmUwmFot5f/A4jmMYRjRjEBExxgqFQrfb9T65wznvdrtRHslSqWTbtveRFF/VpVJJRr8AggJJCEAy8Qi3bdtLGHIcxzTNUqkU5R++xUg2m00vI8k5F4EyajOMCzHGrrzyymaz6eXIadu2W61WZAMljDAkIQD5GGM7duzodrvuHuG2bTcajSuvvDLKMUjQNM3LSFqW1Wq1Ih4oBTFva5qmu5FsNpu2bWMkYSRtmJ+fH3YfiIhSqVR0rtqGiOCcm6bZaDTS6fSABQmxnsNxnEKhgEdOH+dc1/VOp7OmkWw2m2JiyO/uhQjnvFKpxOPxRCIx4OWsGEkYVf3ggSQE4K/6+95nfPjDvV5PVdVVwk0/A2Wz2Wgu7F2diJW1Wk1RFE3TVFVd6SMtyxJXTGAkl9UP6IwxVVVXSpaO43Q6Hdu2Y7FY5rvfzX/1q5RMrm9PAfyFJASwLopFIuL/7/+JaZqZmRk6dlhO/yYEsShYHIKHJ/fqOOeWZRmG0el0YrGYqGqIkXQcR9x2gpEcxNKRVBQlFostGsl8Pp/JZMSXMVWrw+41gExIQgD+m56m8XFa8E+ML9DtdsX18mK7eEDW84oHpOie6CcRiVJWKpUSXR12H4kWjKT4vtEfyeBMKYrSCx1LuiJYiNFLpVLBOeBxoJFst2l8nKpVGhsbUjcB5EMSAvDf+DhNTlJI9tosnH4Sc0/i1ipRJOiXCjRNy2azwQkcAdQfSVVVRaFlYblFhMvwjaSu0/330/79w+4HgDRIQgA+03Uql+nw4WH348Q457VabWZmRlXV1RfSLlw7UiqVAlIfCo7+yu7V14TRsZFstVpiJXIIRrLdpmIxRMke4ISQhAB8tmVLKGYTLMuqVCpi5mvAt4ineLfbxXKchbyMZDi2Ck5PU7EYinAPMAgkIQA/lcs0PR38qYR6vV6r1bLZrIuahDj7MZfLIQwRUb1eX9NxCQuJNTrhiJXj4zQ2RlNTw+4HgAT94HHysHsCMHLabdq1K/gxyLKsRqORy+UGPFdmEUVRMpmMYRhEFIJHuJ/q9bphGLlczt3bGWPpdLrRaFDwR7JaPbr6DTvqYYTgjGkA2YpFKhQCPi8mTthLp9PuYpCgKIp4hMu63TOMRKDMZrNeGunHyqCPZDJJhQKVy8PuB4BMSEIAUk1P0/R08E9e0XXd3aTYIiIM6bru/XbPMOoHSu9NiS17uq57b8pfk5NHv8gBRgWSEIBU5XIoYpA43kZKa+KYnBA8wn2g63oqlZI1kmLXfdBHMpmkqamjZy0CjAQkIQB5xDMs8NuMLcuSUsboU1VVHMkosc1QsCxL7p4vTdNCMIxjY5RMUsATG8DAkIQA5CmXg7+txjRNcbWCxDZFg2L1dHTour7K9WfuiL8XcTh1cImyEFYLwahAEgKQpFymsbGAL5QmIsMw/DjHLxzFDKmkF4SEVCpVq9WkNyuZKAthjgxGApIQgAxi53zgC0JEZFmW9EoGHStmRCcMWZbV6/XkltaEWCzWv/Et0KpVLJ2G0YAkBCBDsUi7dgX/kBXLsvx4ePeF4PkticQl54soisIYC8FIYkc9jAokIQDPxE/GYSgI+ff8JqJ4PB6C57ck0fmTrmZyktptlIUg7JCEADwrl4N/orTg9/O72+362n5wdLtdXzNlOOYZsaMeRgKSEIA3Yi9x4BdK9/k3OxaLxXxqOYBQEzqqUMCOegg7JCEAb4rFUMyLCYwx/8o2vV7Pp5YDKJVK+ffndRzHv4KTfNUqVgtBqCEJAXgQhivGFvL1+eo4TiqV8q/9oHEcx7+Ww5SEkkkaG8McGYQXkhCAW+026XqICkJExBjztZLhU8sBpGmaf3/eXq8XpiRERFNT2FEP4YUkBOBWSHbOL+I4jk9rXDjnfpw0GEz+ZUrHcUJWEyKcOg3hhiQE4Mr0NLXb4SoIERFjLJPJ2LbtvalFFRHbtjOZTMie3x4wxhKJhJSRXMSyrEwmI71Z34k5YpSFIISQhABcKRaDf+f8svL5vJSa0KI9aLZtZ7NZ782GSD6f92Ovu23b+XxeerO+w456CC0kIYC10/Wjq0RDyI9ihm3bkZoaE8RIyp1qDHdpTVxGhjkyCBskIYC1C9XO+aVEMUPigl/btkulkqzWwoIxls1mm82mrAYdx2k2m+EurVWrpOvUbg+7HwBrgCQEsEZh2zm/lKZpuVzONE0prYnL7aNWEBIymUwul5MVhprNZj6fD/dIilopykIQKr4koVar5UezAMM3PU26HtIVQgtNTEwkEgnvj3CxUCaCBaG+TCYTi8W8LxhqNpuMsYmJCSm9GibsqIewkZyEnnrqqWuuuebyyy+X2yxAUJTLIxCDhEKh4DiOl0e4ZVndbrdQKMjrVPgwxgqFQrfb9TKSzWbTcZwRCZTYUQ9hIy0JHTp0qFgsXnPNNU888YSsNgGCRSyAGJUHP2OsVCppmtZoNNa6ZshxHMMw5ufnd+/eHe7ZHBnESM7Pz7seyVgstnv3bp+6NwRi7hiXkUFIbJifn5fSULfbjcfjDz74YLlc3rRp0zPPPLOmt6dSKcypQdBt2ULVaqhXCC2rXq83Gg1VVROJxAnvZ3Ucp9PptFqtfD4/ClM58nDOTdMUIzlIOhzxkZyepmKRDh8edj8AVtQPHtKSkPDYY49df/31SEIwgsplmp6m/fuH3Q9fcM5rtdrMzAxjTFXVpbu4RalDPLk1TQv9wl7fDDiSlmWJc4NCvGf+hMbHKZkcmdlkGD1+JSHDMIrFIpIQjJp2m7ZsocOHZd2t0T+EJlBPQVHVaLValmWJ4hBjrH87h9g0HrTqRb9vw+7IcTCSRETtNo2P0/79obuRBiICSQhgLWT8dLvw6UhEiqL0r5cSj8ZA3bHAj2HHDLtHv2ZZlmEYnPOlI6lpWiqVCuxIBq2QVq/XxTfefmJbOJLZbNZrh8tlardRFoJgQhICGNj0NI2Pk9t/KSIAGYbR6/XEdMnCVCHmSjjn4tBnkYcCFTuCQ4xkrVZTFGXZkez1eo7jYCRPaJCRFF+TsVjMU/lKlIVGcXUdjAAkIYCBjY/T5KS7LWOWZVUqFUVRNE1TVXX1DxZLaLvdbgCnToZOjGQqlRpwWbc4RBsjuVS9Xq/VagOOpMhDjuMUCgWX9SFdp3IZS6chgPrB4+Rh9+TXUqnU0hcRj2DIxE5gVzFIPHKy2eyAlQkRmBKJRKPRaLVaI3K6jAxid9uaRjKdTjuO02g0iAhhqK9SqXQ6nVwud8IMJIhyEedc13WXsXJsjO6/n3R9ZI6fgJBaNmMIqAkBrMrtznnxyMlkMgM+chbqF4dKpRLmdyqVCufc3W1c/eLQSJ3W4wrnXJQn0+m0i7c7jmOa5tatW90cpIkd9RBI/eCBe8cAVlYu09iYixhUr9c554P/5L2IKA7F4/FKpeLi7aPESwyiBSOpR/6UP13XGWPuYhARKYqSyWQsy6rX62t+s/hHVCy6+9QAfkMSAlhBu027drm4c96yrEaj4fqR0yeWZUT5EV6v1zudjse72RVFSSQSLh/ho0IEylVmBwYh6kmNRsPNvSK4jAwCDEkIYAXFIu3atdajUMQcRDqddlcNWiSdTs/MzMi6ND5cLMuq1WreAyUde4QbhuH9ntQwsizLe6AUxEjqut4/EGtQySQVCriMDIIJSQhgOdPT1G67KAjVarVlTxZ2Rzx4arWalNbCRcQgiSOpqmo0R1LXdSmBUmCMKYriZiQnJ6ndRlkIAghJCGA5bu+cN01T7ul5IgpErZghTk084bkDa8IYsywraiMpCopy191rmuZmGMUd9VgtBMGDJASwhFias/aF0qZpqqoqZV5soQgWM0RpTW6biqKkUinDMOQ2G3CGYfgxknQsY61NoUDJJO6oh6CRnITEgbmzs7NvvPGG3JYB1k+x6GJejPx5flMkixnSS2uCWDotvdkgk15aE1KplMt0Xq1itRAEjbQkdPDgwZ07d952221ENDs7e/XVV99xxx0vvPCCrPYB1kmxSIWCu8sBxN1SsjtEiqJE6lQhcQeW9NIaHStmRCcMiSKlHy2L4xbdvDOZxI56CBppZ0xffPHFF198sazWAIZjepp03d0RcJxzPx7eQjwetywraPd3+sSnQBlBLsPKYBRFcfk1OTVF4+M0PY3LyCAgsE4IYIFy2cXOecGyLF+f391u17/Go0NkymH3Yp10u13/viZjsZjLd4ql05gjg8BAEgI4xu3O+XXgfjIihFqtFmpCUqxDTcjlm0U1CDvqIRiQhACOKRbd7ZwXfH3qOI4TnXAQj8d7vZ5/7UequubfjC152ZyPHfUQJEhCAEREVC4fXcvplqZpYu8keOffSDqO4/HSiRDxtZTo9e9obIySScyRQRAgCQEQEbm7Ymwhxph/lQzvl0aFiK+ZMlJpNR6P+9d4r9fzuoS/WiVdp3ZbTocA3EISAvC0c36hSD1l/eNrppTw/A4PTdP8mwqUMGMrqrAoC8GwSdtFDxBWYuf8/LzHZhhjmqb5tAPctu3oPL+JKBaL+TGSnPNIrbjyL1NK+4KcmqItW2hyEjvqYYhQE4LIc3vF2FLZbLbVaklpaiHbtjOZTKSe39ls1rZt6S2LkZTebGAxxnw6Vtu2bSmX21MyiVOnYeiQhCDaxBVIhYKUxkRNSPoaVcuy5Dx1wiOTyfix1Ne27Xw+L73ZIMvn89IzpeM4nHNpmVJUg3AZGQwPkhBEW7ks8QAhxpj0B49t27FYLFJTY+RPMcOyrEiV1gRN0xKJhNxY2Ww2ZZbWcNAiDBuSEESY553zS2UyGcdxZIUhx3GazWZBUskqXAqFgm3bsh7hnPNWqxW10pqQz+ebzaas5fzib0Ty16TYUY/jhWBIkIQgqtpt2rVL1gqhPsZYqVSyLEvKI7zZbObz+agVhATG2JVXXinrEd5sNkulUjRHUtO0XC5nmqb3phzHMQzDl2herR495B1g3SEJQVQVi66vGFudrEd4s9lkjE1MTMjqWOhkMplcLtdsNj22YxhGLpeLZgwSJiYmEomEx5HsVyh9GclkkgoFzJHBUCAJQSRNT9P0tH9XjIlHuGma7ipD4ifvWCxWKpWk9y1cMplMNpttNBruYqUYyYgHSqFQKMRiMdcjyTlvNBrZbNbHzXeTk0f/YQKsL5wnBJEkb+f8SiYmJhhjDz/8sKqqa/oZmnNuGEY+n8fDm4j6IabRaGAkvWCMFQoF0zQbjUY6nV7TynHLslqtlu/Ti/3LyA4f9vGzACyxYd7zgXJSpFIpPw5iAViGrtP999P+/evwqTjnlUql1+sN8hR3HMeyLMdx/JqACLP+SGqapqrq6h9s27ZYtI6RXMo0zYcffpgxpqrqCfOQZVli92KpVFqnbXfj4zQ5KetgC4BV9IMHkhBEz5YtVK2u25m2nHPLsgzD6HQ6jDHGmKIosVhMURQxT8E57/V64nmTzWZRwFjJgCPZarXE2YwYyZUsHElVVcUYiqDjOE6v1xP/FSOZz+fX9TjK6WmUhWB9IAnBCBKLcsS+LbbAcR8kdur6PDW2UvdM0+x2u+I5JF4UPUylUoyx4Bx/PNBIDs/SkRR9EyMZqEOD+ALBHMlardb/66ZjI6lpWjweH9pILvePtD+M4pficpv17xqMEiQhGB3iuVir1YhIFAni8bjjOOLnWnEsYTab1TSN2m3asoUOH/Zjy9gLxmkyAAAgAElEQVQI6I+koihEJEoFdOxMYfHsOTqSsKpFI9nPExjJgbTbND4uCrciq5mmuXAk+yVAUfwLVPaFEEESglHQ/y6ZSqUSiYT4XrmIePaIVSNZy5q48EL/toyFl2VZtVpNzJWsMpKdTgezeKur1+uGYay+MkyM5HDmnsJC1+v1uqFpg4xkt9tFsgQXkIQg9Or1eq1WS6VSA377E6ehENH6rf0MiXq9PvjOLJEsLctKJBLY5L9IpVLpdDqDrOmmBSOZy+UQKxfinOu6zjkXs8Yn/HhxqjvnHAEd1gRJCMJNPHIymcyy1YuV9H+CxA/iQv+Rs9ZrKPojiVgpiK1tiqKk0+k1vbG/YRAjKViWValUBv8Jp89xHNM0EdBhcP3ggZMVIXzEbupcLremGEREiqJompZKpRqNhpTLB0KNc759+/YNGza4uI1LjGQ8Hq9UKnLvSQ0jy7K2b9+uqupaYxAdP5Jy70kNI8uy9u7d626eS1GUTCazYcOG7du3+9E3GGFIQhAy4oHh4pHTJ9ar1mq1iD/CdV138ZP3QmIaSFSVJHYsdHRdz2azg8yILWthGJLbsXARdbW1nvq4UH8kdV2X2jUYcUhCECb1er3T6Xi/UVxRFPEIl9GpUBLxxfsKU1VVI/7gqVQq8Xjc+8SW+LuI8kiKQOl9JBOJhGVZ9XpdSq8gCpCEIDTE/iYv1aCFVFVVFCWaDx7LsmZmZrwHSiGRSHDOo/ngqdfrUgKlkE6nZ2ZmojlvK6K5lJVSYrWWYRgRL/rC4JCEIDQMw/BSOV9K0zTLsiL47bJWq0ncb9x/8MhqMETE16Ss1sRIipOxosY0TbkjqapqNL8mwQUkIQgN0zTlbq5RFEVRlKh9uxThz/WilmWJpetRy5SieLPWZfuri8VivV4vaiNZr9dFjVZim4yxqA0juIYkBOFgmqb075V0rCwkt82AMwwjlUpJbzaVSkWtmGEYhtxASVEtZvg0kkQUzUlbWCskIQiHWq0m/XslRbKYIc5ckd5sLBaL2lSj9NKaIBb8Sm82sERpzY+zlFKpVNQyJbiDJAThIGs15VLxeDw6Dx6x3V16aU20GamDAUWR0o+WFUWJ2gSZH1+QRBSLxSJ+vgMMCEkIQsDvb2fdbtfX9oPDsiz/8oqiKJF6fvsnFosNuwvrR9y/5kfLYiEgwhCcEJIQhICvz2/GWKS+V/r087evLQdQq9XydSSRKaVAWQgGgSQE4eDfUydS3yt9fX7HYrHoVNfIz8pNpDKlZVm+Zsro/OsG15CEIAQYY47j+NS4fyuQAigejw+7C6Oj1+v51LLjONH5mvT1T+rf9w0YJUhCEAKMMf+eOuTz9+JA0TTNv7IN5zw6SSs6f1K/+fpzTq/Xk3iIKIwqJCEIB19rQtF5qiFTyuJ3pozO8zsej6O6BsOFJAQhwBjzdV0zvldKEannN/k8O+ZTywHkX6aM1DCCF0hCEA6aptm27UfLtm1H5/nNGEskEn6MJOc8Uj9/i5H0I53btp3JZCI1kr1ez4/UYllWJpOR3iyMHiQhCId8Pu/HU0d8r4zOU4eI8vm8Hzu0bdsuFArSmw0sxlg2m/UjU9q27cd1KIHFGNu6dWun05HeMuc8n89LbxZGD5IQhINPP4Lbtp3NZuW2GXCMMT8ODohUaU3QNE36MHLOOedRq2T4kSlt204kEpH6IQdcQxKC0Mjn881mU2KDlmUlEomoPb8ZY/l8vtVqSWwzgqU1OpbO5X5NtlqtCJYxNE2TftuabdsRHElwB0kIQkPTtK1bt8p68HDOo/nUISJN0xhjsh48nPNutxupqbG+QqHgOI6seoY4S31iYkJKa+FSKBRs25ZVYzMMgzEWtR9ywDUkIQiTfD7vOI6UR3iz2SyVStH8XskYE49w7w8ex3EMw4hmDCIixlipVLIsy/uCXxHNozySV155ZbPZ9D6SIpiWSiUZ/YJIQBKCMBEPHtu2vYQh8fDO5XLRjEGClAeP4zjNZrNQKGAkTdP0MpKcc8MwSqVS1GYYF8pkMrlczvtIiq9Jef2C0YckBCHDGNuxY0e323UXhjjnjUYjm81Gcw5iIU3TxCPc40hGbXnvUv1HuLuRtCxLxKAoB0rBYxiyLKvVamEkYa02zM/PL3ppdnb2ySefZIydd955a23uxRdfbLVap5566tatW086aQ0xK5VKyV3CCaONc16r1WZmZjKZzODXN+Ib5VKc80qloiiKpmkDjqTjOJ1OR6wNwkj2iZGMx+ODj4koqhFRxKtBi5im+fDDD6uqutaRFDVjX/sGo6QfPBYnoX379lWr1Ww2++KLL7788su7d+++8MILB2nx0KFDt99++xlnnHHOOeccOXLENM1LL730xhtvPOWUU9bUIYABcc7Nv/zLGmOMMVVVVVVd6SPFk7vVaolvlHjkLMI5N02z0WiIkVxlfPojqWkaHjlLuRjJfD6P8uRSnHNd1zudjqqqiURilYwuFg46jpP57nfzTz65np2EsFs+Ce3cufM//uM/vvKVr5x//vlE9LnPfe5f/uVfdF1/97vfvXpzhw4dKhaLO3bsuOqqq8QrL7/88uWXX66qarVaXVOHAAal63T//fyrXxWTC51ORzx4GGOKojiOIy5DEAf5i0kcZKBViKe4YRi9Xm/pSIrl1bFYDBOLJ7RoJBVFicViGEkX+slSDKD4slQURaz0XzyS4+M0NkZTU8PuNYTGMkmoXq+XSqWPf/zjf/u3fytemZubu+SSSzZt2vStb30rFout0tyll166cePGWq228MUHH3ywXC7ffffdf/RHfzR4hwAGtWED7d9PY2PiV5xzy7LEjm7xjVIc1KtpWnBmcBZ1UnxnT6VSgdrxK3oo/j2KToobajGSa8KPCfhIWpYlljf1RzIej4ub/gLSyZVGUvTw1z/etNs0Pk7791MyOcTeQogsTkJzc3O5XO7nP/95vV4XBSHh1ltvfeCBB2666abrrrtupbZee+219773vRdddNGXv/zlha9/73vf+8QnPrFt27Z/+qd/GrxDAAMpFomIBqs4Dt3SIgERMcb6RQKxPhSFqxMSI1mr1USFYOFI9usEhJEcwNKR7BeuxEiGsnAVqm8LMHT94HGy+PVjjz3285//fNOmTQtjEBFddNFFDzzwwL/+67+ukoSEH/zgBy+88MKZZ57Zf+X5558none+852S+w4wPU26TksW+wdTvV4XzxtN0xYtZlr4qBbLHWq1mqZphUIBT/GlxEimUqlcLrdo4YhYlyP+XyyeNQxDjOQQOhps/d0GqqquPpK2bYuRDE0empqi8XGanu6XigEGcbQmdMstt3zta197xzve8fWvf33hbz/11FNi6c+3v/3tc889d6VWPvzhD//sZz97//vff99994kl0nNzc5dddlmv1/vmN785yKJp1IRgDcbHaXKSAv+QE6s+OefpdHqt27Ly+Tx2p/f1N7il0+kB39IfSayRX8iyrEqlkkql1rQtSyxJDsdI6jrdfz/t3z/sfkAI9IPH0Y3u4hdLd9/87u/+rvif1c/JuPnmm4noiSeeuOqqq1588UUi2rFjx2uvvVatVgfcOwYwKF2ndjv4MciyrO3bt2/YsCGbzQ6+z1+UjlKpVKPRqNfrvvYwLEzT3L59u6qqg8cgOjaS8Xi8UqlgJIV6vb53795sNrumBUALR9I0Tf+6J4eoBun6cHsB4XI0Cf30pz8loqXLok8++ej0mdiAs5IPfvCD27dvJ6Jnn332sssu++u//uvXXnvtG9/4xiobmwFcKpeDvw5A/OS91kdOn1gKijBERJZlPfzww9ls1t03E03T0ul0o9EIwSPcZ/V6vdFo5HI5F3WdfkCv1Wpy70mVL5mkqSkql4fdDwiTo0Hn9ddfJ6KNGzeu9HHPPffc6g1NTk6eeuqpO3fu5Jw/+uijt99+++bNm9fUFbHTZxFMmcFxymVKJoO/CEDX9Ww262UqQVGUTCbTbDYDtc9onYlJMSkjWavVgrMZav2JJWi5XM5LI2IJka7rQZ8mGxujZJLKZeyoh4WWzRjCoMdA/8Zv/MYJP+bVV199z3vewxibnZ29+eab9+zZM2gHiYiotZw1tQAjrt2mXbuC/91NHDTs/VGhKIp48Mi6oDt0dF1Pp9MSR1JGp8KnHygHn6Vdiaqq8Xg8BCNZrR6dRgc4ZpWAcTQJ9WfBFpmbmxP/c8EFF6z+OXbu3Fmr1arV6iOPPCI2oN17772f+cxnJHQfQCgWqVAIeEHINE3OuazagzjWJQQPHh+ICChrhl1VVUVRIjuS4qQlKa0lEgmxA19Ka35JJqlQwBwZDOhoEjrrrLOI6Fe/+tWi3+7/MHr66aev0sq+ffseeuihz372sxs3bjzrrLMefPBBsbZR1/UDBw7I7zVE0PQ0TU8Hf4WQ2OYtsUFVVftn30WKaZprWiJ9QpqmRXAYxRGUEqcFFUURC4ZkNeiXycmj3zQATuRoEnrXu95FRK+99tqi3xYrqYlo0TlDC7388st33XXXBRdc0L+xdfPmzV/84he3bNlCRF/60pekdxqiKAwLpUVBSO4SCjGzYxiGxDaDzzRNUcWR2KZoLejFDNlqtZr0nSviKzzosVIsnRZnLQKs6mgSGh8fJ6Knn3560W//3//9HxGpqnrOOees1MSTTz555MiR5PEHnG/evFmsE1raJsCaiUmNwO+cb7VacssYQgSLGYZh+LHzNBzFDKmWLQiJk7i9UFU1BCMplk5HckoU1uRoErr00ks3b978v//7v7/4xS8W/rb4SfSKK644YUPzSw78vfDCCzdt2vSWt7xFUlchwkKyDcQ0TT/21IhiRqTCkGVZfoxkLBbr9XrRWYEuCmBLS2vei22MsRAMI3bUw2COJqGNGzf+1V/9FRF961vf6v/e3Nzc97///Xg8/rGPfWzhe2ZmZvbs2fPCCy+IX37gAx849dRTn3zyyf7yamF2dnZ2dvZDH/qQv38CGHnlMo2NBXyhdJ/cCZ2FzUYnCfkUKIlI3K4Vgke4PP59QYYjU4qyEObIYFW/3kV/7bXXZrNZXddfeukl8co999zT7XbvvPPO0047rf9hc3Nz27Ztu/fee8VRikQUi8U+/elPc87vvPPOhU3fddddb3/722+44Qb//xQwukKyc558K2MIPj3PAsu/P6+iKCF4fkvSarX8G8nQZMpqFUunYXXHbZ6/++67p6amrrzyyj/4gz/4/+ydbYwk1Xnvn13YJV3aLDGnRULcHWZzoQqiC9NINnaVTe602pER2orl6LKOgs32aGVfsOK80M7bCrHbKOEq2ttIzhVs9gZ5CmECrF9iuTsoRunsIEKVjEnoCbKlPjFsW9UssekDxibV4JjZ++GZKZrpmZ7uqnOmq/qc3we0zMuZM/+pOs//ec6b7/s//OEPH3300WuuuWbD9+zfv//NN9+85JJLwo98/OMfv+iii/7yL//yO9/5zm/+5m8CQKPRuPjii0+fPj3p+YoKxbtYXITjx+Hdq9CSCWNMXNQhhLTb7XTcghkboUpK5YRgs5sDOJIOJcMd9SmpKyt2nnc5IU3Ttj0Ocffu3ZtujL/ppptuuumm8H8//vGPc+mfQmqWl6HTSUVBCATH7/hLXFPE6Lt9YpLJZIS2nygYY9lsVlDjafKUhw+D46g76hVbMe4Z0wrFFEjDzvkQXdeFhthE32/AFXHBGwSbgwQi1EOn5plUO+oVI1FOSJFUcO9rqnK4fr8vrmV54rfylLwwDEPcM8nxLPWdoFxWO+oVW6GckCKpLC6mZV4MERpfgyCQJ36DSE/J/ejLJEMIEecp0zdju7SkdtQrNkU5IUUiScMVYxsghARBIGjlRMry73goT8kLQoggT4k2KGVKzs3BwoKaI1MMo5yQInl0OuA46SoIIbZt+77PvVnf9zOZTMqiTgwIIblcTpCSpmnKo6Su63hhKveWKaWmaXJvVjjHjqkd9YphlBNSJI/07JzfgGmaIqKO7/u2bXNvNsnYti3iJElKqWVZ3JtNMpZltdtt7s2m9ZlUp04rNkM5IUXCSNXO+Q0IKmYwxlKZf8dARDHD9/0gCOSZZER0Xed+GHS6S2s4567KQooBlBNSJIzFxRTtnB8GixkcF5O6riubDUIsy2q1Whwb9H2/nPhLfLlDCCmVShzLQkEQtFqtFJfW1I56xRDKCSmSRLW6tqoxtei6XiqV8ObL+OANHhLGbwAwTXN+fj6CGdrUhrquSwiR01Ni/YbXbGOr1bJtO92lNbyMTM2RKdZRTkiRJFJyxdhoTNPM5XLx6xmMsXa7LacNQmzbDoJg0hA+fNI3zldWKhVuPUsVaKa5bGxEaz4Lt74sLYHjQKcz7X4oEoFyQorEkMKd85sSBp44WThjzHXdSqWS1tUYPCCEVCoV3/fjKEkpbbVaMhtKACCEHDp0qNVqxVSy1+vNiKHE2rMqCykAAGDX+fPnp90HAADDMERscFCkhuVlKBYhGU8jFxhj9Xp9ZWXFNM1J7yPDkFMul9M9B8EJxlitVtM0rVAoTPq9rusCgOSGMgSVzGazkz5XuDYIjamgvk2BTgeKRVhamoHsSxGN0HgoJ6RIBsUiHD4Ms5W4M8Y8z2s2m/l8fszYM5shJzahkrqu5/P5cb4FK0nz8/OSV4M2EBr0QqEwpjuklLbbbdu2Z2FSbAOOAw8+CGfOTLsfiumgnJAiSTgOVKtw9uy0+yEESmm9Xu92u/l8nhCyafgJgqDb7eIJipZlzWDI4YHnea7ropK5XG7TShsq2W63CSFKyU1BW9lut1HJrTz6oJIzW57sdGBxcfZyMMWYKCekSBIHDvCtUSfwbikMP/V6HeN32L1wHatpmoZhyLm5aSK2VdK27RSfdrODUEpd1/U8T9O0TCaDeuLOO3yDLMuafSWXl2FxcVbTMMVolBNSJIZqFZaXYxaoMTr2ej3GGK4JxeEbazCWZSUno2XrwPptYlsViqbCVkqigMlUEsM2ISQ5fYOB0gsAbFASV+okp7dpUTJ8ccg62WyWg1crFmFuLtXHmCmioZyQIhl0OnDgAJw9G/luDVz34HmeYRgAQAjB7DZMbWF9E7WaKxkNBpuVlZV8Po8aYoAJgqDf7+N/1fzdODQaDdd1+/3+VkoyxnzfJ4Rg+Wra/U0oaIC2VRLPDY/l0XHp9JkzabzhRxEH5YQUySBGNsYYcxxn9FqHENzTHgSBiuLD4JYijDejlQyjOKxPQu1UH9MBpRS3uW27sntQSbW1bRjP8xzHyefzuLpuxFfieqZerwdxlKxWodNRZSHZUE5IkQBi7JzHkGMYxkSJYBAEnueVSiVlhkIw5BQKhTH3ZCEYxQuFglIypNFoNJvN8fdkIXhigjLogziOM9HuNhjwQxENutpRLyXKCSkSQNSd857nnT59etKQg4QjpkrEIVLICUFbmcvl1IZ/AKjVat1ut1QqRfheZdBDsNDLGIt2r1ksgz7TO1gVmxIaD3XGtGJKOA4ARLBBlNLTp0+XSqVoPgZnLrLZbK1Wi/Dts0Sj0aCUxlHSNM1+v+/gn1JiarUaYyyaDYJ1JV3XbTQafDuWOhzH6ff7ka93xbXezWYzysV/eBmZ9A+znCgnpJgS1WqEK8ZwRUuEs4Y3kMvlAEDmEI6nHMVUEm3lysqKzCHc87xutxvzbnY8QTvmbRhpp9FoMMbiP5Omadbr9YkvWcM76tX9G1KinJBiGlSrsLAQYUrecRzDMOLPamHgWVlZ4XVpfLpAQ2lZ1qTXgAwT1jPkDOGUUlxlFb8pTdPy+TzODcVvLXVQSpvNZkxDiaCSUYq+OCgtLsbvgyJdKCek2HE6nWh3znuehwfwcOlFmDtyaS1d1Ot1LoYSwcAjrZLRVlltCiFE0zQ5leRlKBFc/h+lVHnsGCwvw/Iyr54oUoFyQoodZ3ERjh+PcHQHxm+OHcGKiITFDFzpzLFBQki325VNSUoppXSiPXfbouu6bDICAJZm+e5gMAwD79+dDDVHJiXKCSl2luVl6HSiFYSA91gJABIWMzzPy+fz8efFBsGyUJTAk2Zc1+Vrg2Ddncs2aStCSRwrotjKhQXodFRZSCqUE1LsLNVqtOPLRIyVAEAIwcyee8uJpV6vi1Ayl8tJJSMAeJ4n4lYKwzCkcud4r4uIZzJinoNlIbVaSCaUE1LsILhXK9LZZZRSEcf/YDFDqjWqgq6nlW2qER9IvqU1hBASXrAlA4JsEKwrGeU7y2W1o14qlBNS7CCLixHmxUJERB1sVqqoI/Q8SXmUZIwJeiAhTghPIeKUxFc7opJLS2q1kDwoJ6TYKRYXoVyOXBASF3UymYw855sLjd/ZbFbFb47ti2s8UfR6vUwmE/nb8a7lrYjuKefm1I56eVBOSLEjLC+D40QuCAma0EGExrOkITS+SuUpY8bv0UjlKWPmOQLfX7WjXhqUE1LsCNVqtJ3zCCFkdOanGB9x8RsEbO5LLPI4FdEIfWZizX2rHfXSoJyQQjxRd84P0u/3eXVnA0EQyBO/hS5A6ff72WxWUONJwzAM9UzyQlyeE7ecjLP5qiw06ygnpBDP4mK0nfMhQqOCuHiWQIQqKVX8JoT0ej1BjQudDk4aQj0lxHzm1Y56OVBOSCGYanVt7WEMcHZMUOIYBAHfo6uTDCFEXNSRKn6L/k3lURJE1oQ4uHO8o17Nkc00ygkpBBPpirFhdF0XFMJli9+ZTEbQBJlsNSFxD6RUSuq6LuiB9H3fNE0ODS0tgeNAp8OhKUUiUU5IIZIYO+c3YNu2iH1Jvu/ncjkRJwUnFsuyfN/n3ixGHXniNyFE0LHavu/bts292cSi63oulxNhhnzf51Puxaq2KgvNLsoJKYSBO+fjrRAKwRDLfbj0fd+yLL5tJhzTNEVEHUqpbErati3OU3JvNslYlsU9z8EzFbkpeewYOI5aOj2rKCekEEbUK8Y2hRDCvZgRBAHPsTIlYDGj1WpxbFPC0hqIKWbIVlpDcIJMhJLcmpubg6UltXR6VlFOSCEGvLKnXObYpGmaQRBwNEOtVkuqaYiQcrnMMfAEQSCtkrZtt1otXgt+GWOtVku20hoAEELK5TJHd45rrcpcx5+1pdPqMrJZRDkhhRiqVS4LpQchhFQqFUopl8Djui4h5ODBg/GbSh2EkEOHDm0aeCJoizZItoIQout6qVTyPI9La61Wq1KpyKmkaZrz8/NczFAQBK7rcrZBoA5anGWUE1IIgMfO+U0hhHAJPFhYqlQqPDqVSkzTLJVKw4Fn0rsLWq2WtIYSMU2Ty9Jp13Xn5+fltEGIbdtBEMRXUqA1x7KQmiObOZQTUvCm04HjxzmuENrAwYMHS6VSs9mMXBmilPq+zz9lTBsYwuMo6bpuEAQyG0pYn9np9XqRQzjWMLAdrl1LGVj0jalks9nUdV2gNV9aWjs0XzFD7Dp//vy0+wAAYBiGPHc3zjjFIiwscJ8a20Cj0Wg2m/l8fqLMD1e04IArrm8pgjHmeR4Gj3w+P/43BkHged78/LzkwTskVNI0zYnqaowx13Vt25a5rjYIY6xer6+srEyqpO/7WA0SrmS1Cp2OuGRPsWOExkM5IQVXlpehWIQdeagYY7VaTdM0Qsi2UTwIgm632263VcgZhlJ6+vRpAMjn89vuWlJKjgANOj6QYyrZ6/XK5bLMk2LDhLYyn8/ncrlt/RDOqeES6Z1QstOBYhGWlkQsAFDsJMoJKcRQLMLhw3y3jI2AMUYpdV232+1i7MlkMuG4iZM+uEkqCALLsiTcnzwmGHtc1+33+1sp2e12fd/PZDJKyRGgkvV6XdM0XdfRqYefDYKg3+8zxkIllZvcitAPEUIIIclS0nGgWoWzZ3fuJyoEMMoJvf32288++ywh5IorrojzM1ZXV9vtdq/XsyzrggsuGLNDisSCm64ppWSdjV/hOPDgg3DmzFT6Vq/X0Rhh/Mbgjf00DCNR8WZ7JacECthut1OkJJJMJV3XBYBBJbGHeDhWog6yGlQyUQWq0UpO05RvkfUlVknFMFs6oVOnTi0tLVmW9corr/zoRz+65557rrnmmklbP3PmzN/+7d/2er1SqXTVVVcVi0XlhNJLo9Fot9u4hlHTtEwmAwD9fh8HI13XLctae+F37YIzZ6ZeMUafkZygiGCCi0riaI5KhreeJbDQopTkBYbGpMXFsBDIGNtKyUQZX0iUksvLsLiIZaENSqKMMKCkbduJMr4KZHMndNddd33jG9/48pe/fOWVVwLAF77whS9+8YuO41x33XVjtvvqq6/+yZ/8yb/8y7/cfffdE71CygkljcEi/6YLkzfMmNiMmT/9qVpFOMyG6ZLhJU2hku122zRNwzDUoLkpoZKGYWxaAUIlccnIuzy64t2Eq5JxJnRTJcNpZV3XbdtOlLNMCouLDULcvXvDOeWtlMRjOxLo0SVnEyfUaDQqlcpnP/vZ3//938ePrK6u3nDDDXv37n388cdDkzuCl19++ZZbbnnzzTcffPBB9FIROqRIApTSWq1mGMaYyxWxgp3L5crlsnrPB/E8z3GcSZUslUpJy8WnzkS7BXExchAEhUJBKbkBx3HQA42vJC5yUEoOwhhzHAdXKI6ppO/7jDFVH0oOG53Q6upqqVQ6d+5co9EYNDF33333ww8//PnPf/7Tn/706BZfffXVj3/846+88srDDz88fg1puEOKqYMhp1AoTORpwhGzUqkoM4RgyFFKxiQMOZNuq8at/sqgh6CSjLFJL/RAJZVBDwk3rhYKhUm/0fd9ZdATQmg81k5WfPLJJ8+dO7d3794NtZzrr78eAB555JFtW/y93/u9//iP//j0pz8dwQYpkkOtVsMzUSaNHDj1k81ma7Uar8sHUk2tVsPqThwl45+3m3Yw5PT7/VKpNOn515qmmaa5a9euWq3G93bPNEIpPXr06K5duyLca4ZKYgsi+pYuUAfDMCa1QdPv/uQAACAASURBVACAayubzaaj7i9LEmtO6IknngCA4c1il156KQC89NJLL7744ohWvvKVr3z729/OZDLblo4USabRaDDGIoScEF3XC4UCbuPi27d0gaE3zlWauKJIDZeO4xBCIoQcZNBW8u1Y6nAcJ87CqfBQAMmfSbTmlmVFrjKGtrLRaPDtmyIya04IC0TDazmvvvpq/Mfo3PS+++4DgN/6rd/at2/fG2+88dRTTz3zzDOrq6v8+6sQBqW0Xq9HDjkhuMJa5sDjeV63241/o3g+n89mszIHHrTmhmHEbCeXywGAzEqGZ5DGbEfX9ZWVFZlDOC77i6kkTqu1Wi1V9E0Ia07ohRdegPUtlINceOGF+I9er7dVE9/61rfOnTsHAO9973uPHDlSLBY/+9nPfupTn/rwhz/8+OOPC+m1QgCY6ESuBg2Sz+elzR0ppY7jxDeUCF7tKWfgoZQ2m834hhLWA8/Kyoqc87ZoKLk8k1jPcF1XzhCOtV4uGxIxY8RlW/FbU8RkzQm9+eabALBnz56tvm7E7Ng//uM/4j++//3v//mf//m3v/3tf/3Xf73lllsYY3/4h3+I827jYGzGuL+HIh6NRmOc+wHGR9d1SqmEw6XrupMukR4BhnA8Vk42uFQoQ1DJer3Oq8EUgc8kr9YwhMupJKWUizVH8OBsOZWcCiMMxoVjNjHiaMRutwsAV1555d13340f2bNnz1133fX888//27/9W7Va/chHPrJ79/aX3qu9Y1PEdV2+vlPTNE3TXNeV7UAX3GLDsUGs0nmeJ9XOW7TRfJ9JrHlTSqV6Jj3Pw5eRY5uEENwQLtWOPMdxJrqleBx0XW+1WnzbVGzFsMcIR5g1gxLOgm0gXOtz1VVXbdX6q6++CgC/8iu/suHji4uLANDr9Z566qmJu6zYQXDKgPughmUhvm0mHCyt8Y06AGAYhmyJI98yBoLFDNkKbK7rcn+10VrJNtUowkPjWCHbOJlA1pzQZZddBgBvvfXWhk+HU5gXX3zxVk3s3bsXAH7u535uw8eLxSL+48c//jGPripE4bou91wHpHzJBSmZyWT6/b5USnqeJ6LeQAiRSkY8qFPEMymbp0Tbxz3JAQBppxoTxZoTuvbaawHgjTfe2PBpXEkNACPOjEaT9Pbbb2/4eCaTGedkasXUEVflzmazsgUeEUriTUbyrKzEC8VERB3Z3LkgGwQAhBB5HkgAYIxls1kRLcumZDJZc0JYv3nuuec2fPr1118HgHw+f/nll2/VxK/92q/BgGd6V+u7dwPAe97zHk69VQghvH+RO5lMRp7lX+GFoCLIZrPyDJeyLUARh9BnRqoCW6/XE5TYa5omz6udWNac0I033rh///7XXnvt5ZdfHvw01j9vvvnmEU3cdNNNAPDv//7vr7zyyoZP/dd//dd73vMejovtFdwRZ4NATDE5sYiO3yNOspgxhAYGqeqUvV5PeUouCM1zNE2T55lMJmtOaM+ePbfddhsADJ4AtLq6+vTTT2ez2VtuuWXwe1ZWVk6cOPGDH/wA/3dubg6t0te+9rXBL3v++ed/+tOffvrTnx5n45hiWlBKxU1iSjWnIxSpSuii47fylFyQylPCZuftJb9lxZi841GOHDliWZbjOLgXDADuv//+Xq9377337tu3L/yy1dXVW2+99YEHHhi8gObo0aNXXXXVqVOnwmOH3nrrrb/4i7/49V//9SNHjuzIL6KIiNCQ0+/3xTWeQIIgENeyPMl9NpuV7ckRh7hKhlTPJIgczdTTPnXetXn+vvvuO3bs2KFDhz784Q/7vv/DH/7w0UcfveaaazZ8z/79+998881LLrkk/IimaUtLS3feeecnPvGJT33qU7/wC7/w9a9/3TTNO+64Yyd+CUUMCCHi3sMgCOQ5u0W0p5QqcRTqKeU5mckwDEqpoCdTquVcon9TeZRMJu9yQpqmnThxYvQ37N69e9PzgS655JL7778//N9bb72VS/8UoiGEiIs6UiHaU8oTv3VdF7dDW7anXejvK0/8xulpQb+vbNW1BKJW8CgErkHhcn1mihBayRDUcgIR6in7/b48dUpd19WMLRey2awgJX3fl0fGxKKckAJ0Xfd9X0TLvG4rTAWEEKFKylMTIoTkcjkR7tz3faniN3pKQUrK80ACgGma4tJFeQbJxKKckAJs2xY0VuZyOXmiDgDYti1iNw2lVKqoAwCWZYk4iYoxVi6XuTebWAgh8/PzIty57/tSHY8izp0zxmzb5t6sYiKUE1KsveTch0vZxkoQNlxKqKSu6/1+n/t8hO/7suXfIvIcxpiElQzbtrm7c9/35+fnpUoXk4lyQgoAAcUMHCtlq2QQQizL4uspsbQmW9TBYgbfZxJLa7JFHXTnfJVst9tSldYQfHL42krf96VaSZlYlBNSAADouj4/P99qtbi0FgSB67qVSoVLa+lC1/VMJsMr8DDGWq2WnMVz27aDIOBlKxljvV5PwvgNAOVy2fd9XiEct+XLluQAACGkXC63Wi1epUrXdeVUMoEoJ6RYAwMPlxCOwVu2MgaCwyWvwNNqtSqVirRKVioVSmn8wIPWXE4bBACEkEOHDnHJcxhjchaEEF3XS6US3ksfExwf5EwXE4hyQoo1MPD4vh8zC2+1WoSQgwcP8upY6ggDT8wQ7rquhPNigxBCMPDEUTIIApmtOWKaZqlUimmGwlqvbDOMg5imGX+2kTEmszVPIMoJKd6BEHL77bdTSqO95zhQZjIZlehg4PE8L7KSzWZT13Wl5MGDB1HJaAadMdZsNi3LktmaI6ZpFgqFZrMZzVb6vt9sNsvlssyGEtaLvpdccklkJSml7XZb2lpvMtl1/vz5afcBAMAwDBGbZhURYIzVajUAmGi/EmY5tm2rkBOCSmaz2YmGPN/3sYahlAyhlJ48eTKfz0+kJKUU1wapkBPSaDSazaZSMiaMMc/zMF3J5/NjfheWJwFA8rpacgiNh3JCik1gjHn/638183lCSD6fH/3SUkp9389kMmqgHCYcMVHGEUoGQdDtdpWSW8EYcxyn2+3m8/lcLjfiYlFUst1u44SvCjkbGFRy9GMWKqnKk5tCKXUcB08tH+2HQiVtxg5+5Ss71kPFaJQTUoxkeRkWF9mzz3qe57puv9/HKI7hJ5PJMMbwPgSMN7Ztqx0QI0A/VK/XUUP8L96oikriJild1y3LUkqOgDFWr9dXVlbQ34RKoob9fr/X6+FRdRJumJ8ISqnruqgkahgqiYt5e70eAOADqZTcCsYYKtntdsNUZ4OSmN5YlnXwv/93KBZhaQkWFqbcbwUAKCek2IYDB8LXFV91AGi323hKEAAQQvAYjOSMktgxSinulwYAwzCwbwmpr6CS2L1hJZMzF8YGGFRydE1rJ0ElccQIldR1PZvNQvKUxNdHKRmHDUpms1nUMCGvNgwoiRrida2EEJwcf6efy8uwuAhnz06zr4p1lBNSbI3jwIMPwpkz0+7HuGCdwPM8TMVwEMfCFdYJ1hKyxAzriSWsE8B6uQU/HgRBEAQ4uKv63zg0Gg0spsJA4QpjJCqp6n/jgMVUVBKrVhuUBABUMjmWaHuKRVhYgGPHpt0PhXJCihHs2gVnzqSifotTTv1+f/SKBzwnKQgCXddt205IOp4oGo1GvV7XNG2EkhjCcQ+XcpZbESo5Yu2IUnJbwgnl/PpqxU2/bHB1XWqU7HSgWIQzZ2BubtpdkR3lhBRbsLgIALC0NO1+bI/jOCsrK+Pv3cBBs9frqVW0g4TrZ03THLEMeRCl5KagkoyxQqEwvpKe5+VyuXK5rJQMwU2XmqYVCoXxv6XVapVKpXSYofQMs7ONckKKzVhehmIRkvFIjCAMORHuJcX9wKlJHwUTIeSEKCUHoZTWajXDMCadplG2cgOe5zmOY1nWpGqkSUksC6ml09MmNB7qZEXFANVq8tMUxtjRo0d37doV7Xp2XdfxfLlGo8G9b+mCUnr06FHDMCLYIBhQksvlA6kGjzuKtloF59Gy2WytVuN7T2oaaTQap0+fjmCD4N1K8r0nlT9zc3DsGFSr0+6HYg3lhBTrOA50OpD4A+Adx4mQeQ+iaZppmq7rSh54omXeg6CS9Xo96YFHJFhXKxQKcZTESV7Hcfj1K31QSuv1esztqKEZ4tgxIWA1SO6/eHJQTkixThoKQo1GA/fdxGwHlwbjFBuXjqUOnBSLP4mgaVo6Ao8w0JrHVzKfz2ezWWnNEBpKy7LGXGI1glwuBwBJL/qqslCSUE5IAQAA1SrMzSV80ppSindIcWlN5sDjeR4u7OXSmq7rmqbJqSSaaV5buPFqTzlnG3kZSgDAdW/NZjPpRd+FBZibU2YoCSgnpADodOD48eSfb1Gv1/meGoKBJ+nDpQDq9Toe58gLXdcllBEAPM/jZSgBQNM0wzDq9TqvBtMCHkvI8e3GNUMpUHJpaW1ZgmKqKCekAFhchHI54QUhAKCUjn/Z4Thg4HFdl2ObycfzPLw+hUtreLodzmjIVszwPC+fz8efzRkE/y6y2Uo8N4hvm4SQ8Fjq5DI3B+WyKgtNHeWEpGd5GZaXk79CyHEc7mMlrJeFuDebZPBCTV6thT5AwmKGiPgNAPl8XjYlPc/jfkg0Hkidgjzn8OG1QVgxPZQTkp40LJQGAL7F8xAM5FKZIaxkcG9WtmIGXiEn4twaLGZwbzaxiCitIemYtMWl03jWomJKKCckN7jKNfE75wGAMSZirASAbDabguGSE+JklA3GmAhDCQCapvX7fameyZQ2zg1cOi3lnoOEoJyQ3FSryV8oDeKHM7wnXAYopeKO35XKUwolk8lMuws7R6/XE/RM4gRZCp5JtaN+2ignJDHVKiwsJH+hNESK37iSdxxkm4wQijyest1ui/OU6YjfnBD69qXGU+JQrObIpsSF0+6AYkrgzvmzZ6fdj3GZdE5n/K/PZDLyOCGhs2OpiTqJR6oZTMZYNpsV1Limaal5u48dg2IRlpdTkZ3OGKomJCuLi3D8OMzNTbsfY0EIGb/GMykcT8ZLBeKUlI1+vy+o5SAIkn6HKD+E/qZpetrVjvrpoZyQlCwvQ6eTihVCCCFEXNSRCl3XhXpKvgc2JhlxZQxIV/yOjdDp6X6/n6Y85/Bh6HTUjvqdRzkhKUnJzvlBhMZvoVEtUShPyQtd18UtikpZ/I6HaE+Zpuqa2lE/JZQTkg/cq5mqqWhCiK7rghLHlI2VsVHzjFwQ6imleibFeUrf90U0K5ZyWe2o33mUE5KPxcUUzYuFGIYhYlwLgoAxZpom95aTCXpKEUr6vp/L5eSJ34SQXC4nwp37vi/PAwnrs2MilEzrq720pFYL7TDKCUlGSq4YG8Y0TRFjJaU0lWNlDGzbFrFD2/d9y7K4N5tkLMtqt9vcm6WUSqUkIcQ0TUHu3LZt7s0KZ25O7ajfYZQTkolOBxwnjQUhWE/BuQ+XaR0rY6DruohiRlrz7xjgjC1fJX3fz2Qy8kwyIrZtc38gsbSW1iLlsWPqMrKdRDkhmUjVzvlhsJjBcZkLFoTSOlbGwLKsVqvFsUHXdWWzQQBACLFtm687l9Caw3qew7FUGQRBq9VKcWlNnTq9sygnJA1p2zk/jK7rpVLJ8zwurTHGer1eOQ13rnHHNM35+XleZghPAJdWyUwmwyuEu66LU0VcWksX5XK51+vxspWtVsu27XSX1nANgyoL7QjKCUnD4mLqds4PY5oml9wxCALXdeUM3oht20EQxFeSMdZutyUsYyBoAX3fjz+5gy1UKhUe/UofhJBKpcKl6IvW/ODBg1w6NjXUjvodRDkhOahW11bhpRwMPL1eL04ID4LA87zUp4zxwMDj+34cJRljrutWKhXJlTx06FCr1YpTz/B9X3JrDgCEECz6xjFDlNJerzcjhhLvqFdzZOLZdf78+Wn3AQDAMAwRuzAUa+zaBWfOzIATQhhjtVoNACKsA/B9HyvnqU8ZeYBKZrPZCFYGQ065XJbZBoVQSk+ePJnP55WSMWk0Gs1mM4KSuDYIACqVyuws/ut0oFiEM2fSu74zyYTGQzkhCcD6avqnxgZhjHme12w2dV3P5/PjfEsQBN1uV4WcDYRKFgqFMePHbIac2IQG3TCMiZTE+pzg3qWJ0KDncrkxL6PFQu/8/PwM1tVmcQBPCMoJScPyMhSLkIy/Mnc8z3Ndt9vtjs4gcUEM7spRpaBNaTQaruv2+/3RSvq+j3NAlmUpJYdBW1mv1zVNG+HR0ZTjhnml5KaEBp0Qks/nt3KWg0rObIbT6cCBA7NU1E8OyglJQ7EIhw/D7OVJAzDG6vX6ysoKAGQyGU3T8CaEIAjwCGlCiIo328IYo5Sis4T1G8KVkhHYVEmsbQwqadu2nNvExmdQSXy1wxIRXtDBGEMZZ7w26Tjw4INw5sy0+zFrKCckB44D1SqcPRuzGc/zcM95eI4cIYQQgrMACcnD2DoA0G638VpHXdexq9PuHcD6sL6VktjVafcRYEBJ7GqoZEL+0LBeMACAQSWxe4ZhJMdeDCuJf+4EKonDb/KVxH4mXMnBVxu4KNnpwOLizOe0O49yQnJw4AAsLUWuqQ6W+rHOTwjJZDKwPmLi2JTJZFR2O5pxlAyCQNf1RIWfBBIqmc/nNU3DOkEmk8HCFQwoaVlWcsJkAgkrqYSQYSX7/T4WXZSS2zI4swzrZelQSXwgAcCyrFi1q+VlWFyMn9YqBhnlhN5+++1nn32WEHLFFVdE/gG9Xu873/nOddddt3///ok6pOBGtQrLy5ELqo1Go16vG4YxetEivupq7chWhPEmn8+Pr6RaiTwMY8xxnG3XhMG7144oJYfB9cjbrgmDdSXb7bau6+VyWSm5AUpprVbD9GYcJXu9XqxBsliEuTm1dJojWzqhU6dOLS0tWZb1yiuv/OhHP7rnnnuuueaaCD/gE5/4RKvVevjhh9/3vvdN1CEFH3CR3dmzEfZeYshhjE20Rx33bpRKJWWGQjDkaJpWKBTG/y7cU61s5SAYcnAOccxv4RN7Zg7P8xzHKRQKY+64hAElla0cBHf7j7/jEuIrqXbU82ZzJ3TXXXd94xvf+PKXv3zllVcCwBe+8IUvfvGLjuNcd911E7V+//33f+ELXwAA5YSmRrEICwsR7taIEHJCcItWEARqxIT1kGNZVgQplK0cJELICVFKDlKr1brdbjQllUEPiZYrhsRSslqFTkeVhXgRGo93zphuNBqPPfbY4uIi2iAA+NznPrdv37477rij3++P3/R3vvOdhx9+mG93FZOBlxhHtUGRlwXgzuFsNounqsgMpfT06dPRbBAAaJpmmmar1XIch3fXUgYuwiiVSnGUdF230Whw71u6qNVqjLHISuq6XigUms0mr4v/0ovjOP1+P/L1rqik67pRjnc/fFjdUS+CNSe0urqK0eumm25653O7d3/0ox89d+7cl770pTGb6/f7lUrlxIkT3DuqmIBqNVrSELmGEaJpWi6XAwCZAw9OikXLvEPQVq6srMisJKW0Xq9PNLc4DM5ORgw8swKltNvtxrybHW1lvV6Pf8laemk0Goyx+M9kPp+Pkueoy8jEsOaEnnzyyXPnzu3duzcsCCHXX389ADzyyCNjNnfixIkbbrgh5vumiAW+XZNvtkQrHH9WCwOPzLmj4zjjnzI8grCeIWcIR0NpWdaYpwyPIAw8coZwrPXGDN6IpmkyF30ppc1mk0uAy+fz2Ww2ihnCy8ikrxbzZc0JPfHEEwAwvFns0ksvBYCXXnrpxRdf3LatJ5988plnnvn85z/Pu5OKSahWI8yL4YlBvCxsmDtyaS1dYMrIa9cxhnA5lcSti7wWnGHgkVbJmBXKQXRd1zRNzlIlLjbn1Voul6OUTpznYFlIXcvKlTUnhIuGhncTXH311fiPbf9ar7766p133lmr1S666CLenVSMTbUKCwsRDhByXXf8vSTjgHm8hMUM13UNw+DYICGk2+1KqKTneTjTygsMPBwbTAUYa/m+3fl83nVdjg2mAixyc9wLEj3PwUFezZHxY80JvfDCCwCAR70NcuGFF+I/8JStEdx5553lcplvDFBMRqcDx49HWyjNfawEAMMwZEvBuY+VsD5cyhZ4PM/DsxM5tomtyVbM4G7NYf0Jl81Wck8XAYAQEqUsBADHjqml0xxZc0JvvvkmAOzZs2errxs9O/aVr3zlJz/5yZEjR+J0xdiMOA1Kx+IiHD8e4agJEW84AGQyGdmKGYKUlLCYgadIc2/WMAwJPSXf0hoi26StoHRR07SIz6SaI5ucEQbjwjGbuOCCC7b61Pe///377rvv0UcfjdlLdZ5QLJaXodOJUBACAEopx8nvECxmUErlOaqfUmrbNvdmw6lGSZTEW1xEHEmFF8rKo2T80loQBJt+OyGk1WrF6FrKYIyJsOYAkMvlIiq5sLB2kYC6o348hj1GaIbWakLhLNgGVldX8R9XXXXVVl/wx3/8x3/0R3/0i7/4ixx6qohM1J3zsH71lSC2nVedGYTKqGmaPGUhSqm4kzmH1wAoRrCVi8Jr4eXZi9dutxN3WqzaUc+PNQN02WWX+b7/1ltvbfh0+KBffPHFm37/0tLSCy+84LrupvW9v/mbv/n617/+/ve//2Mf+xi/PiuGwB2VMTIDvgsyQggh8jghofFb0B8osYj7fdFTSlITarfb4pTMZDKCSndSoWlav9+PqGS5DA8+CI6j7qiPyZoTuvbaa33ff+ONNzZ8GldSA8CGc4ZCzp49+5Of/OTLX/7ypp9dXl/PpZyQWBYXI9+0Kjr/lidrBJHxmxDSbrcluehAaPyWzVOKq4FJVRMStIQAieUpl5bW7lZSl5HFYM0JFYvFv//7v3/uuec2fPr1118HgHw+f/nll2/6/YcPH/6N3/iN4Y9/5jOfAYDPf/7zuq7/8i//Ms8uKzawuAjlspoqnjqMMXFRNggCQS3LRiaTkadOyRjLZrPT7oVie6J7yrm5tQVD6jKyGKw5oRtvvPHuu+9+7bXXXn755csuuyz8NM553XzzzVt9/5VXXrlVuQgArrvuujFvYFVEZHkZHAfOno3cAK4h5dijQaQqnuu67rquuGkXeZTMZrOvvvqqoMbjX5WQIgghUr2D4sBxUlCq0+/3Y40bx45BsaiWTsdhbcX0nj17brvtNgB4/PHHw8+trq4+/fTT2Wz2lltuGfyelZWVEydO/OAHP9jJjio2p1qNtnN+EKH1BnlGYdGeUp7kXtd1oWUbeZ5Joc8Mx7PUU4G4cTIIgljPpNpRH5t37qI/cuSIZVmO44TZ2P3339/r9e699959+/aFX7a6unrrrbc+8MADR48e3enOKjbgOJF3zocQQgghgl7yfr8vT/wWjTzxGwCEekp54rdQTynVjK1hGIKeST4yYjVIHbQYld2D/3Pfffd98IMfPHTo0PHjx48cOfLNb37z0Ucf/cAHPrDhe/bv3w8Al1xyyc51U7EpnOaGsYQev51her2ePPGbEJLL5QQpKVX8xmdGUKCVKn6Lq1Picy7P2y3OUzLGTNOM24raUR+Pdx0jpGnaiRMnRn/D7t27n3rqqW3bVcckCqdaXVsrFxvbtk+ePMn93DA8H4/DS54eLMtqNpvcw4Pv+7lcTp6oQwiZn5/vdrvczZ/v+6ZpSqUkunMRz2RZpp3bKKAgJfkcx4rbxyLdwK3Yvf2XKJJJpCvGNoUQImK7O0Ydvm0mHF3XRdSEfN+3LIt7s0nGsizf97k3SymVUEkReanv+/IUKQGAECLimeScLi4trS2ZUEyIckLphOvOeUEvObdcJz1gCs73FgIJS2sAoOs696lGLK1JFb9h3Z1zV1Kq0hpimqaIdJHnIBnuqFdMiHJCKQR3znM9PcI0zSAIOJoh13UlHCsBoFwu8w087XZbNkOJWJbVarV4LesJgqDVakmoJCGkXC5zdOeMsVarJVtpDQAIIaVSia+SQRBwPi712DFwHLV0elKUE0ohAg7RwuGSUsol8OC51VItIwghhBw6dIjXcOm6LiFEkqOlN2CaJsfAgzZItoIQYprm/Pw8LyXb7XalUpFWyUwmw+UGwCAIXNflP0jOzcHSklo6PSnKCaUNvGJMgMnQdb1UKnmeF7Mdxpi0ZQyEVwjHwlKlUuHRqVSCZcX4gQetuZyGErFtOwiC+EqiNZfTBsF6xuj7fvyir0BrjkunMVIoxkM5obQhcmvAwYMHS6VSs9mMXBnyfd91XWlTxhDMHTe9lnhMKKXtdlvOuloIBp5erxcnhFNKe72ezIYSAAghlUrF9/3ISmINA9vh27d0ERZ94yspypqrgxYnZ9f58+en3QcAAMMw1Mb77alWYXk58mWrY9JoNJrNZj6fn9TNYMgpl8uS2yCEMeZ5XrPZNE1zokP6cUULAFQqFQkXWg0TU0kVvEMYY7VaDQAmXeUTBIHnefPz85Jb8xBUMpvNTjrWMcZc17VtW3iFslhcmylTbE1oPJQTSg+dDhw4AGfP7sCdw/iea5qWz+fHCcaUUtyYo0LOBkJbmcvlto3iQRB0u13f91XIGSaCkjhLK/Ok2DChrRwz1QmVVIXeDYRK6ro+zmFsqOTO5YqdDhSLcOaMuqN+BMoJpZBiERYWduzULHzPXdfF2wEJIRvCD86g4SiJ+/BVyNkUVLJerxNC0FmOVlIV1baCMVav11dWVkIlN3zBoJK2bcu5e3EcKKWu645Wst/v+74fBIFlWUrJrcBBstvtooybKonpTSaT2elBslqFTkeVhUagnFDiwCV4W16qsLwMxSLs+B+LMYaDJk6Ka5qWyWRg4Kz9BI6S4WLGpPUqVBKd0LCSSbOSiVXS87x2uz2sJPYzmUpi95KvZL/fDy8ETaySSUsVwryRMRYOkoNKoi/f6W5hWWhpadOT55Kp5A6jnFAiGByJAAAHI3x5CCGGYbxjMopFOHxYxJaxiXoL69twKQxErAAAIABJREFUkjymw2ZKJmpAH1QyaSMR2jX0bYMywoDxnXYf34Gtk0AlG41Gu93G7iklIxO+2psqqeu6ZVlJ63CYQky/Y44D1SqcPQsjB0lIpJI7gHJCU6bRaODEE9ZUM5lMOGOCFf5+v88Y6/V6uq5bP/2p/sgjohdKp5HBKbzh6jQqiQNTEARyvupjEk7hhYvDNlUSz95MYCEwOWyrJJYKlJLbEioZzikPK4nP5BQmnlJEscgOHqwT4nmeYRgbwg0MKTmd8tWUUE5oajDGHMfBeeVto3I4x1z6b//t4O/+7s70MC3gsm5cxrTtisV3lCyV1Ii5AUpprVYzDGP8xci9Xk/FnmE8z3McZ3wl8SxTpeQwE+1gxSgeBIHabjlMrVYbP9yE2Y4kSionNB3CkDNRZSKMPZI8neOAIceyrIkECWOPUjIEQ06hUJhUSc/zlK0cBEOOUjImmCsyxibd6o+neChbGaKU3BblhKaA53mnT5+edKAMwadTqtLlVkQLOchO72VNNrVaLcJAiSiDHhI55CChQb/nnnu49y1dRMsVQ5StDFFKjkNoPNQZ0zsEpfT06dOlUilyzNB13TCMer3O/T7kdNFoNBhjkZXUNA1n0xzpT6OPY4NgXclsNquUdByn3+/HVFLTNKVkvV6Ps5hP0zTTNF3XbTQafDuWLnDlQHwlm81m/PuXUoFyQjsBPpeFQiFmO4SQbDaLp8TKCaW0Xq8bhhGznXw+L3kIp5R2u934N4rncjnGmMyBB615zLcbzdDKyorMSqI1j1lf1DStUCiEB3/ICS5Wi6+kaZqS5N7KCe0EXJ5LRPLcERMdLkrmcjlKqZyBByvn8a05rAceeXLHDVBKm81mfEMJA/UMOUM4GkpeSmLRV4YQPgwaSi5T/5qmSZJ7KyckHM/z+B5gpeu653kSDpeO44x5+8c4hLkjl9bSheu6kderDYNK1ut1Lq2lC8dxuBhKBEO4nEpyqfWG5PN5TdMkVBJPAuNiKBGMXDOf5ygnJBzXdce5lWZ8cLiUMIRTSvmuccZ9zjP/kg/jeR7fZxJNlWzuHJMcvqvFCSEYzDi2mXzwgeSrpK7rsskIAHj8Et82cX0q3zaThnJCYqGUUkq5P5oSvuToVya6inwcZHjJN9BoNHg9kHjiIiJhMaPdbnMsCCGapmmaJluewz1dhPWxQrZxknu6COt3sMy2ksoJicV1XY4l3xAJixkixkpYv7Jqtl/yDXBUctCYYjGDS7NpwfM8EccHyJbnYLooQknZ8hzP89BJ821WhlkI5YTEQinN5XIiWs5ms1IFHkFjJQ4c8gSe8G6pib5rsPazFbKl4GiDuEcdANA0DW8/4N5yMmGMiUhyACCTycgjIwC0221M7bhDCJntV1s5IbGIew8JITN/FuUGREQdcc0mk2jrWsaUSNM0qQKPuCdHqhDebrfFvdqD96HKgCAlBRms5KCckHDEDZfyvOGCCkKIVJ4yvM1bBFI5IaFKgkxvN4gMtFJN2oobJ2feUyonJBBKqdCsUVDLCURFHV4IVTKTycjjKXu9nrh3UKq5b6F5Dkj2dotrfLY9pXJCAhH6ekuVfxNCxlmqEqd9cY1LhVKSC0Kf9qRBCOn3+4Ial2ruWyj9fn+G327lhNIK39Mak4+4sTIIghl+wzeg63qv1xPUeL/fz2azghpPGtlsVtwzCZJ5SnHOT6pxUtd1oeOkoJaTgHJCAiGEZDIZQQ+QVPFb6G8qVfwG5Sk5QQgR5ym5H9iYZAzDUPGbF6p2Hg3lhMQirvArNB9NGjg7pjxlfEQvyFBKpqX95CDUU4JMSorzlL7vz3ZpTTkhsRiG4fu+iJZ7vR7Hy2WSj67rgtZFzfxLPgghBG+PF9F4EARSKSno1B/f9zOZjDzxW9ycju/7pmmKaDmZ6LouKNzMfJKjnJBYTNMUMVbihkZ5og4A2LYt4mgvHCtn+yXfgGVZInZ4tVotqaIOIWR+fl5E4GGM2bbNvdnEgu5chJJ87yJNPhvyHI5FdN/3Z/uZVE5ILIJect/3y+Uy3zYTjq7rIooZvu+LuA4lyWAKzl1J2eI3ANi2LagmJJWnBDF5ju/7UhUpAYAQYllWGG547ZuTIV1UTkg43F/yIAikmtAJ4V7MwNKabFFHRDHD9/1cLjfbY+UwmOfwfbsppbI9kLC+uYSvrZQwXYT1VQR8l1T6vj/zpTXlhISDxYxWq8WrwVarZdu2bFEHAHRd53j9TRAErutWKhUuraUL27aDIOAVeIIgwGeSS2vpolwu+77PS0nGWK/XkzB+E0Js2261WrxCOI4ScnrKUqnE8XJu13UJITOfeCsntBOUy+UgCLiEcHwuDx48GL+p1EEI4Rh4MHjP/Bu+Kagkr8DTarUqlYq0Sh46dIhLnoPWXEIbhJimWSqVuCjJGGu329IqefDgwfn5eV5KAoAM6aJyQjsBIaRSqcQP4TijIcNzuRVh4IkZwlutlrSGEtF1nUvuKEnKOAIuITysq0muZPyiLyoprTVHsOgbX0l5rLlyQjtEGMIjP52UUjlnvjeAgcfzvGhK4usdBIHMhhI5ePBgqVRqNpvRbCUqiS6fe9/ShWmahUIhjpKe5+m6LrM1h/VSZa/Xc103WguMsWazeejQIZltEKzn3r1eL3K48X2/2WzKYyh3nT9/ftp9AAAwDEOGuxsZY7VaLZvNTvR4YZajQs4gkZX0PG9+fl4ZypBGo9FsNvP5/ERKMsZc17VtW/LgPciYSgZBMLipx/d9VcMYhDHmeV6z2TRNc6LdT5RSXGWllEQiK4lOVAYlQ+OhnNBOwxjz/vf/br79dj6fz+Vyox/QIAi63W673VYhZxjGmOM43W53nCiOtWIsqkm4jnI0aCv7/f44Svq+j7O0MgyUkxIqqet6Pp8f/cX4QGYyGaXkMGgrCSH5fH707hAcJHH3osoVh5lUyXa7re/dW/m//3fHejhFlBOaHp0OHDjAnn3We/llfEAJIeiHwhvXGWP9fh9HScuylAcaAWOsXq+vrKyESmYyGU3TlJITwRijlLqu2+12h5Xs9/v433a7jWeWKCW3YiIlbdtWvnwrsKTRbrcx20ENMZajhrjsEhNFXdeVm9wKVNJ1XfToADCsJF5nZFmWedll5H/+T1hagoWFKfdbPMoJTY9iERYW4NgxWB802+02WwcAcPQ0DIMQkpxREvtGKcVj1/EtSs7QM6wk9jCZSg52MslK4iKDsIfZbDZRB6wNKxnqmQQw/PR6vbQoGXYygUrW63VYfzhhoJPZbDZRpjzJSg6+2rB+0MDmSjoOPPggnDkzxd7uDMoJTYnlZVhchLNnp92PccHRvF6vY9Uqk8lks1nMHjC7VXntmGxQEksFoZKZTEbXdcuykmOJEssIJdESKSXHBB2G53lh1Qo/rpSclEaj4bouY2wrJS3LSpT33YZOB4pFGcpCyglNiQMH0vJ4haOkYRhbrWfC9xxXjagZk63AuZKVlZURK8OUkuOABmj0eqZw1YiaDx0BRu5xlFSzeKNpNBpoyrdVstfr6bqemkNx05a0R0M5oWmQnpKj53mO4xiGMWY6GL7qlUolHe/5TjHpzizcJwgASskN1Gq1brc7zkpkWHeWlNJSqaTM0CC4z4AxhrPG2369UnIrQiULhcI4O7PCQTI1Bn1gIcesopzQNNi1C86cSX5BCENOoVCYNBLjLtbUvOeCCQfKSa/sCUdMlYgj8ZVUthKhlNZqtfEznBDceomncCklIZ6Snuelw1biHNmZMzA3N+2uiGKUE3r77befffZZQsgVV1wxUaOrq6srKyv/+Z//ee211+7fvz9ah2aWxUUAgKWlafdjG2q1WoSQE5Km91wkjLGjR49GGCgHW8AbAyRfpRE55Ay2oI6ZAQBK6cmTJyNkOIiylSGe550+fTq+kvfccw/3vnEmJWErMqHx2HjG9KlTpz70oQ899thj1WrVtu3nn39+zBZPnTr1vve977d/+7ePHDny/ve//1Of+lSn0+Hb6RSzvAyOk/znKaYNAgBN00zTdF2X7wXdqWOiucVNwV1vWAvh2LHUUa/XYy7axQk1x3H4dSp94EFHkYM3AGiahrveJFeSUuo4TnwlNU1LgZLHjsHyMiwvT7sfwnmXE7rrrrtOnjz50EMP3XvvvQ899NBHPvKRT37yk88999y2rdx999333nvvxRdfvLCwkM1mAeCZZ565+eabZ7zMMz7VavJtEKW02+3GsUEILh6UOYQ3Gg3GWPwKBG5trdVqXHqVRtCax69A5PN5yUM4WvP4SuZyOcZYo9Hg0qvUgRO1lmXFV1LX9ZWVlaQrOTcHx45BtTrtfgjnHSfUaDQee+yxxcXFK6+8Ej/yuc99bt++fXfccUe/3x/RxHPPPfcP//APDzzwwJkzZ06dOvX0008fO3YMAH784x//6Z/+qdDepwPHgU4Hkn29Q5gycmlN5sBDKW02m/ENJYJ2Sk4lPc+LWaEcJJfLUUrj3zibRjAt4TI5qGka3rAmZ9HXcZxsNstlcjA15XNc2DrrQ9CaE1pdXcXU86abbnrnc7t3f/SjHz137tyXvvSlEU189atfPXny5A033BB+5Hd+53c++9nPAsB3v/vdF198UUjHU0QaCkL1en3bs9gnIpfLdbvdpL/kAqjX63zXoxQKBQllBIB6vW4YBq/WNE0zDAMP6JMNz/N4JTmwPrkjoZKUUkopx7db07RsNhv5utkdQo6y0JoTevLJJ8+dO7d3796wIIRcf/31APDII4+MaOKaa66Zn5/f8MFbbrkF/4FHpMhLtQpzc8nfL4ZXYXNsEOfIkv6S8wb3G4+zzXt8cIOubMUM/H35rszF1mSzlZ7n5fP5iS7g3BZCCNoCjm0mH9d1+b7asF6q5NsmfxYWYG5ubfX0jLLmhJ544gkAGN4sdumllwLASy+9NKK084lPfGL4g9ls9sILLwSA9773vbz6mj46HTh+PPkFIRFjJaTlJecKlta4NythMUNE1AGAfD4vm5Iinkk58xzu6SKkKM9ZWoLlZZjdXVBrTgiXNg+/MFdffTX+Y9KQ9vbbb//sZz/7pV/6pUm34s8Ui4tQLif/MAbXdUVsi8WXXCozJGKsBCmLGdxLawghJLzgTwbCiwK5t6zrulQPpKB0EQAMw0iBp5ybg3J5hufI1pzQCy+8AACZTGbDp7GuAwC9Xm+idr/1rW8BwK233hq3g+kFNx8mviAEAILGSgDIZrNSDZew7v9EIFX8FvRA4l9HHiUZYyIMJQBomiaVp8Q7xUS0nMlk0iHj4cMzvKN+zei8+eabALBnz56tvm7Shc9f+9rX3vve937yk58c/1s2XR2Z4n34aVgojQh9ydvttiSnLFJKxdmgbDabjuGSB+IeyLB9cY0nCqFKYoFNklMWe73ecKWAC+gpRbTMGVw6nebLyEbswLhwzCYuuOCC8X/e9773vXq9/tBDD1100UXjf1eKTc8wuOcw2TvnEaHxGy8JF9R40hAaFaTylEIDg1SeUlz8lg1KKcedjBvAFegpOAN9YQEefBAcJxWhbZhhjxH+Tddmx8JZsA2srq7iP6666qoxf9jq6uqf/dmf/cEf/AHuO5OUajVFF9eJGytTU/jlgdDfVGiNJGn0ej2hnnLSuf70IrQmJNvct/KUM7yjfs0JXXbZZQDw1ltvbfh0OLhffPHFY7b4l3/5l1deeeXtt9/OqYcppFqFhYXk75wPGX1yZjJbTiCEEHEFsCAIJJmGAIBsNiv0mcRz8CVBPZNcIIQIfSZToySGtpnbUb/mhK699loAeOONNzZ8GldSA8CGc4a24qtf/Wqn00nBxXLiwJ3z6SkICX0DgyBIQcmXE0KVlM1TiivbSBW/DcMQ9+TIs0hINClbQjCLl5GtOaFisQgAw1eMvf766wCQz+cvv/zybdt68skn/+7v/u6v/uqveHcyVSwuwvHjyd85H4KVDEGvomzxW9zvGwSBuGUKSUNofJUtfguNsvIoaRiG0OnvNCk5izvq15zQjTfeuH///tdee+3ll18e/DSec3DzzTdv29A///M/33///X/913+9YZV0r9f7wQ9+wK/DyQbPnkpPQQjRdV1QCJctfouLOvIstwLBnhLSFXXioeu6mh3jhaA6pe/76ZPx8GHodGapLLTmhPbs2XPbbbcBwOOPPx5+bnV19emnn85ms+HVGcjKysqJEycG/c1TTz31hS984dSpU/v27dvwlZ/5zGd+/ud/XuBvkCjSs3N+EMMwBF2K4vu+PLNjIOy4OSzamabJveVkQgjBO8+5t+z7fi6XS1/giYq4kyR935fngQQA0zQFuXOO1wzvHOGO+lnhnbvojxw5YlmW4zivvvoqfuT+++/v9Xr33nvvoL9ZXV299dZbH3jggaNHj+JH/umf/um222777ne/e8MNN1wzgGEYhw4d+tVf/VVZtr3gzvn0LJQOMU1T3FgpT9QBANu2RXhKSqlUUQcALMsScayG7/vpizoxIISIeyZlUzKXy4lQMq2eEq9PmJU76ncP/s999933wQ9+8NChQ8ePHz9y5Mg3v/nNRx999AMf+MCG79m/fz8AXHLJJQDwzDPP3H777T/72c9+9rOf/fTd4Bd/7GMf25FfJAEsLqZuXgzBl5x7MUO2sRIAdF0XUczwfd+2bb5tJhxd17kXM4IgYIylMurEQESeg6U1qcq9AGDbNvdBMt3p4tLSzKwWetcxQpqmnThxYvQ37N69+6mnngr/9/rrr5+pExEjg1eMpbAghNi2ffLkyVwux6uA5/t+JpORbawEAMuyTp8+XSqVeDWIBaG0jpVRwWJGq9Xi+Iu3Wi3ZbBAM5DkcX0YJrTms5zl8laSUpvjEmbm5tR31KVwTsoHd23+JYluWl8FxUloQQnRdL5VKrVaLS2tBELRarXI6zyGNiWmauVyOl5KMsV6vJ2HUAQDTNDOZDK8sHNuR85ksl8u9Xo9XZQgvbJbQUwJAuVz2fZ+jkqVSKd3p4qzsqFdOiAfVarp2zm8KFh64BJ5Wq1WpVNL9hsegXC4HQRBfySAIXNctl8uyFYQQQgivwMMYa7fbctogWFey1WrF30eGf4tKpcKjX+mDEHLo0CEueQ5eM5z6+3Nm5dRp5YRik86d88PgcBkzhGPwJoRIa4MAgBBSqVR834+pZKvVsm1bciUx8MQJ4fhMymzNYb3o63leHCUZY2jN+fUrfZimWSqV8HyZyPi+PzvWHNeEpLwspJxQbGZilhQhhNx+++29Xi9aCA+CwPM8XdelTRlDCCF33nlnZCUZY81m07Ks1KeMscHA43leNCV93282m+VyWWYbhBw8eDCOkpTSdrstuaFETNO0LKvZbEazla1Wy/f9SqUyI7XemdhRv+v8+fPT7gMAgGEYqVx5Xa3C8jKcOTPtfvCEMeZ5XrPZLBQK47+raqAchjHmOE632zVNc8yl6EEQdLvdXq+ngvcgjLFarZbNZsdf1I9FNQBQSg4SKjm+JqgkVjqF9i1dNBqNZrOZz+eVkgAAxSIsLKRubiQ0HsoJxWPXLjhzJr1bxkbQaDRc1+33+7qu5/P5rb4MI3e73cbJNRVyNoC2sl6vE0Ly+fw4Sqqi2qaEBh2VHOHRQyVt21ZFtWEYY/V6fWVlZRwlKaVBEKjy5KaEqU4+nx/t0SmluJ12ZpXsdKBYhDNn0rVeVjkhHmA9cFamxoZhjFFKXdftdruZTEbTtHDQ7Pf74W1llmVJuM17IgaVRKEIIZqmBUGASjLGcJRUSo4G/RB69EElcSXvoJKzGW/4MVrJXq/X7/eVkuMQenQcJDVNw3+ESuJVd7OvZAoDonJCsVlehmIRYquHMRI3S+ObQwjBu7p0XU9IUMROAkC73ca3OpvNAoCu68kpAo1QMjk7ftOipOd5MDCIA4BhGIlaCI9/6/DPjUoSQpLWyfDPDev3nSVKSbYO9nBQyUSNP4MvDqRESRx8kqYkvjgwoCS3F6fTgQMH0jVJopxQbIpFOHwYYiz+D6efMBWDgSs8GWP4D13XLctKyKueTDaktkrJyAwriantBiVV4WpbwilRLKMOKqmKqRMxqCTOLIdKYjhXJcAxwSlRz/PC7AsfvA1K2rYdK290HHjwwRQtnFVOKB6OA9UqnD0b7bs9z3McB9/tEbEZlzvg7HLcB3RGaTQaOEqOs5gJlZydLRtcQSUNwxi93CFcgmOapm3bSskNhEtwtl04opbgjGZwCc7oBAZPnFJKbgWl1HGcfr+/bbhhjOHFatGV7HRgcTFmjWAnUU4oHgcOwNJStBpgrVbrdrsTbcvyfR9vjlTveQgOlIyxQqEw6bYspeQgoZLjXxIXKqkM+iCU0lqtZhjGRJuJUEll0AeJpiQ6S6XkILjBbXSiuAE8DKVUKkUcJJeXYXExcplgh1FOKAZRd85HCDkh+HTmcjm1qwgiDZQhcd/z2SKOkrgkQtlKBEPORBlOCKVUGfSQyEoqg74BzLrHP8IjJK5BLxZhbi4VS6eVE4oKLgo7e3bSvYKMsaNHj0YLOQg+nefPn5fcDKGSlmVFzvzwVA9d12fkjNeoUEpPnjwZLXgjylYiGLwjhJwQVPL222+XfClbrVaLliuGhDerKCX7/X6hUIjcAu7qiGKG0rOjPjQe6ozpCVlcjHbFmOM4cWwQAGialsvlGGONRiNyIzOA4zhxbBAAaJpWKBRWVlZkVhJP2ItjgwBA0zTTNF3X5XVPahqhlNbr9fFnaTcFn0msGXPsW7qglHa73Tg2CADwkCTHcTh1KpU0Gg1cORCnEcMwstlsFCXn5qBcTtdlZMoJTQJeujv5MZr4XMbPUXC4bDab0gYeTBnjrwNQIRytORclMfBIG8LjW3MEN/XUajUuvUodoTWP31Q+n48YwmeC0JrHbyp67n34cLruqFdOaBKq1Qhzn/hcxkx0QsLckUtr6cLzvPgpY0gYwrm0li54WXMEzymWU0nHcfA4Fi6t4V9EzlIlL0OJ5HK58DAn2UAl41QoQ6Ln3mm7jEw5obHBgX7ylSWu6+IRW7zAwQLPvpMK13X5zv2jkhIOl9yfyXw+j8fKcWwzFeA+Bo4NFgqFmPecpxF0LRz3fGmaZhhGvV7n1WBa8Dxv8DKA+GDGGOWZXFiAuTlISYKknNDYVKvRrpfjPlYCgIQvOY6V4+8FHYfoL3maQQ/Nd6cxXjIgmztvNBr5fJ5L8h2Crcnmzl3X5TKbM0gmk+l2uxIqyf0QASywTfxtWBZKyWoh5YTGY3ERFhYiHCDkeR73sRIAMplMv9+X6iV3XZevDUIIIVLJCMKUlNBTilNStjwHzz7m26aEec6Y6SIecT4+GL+iTNpi0EzDHJlyQmPQ6YDjRCsIiXDosP6SSxXCKaUitsXiSy5VMYN7aQ2RbaoR728S8XbL5s4FpYsQuZiRWsZ8tSNIHf2Ym2PHUrF0WjmhMYi6cx7WbzTk3SEAgEwmk44TmDjBGBMxVgJANpuVZ4ELpVSQjLLBGBNhKAEA13nIE8LFvX3hhfCS0Ov1xIWbiEqmZI5MOaHtWF6GTidaQQhExm+p4pk4GUEyTynOmgNANptV8VsxKeLiNwBomibPMyk0z4n+wC8sQKeT8LKQckLbEWnnPCJ0rIxu0lMI330lG5DKU4qm1+tNuws7hND4rTwlLzKZjLjGE4ig3xe3RER8JtOwo145oZHgDsBIN62C4PxbtsLvpKv8JkIeJUVX1wS1nEBEPzPyeEoQmY1INU4KfbtjUS4nfEe9ckIjWVyMPC8GAISQfr/PsTuDBEEgz5XLQn/TIAikuqJInKcU97QnEMMwhL7dfA98khah6WjSIIQItX2xlFxagmoVOh1uveGKckJbs7gI5XLkghAAEELERR2OZwQnH6GeUip0XRf3TMoWv4UqKajlBJLo+J0qRGeMsdqfm4OFhcQunVZOaAuWlyPvnB9E13V5arPiEO0p5YnfouuUglpOIEI9Zb/flyfPyWaz4hqXrXYuKNzwKa0leEe9ckJbUK1G3jm/AUHDpVTxG0R6SqniNwAEQSBISanit5r75oWu677vi2jZ9315ZAQAwzAEjWZ8lhAkeEe9ckKb4Thxds4PYtu2oD0gvu/LE3UAwLIsEXvd8bYs0zS5t5xMCCGmaYpwQr7v53I5eQIPIQRv6ubeMqVUngcSAAghgnbCMsZs2+bebGIRly76vs/n6mtcbZK8spByQpsRY+f8BgQNl77vm6YpT9QBAF3X+/0+94zH932pxkoAsG1bRArObaxMD7Zti3DnsilJCLEsS9AzKVW6iOGGe+6N6SIfJZO6o145oSGq1bW1XTwQ9JJTSqUaKwGAEDI/P9/tdvk2i56Sb5sJR4Q7l620hmAqwldJLK1JFb8BQESdst1uy5Yugpg8x/f9crnMrTm8oz5hc2TKCQ1x/DiXebEQHNQ4vueUUgnHSlh/yTkq6bquhGMlAFiW1Wq1OBbY2u22bKU1ACCE2LbdarU4tkkplVPJUqnEUckgCCRMFwFA13W+ZSHGGP/S2tLS2hKUxKCc0LuJvXN+GELIoUOHeAUexli73ebp0NNDqCSX1nCwkFNJ0zQ5Bp5Wq0UIOXjwIJfW0oVpmrlcjpeSruuWSiUJkxwAME0zk8nwCuGtVqtSqcipZLlc7vV6XDLGIAhc161UKpzTxeTtqFdOaADcOc9phdAguq6XSqX4F56Lei7Tg2ma8/Pz8QOPzIYSwWJY/MDDGAuCoFKpcOlVGimXy0EQxJ+SwCtl5DSUAEAIKZfLXIq+rusSQuS0QbCuJJfcu9Vq2bYtRMljx8BxkrN0WjmhAfgtlB4GQ3iz2Yz8dAZB4HmeqOcyPdi2HTN3ZIyhoZRZSRwue71eHCV933ddV2ZDCQCEkEqlQimNoySltNfrKSWx6BtHSUyTZLbmMJB7xwk3aChFWfO5OVhaSs7S6V3nz5+fdh8AAAytAMPzAAAW8klEQVTDmPJ94I4DDz4IZ86I+wmMMc/zms1moVCYtKjj+36r1SqXy7ItSt2UUEnTNCe9ZycMOTLboBDGmOM43W43gpKYdColEcZYrVbLZrOTqhEEAU4vSh68Q5SSvGg0Gs1mM5/PT6ok5oq2bYutUHY6sLgIhw/D9BKA0HgoJ7TOgQOwtMR3hdCmUEpPnjyZz+dzudw4sQdfbwBQIWcDk77naqDclNBWjq+k7/t4Zp1ScpBQSV3X8/n8ON9CKcXF5tJOim1KaNDHTBqDIOh2u0rJYdBWapqWz+cnUnKHSubLy7C4CGfPCv9BW6Cc0LupVmF5WWhBaJBwxCSEjHhAKaW+72cyGcuy1Ou9KYyxer2+srIyQkl8t5WSo6GU1uv1breLMo5Qst1u49kQSslN8TzPdV1UcqtsZ1BJleFsCg6S7XYbldxKolBJ0zRt25Z2AeUIUEnXdfEI+K08Ou62w/PVdnRHbbG4NlM2DaRzQqOuTel04MABOHuWy90aE3WJUuq6LqVU07RMJoODZngZAu7RTdp0WALvdh581QFgWEld1y3LUkpuCypZr9dRQFQSlxqgkjs9So5HMpWs1+ue56GS2L1QSbSSCVQygeAgOawknrOqTPmYjAg3U1ay04FiEc6c2eH4i8y+E8IxHTcThuvvyDqGYbwTF4tFWFjge4bQpF2F9bPp8CjPrZLyqTCBktMGlRzsZKKy7TDNhfVO4l8ZlbQsKzm9TYuS+MpAspUMOwnpUVLXdVypk5zesgGwV8npGwB4noc7UjdVMlGuN3FKvntOptFobBVustksX682y04ozGtROLzUJkxt0f/illdd161f/mX9ox+FZIiQNMK81jAM1HAwtR1UUiW4o8Fgs7Kyks/nh5XEcTNUUiW4I2g0Glj820rJfr+vZkK3ZbCMGk4rbyi39Pv9drudzHpqchgso26lJJ40gUomyr0lhU4HikX2f/6Pd9FFg0oOF664KzmzTqhWq42eVw55Z5HdNdcc/N3fjf+jZ4lwxeL4SvZ6PRV7hplUSUppEARKyWEopbj2c9v1yDhiorNM4Pzy1EElMdiMr6TMx5htRaPRqNfrhmFsu/1lcLWiUnKYxuc/33z77XE2EoVKlkql+IPkDDohDDmMsYlOWA+juHo6Q3CgNAxjItONxx3lcjm1nygkjpJc3vOZAfcJTnr8BM5WKFs5SDQl8ewJpWRItOMnwnCjlsmHTDdwz5oTihZyBr9dPZ2I53mnT5+OcOIRKFv5bqKFHEQpOQgWeiOceATKoL+bWq02acgJUQY9JNyaXigUon27MugIl8AdR8nQeMzCGdP4XMaZONR13TAMdKZ8+5YuKKWRbRAA4MxFNput1Wrc+5Yu0AaVSqWYSjqOw7trKQODd6lUimCDAEDTNLznXClZq9X6/X7kS0lRSdd1G40G346lDsdx8vl8NBsEAISQQqHQbDY53pOaRrgE7kKhgBviYnZmFpyQ4ziWZcVMnXF5tcwhHJ/LyDYoRIVwPJsn8kAZksvlGGMyBx5KabfbjXmjOObuKysrMivZaDQYYzGfSVSSS+BJL2jNxzw5cytQSclzb8dxDMOIGW5weXX8cMPZCb399tvf+ta3vve97/FtdgT4XHKZQUBnKm0I5/JcIrlcjlIqbeDhYs1hfbiMeQ1TegmtefymwnqGnErysuYwEHjkDOGNRiO+NUckz73xEeKyHCWfz8fPvXk6oVOnTn3oQx967LHHqtWqbdvPP/88x8Y3xfM8SimX5xIpFArYJq8G0wIehsFrmVSYO3JpLV04jhNu7Y4Pr4wnjTiOE79CGYJK1ut1Lq2lC7Tm0aYXh8nn85qmyakkL0OJ4HjreR6vBtMCHj3AMXBj7h0ncHNzQnfdddfJkycfeuihe++996GHHvrIRz7yyU9+8rnnnuPV/qa0222OzyUAaJpmGIaEIdx1XcMwODaIw66EL7nneXzX3aMVkNCdU0pjzkFsgBAyeFybJHie1+/3+a6713VdNhkBwPO8MW/vGh/DMCT0lPV6ne+rHT/P4eOEGo3GY489tri4eOWVV+JHPve5z+3bt++OO+7ACxAE4Xke95016C75tplw0E1zV1LClxzHSl7Jd4iExQxclMq3TU3TNE2TLc/B0xH5tilnnsM9fgNAJpMB+fIc7ukirOc5kSdtOTih1dVVnOy86aab3ml39+6PfvSj586d+9KXvhT/R2xKo9EQEXUkfMld1920tIbn9kZGwmKG67oiNr1LWMyglIo40kLCYga6c+7Nypbn4PoB7m+3hJO2gtJFzHMiB24OTujJJ588d+7c3r17w4IQcv311wPAI488Ev9HbEqv1xN01Eo+n5cqcdyqIBT/Yc1ms1IFHu4TOgj3USPhYG4n4rfWNK3f78vzTAqyQQCQyWSkWjQdf7/YVmCeI6LlZNJut8UF7sinEnJwQk888QQAXHHFFRs+fumllwLASy+99OKLL8b/KcOImNBBJAw84n7lXq8nqOWkIXQ4k8pTCjKUCM5HKGKCKbg8z6S4xBsEDx1JQ9wvG8edc3BC6MKGR66rr74a/yHobREXv6VKd4T+plKlO+KsOSKPpxSKVPFbXP4NknlKceMYekp5xkkRk4zxuTB+Ey+88AJs9lZceOFa42kcwRljUK1Ouxc7Ad27V+hYKY+SsHevuNIaIaT37LPw/e8Laj9RtAG0n/95QY1rmgbLy/Av/yKo/cRx6aWCGtY0jf6//6cL+0slCvbWW0LrlKxWIxddJKj9RCGuhIFz39GcFgcn9OabbwLAnj17tvqCMWfHNt3FvdW0n9AJnbWWOx1B7ScKctllQttnjMFPfyr0RyQERgj8wi8IajwIAvLGG/DGG4LaTxRZQl4VFl8zmUyPMZAjBWf79mXn5sS1T37yE0mUhLfe6huGuKAjyTjJ9u2b4k8fcVIMBye0LRdccME4XzbRWidCSMydTSNYa3lpSVD7iYIw1v/zPxfU+NppjXJcfqlT6go9AvF//A8olwW2nxwaDRA2gcUYK33mM2CagtpPFMRxxE1GBEEA5bIsSoo8DLrf7+v33APJmzPiDgEgR48GQSDIUwZBMOJpH/YYoTfisE4onAXbwOrqKv7jqquuiv9ThhG3BoXjacupQJynhPW99DJACBF3ehZjLJvNCmo8aei6nsYp9QQi9Jnp9/vyjJNClzyOjt8zhrhxMo6MHJzQZZddBgBvvfXWho+Hz83FF18c/6cMI/TRkeq5FOop5YnfoDwlJ0R7Snnit1BPKVX8FjeOCR00Eoi4+Zw4rzYHJ3TttdcCwBtDKxhwJTUAbDhniBeGYfi+L6Jl3/f5Xj2RcJL5aKYOQoiu64I8pe/78igJAEEQiFAyCAKp4rc4TynbA6nruqBwwxgz5ZhhRMQF7jgjBgcnVCwWAWD4irHXX38dAPL5/OWXXx7/pwxjmqa4SoZUj6Zt2yL2Ffu+HwSBVMOlZVmRj/Yage/7pmlKFb9N0xQxXFJKpXq1CSG5XE6Ekr7vc7xBM/noup7L5UREHL6XiCcfXddxhxf3ln3ft2072vdycEI33njj/v37X3vttZdffnnw43hM88033xz/R2yKoJdctrEShL3kjLGyJCt81xH0kssWdQDAtu2kjZUpRVCeI1u6CGLyHN/3M5mMVOkiIWR+fp574I6ZLnJwQnv27LntttsA4PHHHw8/uLq6+vTTT2ez2VtuuSX+j/j/7d1vaBNnHAfwn1o7EtRBL/5vUcZMNqVWx6ZrWCfiC6UzghvWMZ0EynQqoiyvJqjVsU4pOpzYWtTZF3UKoxOaTpzYsWJ3JRXsFaeYw8lG6p/q3XTDxn/NdS8edpR01jb3XGLu+X5exVPuHn/PPfn9nucud89ixyAXMOuQDYM8Ho+Ltn5O9gxy9uoJASPJfZ4j2tIawyLJt6xUFEW0Moj+m+fwvZFAwNKc7JnnWFxa4/Mu+vLycr/fX1dX99dff7Et1dXVmqbt27dvjJ3PD2CLGYqi8NqhLMv5+fmiZR0i8nq9kiRxLCsVRQkEAqJlHSJi32scx7miKCExHkOQJBgMqqrKK5LxeFxRFAEnOZIk+f1+RVF4pXBd18XM35IkLVq0iOPLuVmhL2BNySLJMXGrqmoxcfOphIjo4MGDb7/9dllZWUVFRXl5+U8//XTy5Mn58+fz2v+zBINBtvxgfVesDhAz60iSFAwGY7EYl8SjKIokSUuXLrW+q6wjSVJZWRmvxCPL8qJFiwQszalfJLnsTVGUYDAoZiSLi4t5JZ54PC7LcigUEnCSQ0RLly7lNffWdZ2dk9Z3lY2Ki4tdLheXubeu65qmWUzc3Coht9tdVVV17ty5ioqKo0ePhsPhwsJCXjsfhCRJoVBIVVWLiUfX9Wg0Kux5SfxSuK7r8XhczIKS8Xq9XOaO7KVRYhaUTHFxcVFRkfXEI8syuwubS6uyEbssaD3xsLVeMQtKhs29LUaSrVCGQiFhI8lr7s1Kc+uJm1sllEEshbe1taV8dsZiMTbREfa8ZNjcsa2tLeWzU1VVwQtKhkWyubk55bJSURQBbzkfKBAI5OfnpxxJ9kXJ5kvc25ZFWOLRNC3lL0kzkiKX5vTf3NtKJHVdb25uLisrEzzdmHNvi5HkstY7oq+vz+IuuPD5fBbv2NV1fe/evR6PZ7hBYasgwq6cD6Sqak1NTUFBwbACwmY5SDn9NTU1NTc3I5IW6bre1tbW3Nw8Z86cYV2U0XVdluVAICB48jaZkSwuLh7W6w4QySS6rtfV1XV1dQ03kmyuiFm3KeXEraqqpmkWE7dZeDinEqJ+43wouScej3d1dcVisfz8fKScJOzsZE/Tf+4bmFkko9EovigHYpF0u92SJCGSVrACnYXxufWQGUmknIFYgT70SLJ7DzBXTNI/3eTn5z+3HlJVlf1mXti7rJ4lg4nbmZUQo6qqLMudnZ1m7jFPO7bAzp74wvKN1+vF8P5fuq6zSHZ1dZnfmEmRZD/wjsfjfr9fwN8nD9HASLpcLvN7k0Wyq6uLvRUBkRwE+8aUZfnhw4f/G0k2tFm+8fv9qCafhUUyHA673W6v1+t2uxHJ1JhZnL22iM15zL81I8nu+UMkB6HrejgcZok7KZJJiVuSpEAgwOW2PydXQgw7QaPRKMvWbrebRZNF2efz4YwcIkSSFzbU9f+wSJolJiI5RKyyZCekqqosf5uR9Hq9Pp9P5Jujh27wSKIoHzpztkNELJJJX5KI5BA9N93wjaTzK6Ekuq7jRLSO3UmNSFqHSPKCSPKCSPKCSPJidyTNwiPHpgO8aHBScoEw8oJI8oJI8oJI8oJI8pK2SDrhV/QAAAAAqUElBAAAAOJCJQQAAADiQiUEAAAA4kIlBAAAAOJCJQQAAADiQiUEAAAA4hKlEvL5fJluAqQPulso6G6hoLuFkp7uFqUSAgAAABgIlRAAAACIC5UQAAAAiAuVEAAAAIgLlRAAAACIC5UQAAAAiAuVEAAAAIhrRF9fX6bbQIRHRAAAAEB6RaNRenEqIQAAAID0w9UxAAAAEBcqIQAAABAXKiEAAAAQFyohAAAAEBcqIQAAABAXKiEAAAAQFyohAAAAEBcqIQAAABAXKiEAAAAQFyohAAAAEBcqIQAAABAXKiEAAAAQFyohAAAAEBcqIQAAABCXEJVQIpGIRCLXrl3LdEOAD3QoJIlGo5luAnCD3gTDMDo6OlpbW//55580HC4nDcfIrNra2mPHjvn9/rt3796/f7+ysrKwsDDTjYLUWezQ999//+bNm/23lJeXf/LJJ7ybCWly8eLFffv2dXZ2Xrp0KdNtAaus9CaGtmPU1tbW1tb29PSwP86bN++LL76YPn26fUd0eCW0ffv2xsbG77//fsaMGUS0f//+1atX19XVzZ07N9NNg1RY7NCmpqbLly/335KTk7N8+XJb2go2a29vr6mpiUQiiUQiNzc3080BSyz2Joa2Y+zatev48eNTpkx56623fvvtN03T2tvbV6xYUV9f7/P5bDroiL6+Ppt2nXFNTU2hUGjDhg2bN29mWwzDKCkpyc3NPX36tMvlymzzYLisd2hpaemHH37o8XjMLR6PZ968eXa1GOykaZrH4/nuu+927tyZm5uLNaGsZrE3MbSdoaOjY+PGjXv27CkpKWFb2ClBRDNnzjx16pRNx3XsmpBhGHv37iWi0tJSc+PIkSMXL158/Pjx+vp6rJpmF+sdeubMmby8vDVr1tjbUEgXlvamTp2a6YYAB1Z6E0PbMRoaGmpqaoqKiswtH3300d27d6urq69cuXL9+vVXXnnFjuM69o7plpaWmzdv5ubmsssoJjZLOHHiRIbaBSmy3qEHDx7EarnzjB49OtNNAG5S600MbccoLCzsXwYxq1atYh9isZhNx3VsJXT27FkievXVV5O2T5gwgYhu3Lhx/fr1DDQLUmWxQ8+dO6eq6tatW994442tW7fixykAzoCh7SQrV64cuNHj8eTk5JCdC8COrYTYeCgoKEja/vrrr7MPqqqmu01ggcUOPXDgAPvQ09PT0NCwbNmyioqKx48f29BSAEgfDG3HSyQSvb29kyZNGjgT5sWx9wn9/vvvRDTwLlpWWhKRpmnpbhNYYLFDT548qarqrVu3WlpaGhsbe3t7T5w48eeffx45cmTUqFE2tRkA7Iah7XiRSISIbL0PzLFrQo8ePaJBrzrj6lh2sdihLperqKhoyZIlX3311S+//PLuu+8SkSzLX3/9NfemAkDaYGg73g8//DB16tTVq1fbdwjHVkLPhemCwwy9Q8ePH3/48OH33nuPiI4dO5aeZ5gCgN0wtJ3n2rVr4XB49+7dL730kn1HcWwlZF40SWIYBvvw2muvpbE5YBX3Dv3yyy+nTJnS29vb3t5utXEA8MLA0HYMwzA+//zzLVu22P1oKMdWQpMnTyaigffN6brOPrz88svpbhNYwL1DXS7XBx98QETmM90BwAEwtB1jz549M2bMWL9+vd0HcmwlNHv2bCJ68OBB0nZ24y0RJT2WBl5wdnTozJkzicjWRVcASD8MbQdoaGj4448/Kisr03Asx1ZCCxcuJKKOjo6k7X///TcRFRQUTJs2LQPNglTZ0aHsytrAB3kBQFbD0M52LS0tp06d+uabb9JzOMdWQkuWLBk3bty9e/du3brVf7ssy0S0YsWKDLULUmRHh164cGHx4sXsuhsAOAaGdlZrbW2trq4+dOhQ0qqepmnd3d12HNGxldDo0aM//fRTIjp9+rS50TCMX3/91ePxmE/vhmwxrA7t7Oysqqoyx4ymaWfPno3H40n/5syZM9u2bbO/7QDAB4a2450/f37//v21tbVjxozpv72zs3Pt2rVjx46146COfbIiEZWXl7e2ttbV1S1fvjwvL4+IqqurNU379ttvk0IMWWGIHWoYxpo1ax49enT16tWjR48S0e7du8Ph8KRJkz777LPS0tKenp7Gxsb6+vpDhw6NHz8+Y/8f4IFlwUQi8fTpU7yDLNsN3psY2o73888/b9q0iYjMd9EzT548IaJAIOB2u+047oi+vj479vuCiMfjO3bs6OjoeOedd2Kx2J07dyorKwsLCzPdLkjRUDrUMIwFCxbcuXNn2bJlVVVVRBSJRNavX2/+kGTs2LErV65ct27duHHjMvB/AE4ikciPP/7Y0tJy+/ZtIpo9e/abb74ZDAYnTpyY6abBsA2lNzG0na29vf3jjz8e5B8cOXIkqULixeGVENPd3X316lWPxzNr1qxMtwU4eG6Hdnd3X7p0qaSkxLzMnEgkZFk2DCMvL2/WrFkjRzr2ujCAg2Fogx2EqIQAAAAA/hfKZwAAABDXv2Vf5mbI4/x0AAAAAElFTkSuQmCC\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44491,"title":"Shuffle","description":"Shuffle a vector by breaking it up to segments of |n| elements, and rearranging them in a reversed order.\r\n\r\nFor example, the vector:\r\n\r\n vector = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\r\n\r\nshould be shffuled by segments of |n=3| like so:\r\n\r\n cetvor = [8,9,10,   5,6,7,   2,3,4,   1]\r\n\r\nThe shuffled vector should have the same dimensions as the original one.\r\n\r\n*You must call the functions \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44486 push()\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44490 pop()\u003e.*","description_html":"\u003cp\u003eShuffle a vector by breaking it up to segments of \u003ctt\u003en\u003c/tt\u003e elements, and rearranging them in a reversed order.\u003c/p\u003e\u003cp\u003eFor example, the vector:\u003c/p\u003e\u003cpre\u003e vector = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\u003c/pre\u003e\u003cp\u003eshould be shffuled by segments of \u003ctt\u003en=3\u003c/tt\u003e like so:\u003c/p\u003e\u003cpre\u003e cetvor = [8,9,10,   5,6,7,   2,3,4,   1]\u003c/pre\u003e\u003cp\u003eThe shuffled vector should have the same dimensions as the original one.\u003c/p\u003e\u003cp\u003e\u003cb\u003eYou must call the functions \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44486\"\u003epush()\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44490\"\u003epop()\u003c/a\u003e.\u003c/b\u003e\u003c/p\u003e","function_template":"function cetvor = shuffle(vector, n)\r\n    cetvor = vector;\r\nend\r\n\r\n% You must call the following functions from the shuffle() function\r\n% (copy-paste your solutions)\r\nfunction [v, n] = push(v, x)\r\n    n = [];\r\nend\r\n\r\nfunction [v, w] = pop(v, n)\r\n    w = [];\r\nend","test_suite":"%%\r\nfiletext = fileread('shuffle.m');\r\nassert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 1;\r\nw_correct = 8 : -1 : 1;\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1; 2; 3; 4; 5; 6; 7; 8];\r\nn = 2;\r\nw_correct = [7;8;  5;6;  3;4;  1;2];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 3;\r\nw_correct = [6,7,8,  3,4,5,  1,2];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1; 2; 3; 4; 5; 6; 7; 8];\r\nn = 4;\r\nw_correct = [5;6;7;8;  1;2;3;4];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 5;\r\nw_correct = [4,5,6,7,8,  1,2,3];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1; 2; 3; 4; 5; 6; 7; 8];\r\nn = 6;\r\nw_correct = [3;4;5;6;7;8;  1;2];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 7;\r\nw_correct = [2,3,4,5,6,7,8,  1];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1; 2; 3; 4; 5; 6; 7; 8];\r\nn = 8;\r\nw_correct = [1;2;3;4;5;6;7;8];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n\r\n%%\r\nv = [1, 2, 3, 4, 5, 6, 7, 8];\r\nn = 9;\r\nw_correct = [1,2,3,4,5,6,7,8];\r\nassert(isequal(shuffle(v, n), w_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":140356,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":333,"test_suite_updated_at":"2018-01-07T22:04:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-01-07T21:23:35.000Z","updated_at":"2026-04-03T03:05:46.000Z","published_at":"2018-01-07T22:04:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eShuffle a vector by breaking it up to segments of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements, and rearranging them in a reversed order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the vector:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ vector = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eshould be shffuled by segments of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en=3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e like so:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ cetvor = [8,9,10,   5,6,7,   2,3,4,   1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe shuffled vector should have the same dimensions as the original one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou must call the functions\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44486\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epush()\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44490\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epop()\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"term":"difficulty_rating_bin:hard","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"difficulty_rating_bin:hard","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"difficulty_rating_bin":[["difficulty_rating_bin:hard","","","hard",""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f2f6a071f48\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f2f6a071ea8\u003e":["hard"]},"filters":{"#\u003cMathWorks::Search::Field:0x00007f2f6a070148\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f2f6a072308\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f2f6a0721c8\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f2f6a072128\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f2f6a072088\u003e":"difficulty_rating_bin:hard"},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f2f6a072088\u003e":"difficulty_rating_bin:hard"},"queried_facets":{"#\u003cMathWorks::Search::Field:0x00007f2f6a071ea8\u003e":["hard"]}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"difficulty_rating_bin:hard","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"difficulty_rating_bin":[["difficulty_rating_bin:hard","","","hard",""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f2f6a071f48\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f2f6a071ea8\u003e":["hard"]},"filters":{"#\u003cMathWorks::Search::Field:0x00007f2f6a070148\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f2f6a072308\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f2f6a0721c8\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f2f6a072128\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f2f6a072088\u003e":"difficulty_rating_bin:hard"},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f2f6a072088\u003e":"difficulty_rating_bin:hard"},"queried_facets":{"#\u003cMathWorks::Search::Field:0x00007f2f6a071ea8\u003e":["hard"]}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":52709,"difficulty_rating":"medium-hard"},{"id":3098,"difficulty_rating":"medium-hard"},{"id":42580,"difficulty_rating":"medium-hard"},{"id":44779,"difficulty_rating":"medium-hard"},{"id":1187,"difficulty_rating":"medium-hard"},{"id":1092,"difficulty_rating":"medium-hard"},{"id":44345,"difficulty_rating":"medium-hard"},{"id":42503,"difficulty_rating":"medium-hard"},{"id":1288,"difficulty_rating":"medium-hard"},{"id":81,"difficulty_rating":"medium-hard"},{"id":59516,"difficulty_rating":"medium-hard"},{"id":59217,"difficulty_rating":"medium-hard"},{"id":44374,"difficulty_rating":"medium-hard"},{"id":56423,"difficulty_rating":"medium-hard"},{"id":58019,"difficulty_rating":"medium-hard"},{"id":60406,"difficulty_rating":"medium-hard"},{"id":46636,"difficulty_rating":"medium-hard"},{"id":44793,"difficulty_rating":"medium-hard"},{"id":2266,"difficulty_rating":"medium-hard"},{"id":60834,"difficulty_rating":"medium-hard"},{"id":60749,"difficulty_rating":"medium-hard"},{"id":1949,"difficulty_rating":"medium-hard"},{"id":53990,"difficulty_rating":"medium-hard"},{"id":55315,"difficulty_rating":"medium-hard"},{"id":54720,"difficulty_rating":"medium-hard"},{"id":54750,"difficulty_rating":"medium-hard"},{"id":61010,"difficulty_rating":"medium-hard"},{"id":53125,"difficulty_rating":"medium-hard"},{"id":61176,"difficulty_rating":"medium-hard"},{"id":60411,"difficulty_rating":"medium-hard"},{"id":61277,"difficulty_rating":"medium-hard"},{"id":55,"difficulty_rating":"medium-hard"},{"id":803,"difficulty_rating":"medium-hard"},{"id":1286,"difficulty_rating":"medium-hard"},{"id":1499,"difficulty_rating":"medium-hard"},{"id":45426,"difficulty_rating":"medium-hard"},{"id":520,"difficulty_rating":"medium-hard"},{"id":733,"difficulty_rating":"medium-hard"},{"id":875,"difficulty_rating":"medium-hard"},{"id":2237,"difficulty_rating":"medium-hard"},{"id":44080,"difficulty_rating":"medium-hard"},{"id":42829,"difficulty_rating":"medium-hard"},{"id":375,"difficulty_rating":"medium-hard"},{"id":579,"difficulty_rating":"medium-hard"},{"id":46938,"difficulty_rating":"medium-hard"},{"id":57477,"difficulty_rating":"medium-hard"},{"id":53064,"difficulty_rating":"medium-hard"},{"id":57815,"difficulty_rating":"medium-hard"},{"id":60461,"difficulty_rating":"medium-hard"},{"id":44491,"difficulty_rating":"medium-hard"}]}}