{"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":2319,"title":"Pandigital number n°1 (Inspired by Project Euler 32)","description":"A little warm-up to begin...\r\n\r\nAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\r\n\r\nFor example, the 5-digit number 15234, is 1 through 5 pandigital.\r\n\r\nGiven a positive integer find whether it is a pandigital number.\r\n\r\n","description_html":"\u003cp\u003eA little warm-up to begin...\u003c/p\u003e\u003cp\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\u003c/p\u003e\u003cp\u003eFor example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/p\u003e\u003cp\u003eGiven a positive integer find whether it is a pandigital number.\u003c/p\u003e","function_template":"function flag = is_pandigital(x)\r\nflag=2;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = true;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 0;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 123;\r\ny_correct = true;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 1203;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 5432;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 54321;\r\ny_correct = true;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 2361457879;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 1234567809;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 987654321;\r\ny_correct = true;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":114,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-13T22:49:33.000Z","updated_at":"2026-03-09T20:20:18.000Z","published_at":"2014-05-13T22:55:20.000Z","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\u003eA little warm-up to begin...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 positive integer find whether it is a pandigital number.\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":52639,"title":"Determine whether a number is unprimeable","description":"The number 204 is unprimeable because no single digit can be changed to make it prime. In contrast, the number 207 is not unprimeable because changing the first digit to 0, 1, 3, 6, or 9 or the second digit to 2, 5, or 7 would make it prime. \r\nWrite a function to determine whether the input number is unprimeable. ","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: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; 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: 384px 8.05px; transform-origin: 384px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 204 is unprimeable because no single digit can be changed to make it prime. In contrast, the number 207 is not unprimeable because changing the first digit to 0, 1, 3, 6, or 9 or the second digit to 2, 5, or 7 would make it 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; 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: 221.983px 8.05px; transform-origin: 221.983px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the input number is unprimeable. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnprimeable(n)\r\n   tf = f(n)\r\nend","test_suite":"%%\r\nn = randi(199);\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 200;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 202;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 207;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 322;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 845;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 848;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 3505;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 5454;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 6002;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 14610;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 14617;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 28725;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 28735;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 39998;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 40005;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\ndn = [0 2 4 5 6 8];\r\nn = 47000+dn(randi(6));\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 55545;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 55555;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nk = randi(100000);\r\nn = 2310*k+510;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nd = [1 3 7 9];\r\nk = randi(21214);\r\nn = 10*k+d(randi(4));\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = [595631 1203623 872897 212159];\r\nassert(all(arrayfun(@isUnprimeable,n)))\r\n\r\n%%\r\nfiletext = fileread('isUnprimeable.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-29T15:22:09.000Z","updated_at":"2025-11-29T20:38:34.000Z","published_at":"2021-08-29T15:24:50.000Z","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 number 204 is unprimeable because no single digit can be changed to make it prime. In contrast, the number 207 is not unprimeable because changing the first digit to 0, 1, 3, 6, or 9 or the second digit to 2, 5, or 7 would make it 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 to determine whether the input number is unprimeable. \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":2337,"title":"Sum of big primes without primes","description":"Inspired by Project Euler n°10 (I am quite obviously a fan).\r\nWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\r\nFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\r\nBut how to proceed (in time) with big number and WITHOUT the primes function ?\r\nHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\r\nhttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes","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: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; 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: 183px 8px; transform-origin: 183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Project Euler n°10 (I am quite obviously a fan).\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: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\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: 208px 8px; transform-origin: 208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\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: 255.5px 8px; transform-origin: 255.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut how to proceed (in time) with big number and WITHOUT the primes function ?\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: 288.5px 8px; transform-origin: 288.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\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\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = big_euler10(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('big_euler10.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'primes'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = 17;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = 1060;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000;\r\ny_correct = 76127;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 10000;\r\ny_correct = 5736396;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 100000;\r\ny_correct = 454396537;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000000;\r\ny_correct = 37550402023;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000000-100;\r\ny_correct = 37542402433;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 2000000-1000;\r\ny_correct = 142781862782;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%% Solution of Project Euler 10 with n=2000000\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":5390,"edited_by":223089,"edited_at":"2023-06-05T10:25:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":239,"test_suite_updated_at":"2023-06-05T10:25:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-27T21:25:58.000Z","updated_at":"2026-03-29T22:02:38.000Z","published_at":"2014-05-27T21:51:18.000Z","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 Project Euler n°10 (I am quite obviously a fan).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input 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\u003eFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 how to proceed (in time) with big number and WITHOUT the primes function ?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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":2320,"title":"Pandigital number n°2 (Inspired by Project Euler 32)","description":"After Problem 2319.\r\nAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\r\nFor example, the 5-digit number 15234, is 1 through 5 pandigital.\r\nFind the number of pandigital numbers in a given interval [xlower,xupper] (inclusive if it is not explicit enough).\r\nThe test suite is simple here, but how to compute this number with BIG interval (pandigital number length \u003e 7) in Cody time?\r\nFor example, between 58755 and 99899923?","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: 192px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 96px; transform-origin: 407px 96px; 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: 15px 8px; transform-origin: 15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 2319\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\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: 257px 8px; transform-origin: 257px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\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: 204.5px 8px; transform-origin: 204.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the 5-digit number 15234, is 1 through 5 pandigital.\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: 343px 8px; transform-origin: 343px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the number of pandigital numbers in a given interval [xlower,xupper] (inclusive if it is not explicit enough).\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: 370.5px 8px; transform-origin: 370.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe test suite is simple here, but how to compute this number with BIG interval (pandigital number length \u0026gt; 7) in Cody time?\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: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, between 58755 and 99899923?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pandigital_nb(xlower, xupper)\r\n  y=xupper-xlower;\r\nend","test_suite":"%%\r\nxl = 1;\r\nxu = 10\r\ny_correct = 1;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 10;\r\nxu = 99;\r\ny_correct = 2;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 100;\r\nxu = 999;\r\ny_correct = 6;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 1000;\r\nxu = 9999;\r\ny_correct = 24;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 10000;\r\nxu = 99999;\r\ny_correct = 120;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 1;\r\nxu = 999;\r\ny_correct = 9;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 1;\r\nxu = 9999;\r\ny_correct = 33;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 100000;\r\nxu = 999999;\r\ny_correct = 720;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":5390,"edited_by":223089,"edited_at":"2022-08-09T08:36:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":68,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-14T08:11:36.000Z","updated_at":"2026-03-10T00:41:57.000Z","published_at":"2014-05-14T08:12:54.000Z","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\u003eAfter\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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2319\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:r\u003e\u003cw:t\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of pandigital numbers in a given interval [xlower,xupper] (inclusive if it is not explicit enough).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 test suite is simple here, but how to compute this number with BIG interval (pandigital number length \u0026gt; 7) in Cody 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:r\u003e\u003cw:t\u003eFor example, between 58755 and 99899923?\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":52881,"title":"List the cuban primes","description":"The number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \r\nWrite a function to list the cuban primes less than or equal to the input number. \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: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; 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: 295.108px 8.05px; transform-origin: 295.108px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \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: 245.3px 8.05px; transform-origin: 245.3px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the cuban primes less than or equal to the input number. \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 8.05px; transform-origin: 0px 8.05px; 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 q = cubanPrimes(n)\r\n  q = n^3;\r\nend","test_suite":"%%\r\nn = 100;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 1000;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61 127 271 331 397 547 631 919];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 10000;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61 127 271 331 397 547 631 919 1657 1801 1951 2269 2437 2791 3169 3571 4219 4447 5167 5419 6211 7057 7351 8269 9241];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 100000;\r\nq = cubanPrimes(n);\r\nqhi_correct = [10267 11719 12097 13267 13669 16651 19441 19927 22447 23497 24571 25117 26227 27361 33391 35317 42841 45757 47251 49537 50311 55897 59221 60919 65269 70687 73477 74419 75367 81181 82171 87211 88237 89269 92401 96661];\r\nassert(isequal(q(q\u003e10000),qhi_correct))\r\n\r\n%%\r\nn = 1e6;\r\nq = cubanPrimes(n);\r\nqhi_correct = [102121 103231 104347 110017 112327 114661 115837 126691 129169 131671 135469 140617 144541 145861 151201 155269 163567 169219 170647 176419 180811 189757 200467 202021 213067 231019 234361 241117 246247 251431 260191 263737 267307 276337 279991 283669 285517 292969 296731 298621 310087 329677 333667 337681 347821 351919 360187 368551 372769 374887 377011 383419 387721 398581 407377 423001 436627 452797 459817 476407 478801 493291 522919 527941 553411 574219 584767 590077 592741 595411 603457 608851 611557 619711 627919 650071 658477 666937 689761 692641 698419 707131 733591 742519 760537 769627 772669 784897 791047 812761 825301 837937 847477 863497 879667 886177 895987 909151 915769 925741 929077 932419 939121 952597 972991 976411 986707 990151 997057];\r\nassert(isequal(q(q\u003e100000),qhi_correct))\r\n\r\n%%\r\nn = 1e7;\r\nq = cubanPrimes(n);\r\nqhi = q(q\u003e1e6);\r\nqhi26_correct = [1021417 1570357 2129419 2676241 3483019 4476187 5382781 6138991 7073281 8401807 9779491];\r\nassert(isequal(qhi(1:26:end),qhi26_correct))\r\n\r\n%%\r\nn = 1e8;\r\nq = cubanPrimes(n);\r\nlen_correct = 1200;\r\nqhi20_correct = [67987081 71282251 74326519 77892361 81510469 84891241 88210519 92991169 95954041 99896011];\r\nassert(isequal(q(1020:20:end),qhi20_correct) \u0026\u0026 isequal(length(q),len_correct))\r\n\r\n%%\r\nn = 1e9;\r\nq = cubanPrimes(n);\r\ns = sum(q(primes(length(q))));\r\ns_correct = 127462233426;\r\nqmax_correct = 999461269;\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(max(q),qmax_correct))\r\n\r\n%%\r\nfiletext = fileread('cubanPrimes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin') || contains(filetext, 'persistent');\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2021-10-10T13:54:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-10T13:40:55.000Z","updated_at":"2025-12-14T17:50:30.000Z","published_at":"2021-10-10T13:52:53.000Z","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 number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 list the cuban primes less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\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":42377,"title":"Bouncy numbers","description":"Inspired by Project Euler n°112.\r\n\r\nWorking from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number. For example: 134468.\r\n\r\nSimilarly if no digit is exceeded by the digit to its right it is called a decreasing number. For example: 66420.\r\nWe shall call a positive integer that is neither increasing nor decreasing a bouncy number. For example, 155349.\r\nClearly there cannot be any bouncy numbers below one-hundred, but surprisingly, these numbers become more and more common after.\r\nFind the least number for which the proportion of bouncy numbers is exactly p%.\r\nAs always this type of problem is difficult to solve with usual Matlab functions (num2str).\r\nSo keep an eye on time...","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: 315.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 157.583px; transform-origin: 407px 157.583px; 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: 99.5px 8px; transform-origin: 99.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Project Euler n°112.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; 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 51.0833px; transform-origin: 391px 51.0833px; 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\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; 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 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 256.5px 8px; transform-origin: 256.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWorking from left-to-right if no digit is exceeded by the digit to its left it is called an\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 66px 8px; transform-origin: 66px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eincreasing number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example: 134468.\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\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: 204.5px 8px; transform-origin: 204.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSimilarly if no digit is exceeded by the digit to its right it is called a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edecreasing\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number. For example: 66420.\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: 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: 230.5px 8px; transform-origin: 230.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe shall call a positive integer that is neither increasing nor decreasing a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.5px 8px; transform-origin: 25.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ebouncy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.5px 8px; transform-origin: 98.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number. For example, 155349.\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: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eClearly there cannot be any bouncy numbers below one-hundred, but surprisingly, these numbers become more and more common after.\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: 252.5px 8px; transform-origin: 252.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the least number for which the proportion of bouncy numbers is exactly p%.\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: 273.5px 8px; transform-origin: 273.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs always this type of problem is difficult to solve with usual Matlab functions (num2str).\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: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSo keep an eye on time...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bouncy_numbers(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 0.01;\r\ny_correct = 102;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.05;\r\ny_correct = 106;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.1;\r\ny_correct = 132;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.2;\r\ny_correct = 175;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.5;\r\ny_correct = 538;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.8;\r\ny_correct = 4770;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.9;\r\ny_correct = 21780;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.95;\r\ny_correct = 63720;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.96;\r\ny_correct = 152975;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.97;\r\ny_correct = 208200;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.98;\r\ny_correct = 377650;\r\nassert(isequal(bouncy_numbers(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2021-07-22T06:29:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-14T23:04:12.000Z","updated_at":"2026-03-16T15:11:37.000Z","published_at":"2015-06-14T23:09:36.000Z","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\u003eInspired by Project Euler n°112.\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\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\u003eWorking from left-to-right if no digit is exceeded by the digit to its left it is called an\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\u003eincreasing number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. For example: 134468.\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\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\u003eSimilarly if no digit is exceeded by the digit to its right it is called a\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\u003edecreasing\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number. For example: 66420.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe shall call a positive integer that is neither increasing nor decreasing a\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\u003ebouncy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number. For example, 155349.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eClearly there cannot be any bouncy numbers below one-hundred, but surprisingly, these numbers become more and more common after.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the least number for which the proportion of bouncy numbers is exactly p%.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs always this type of problem is difficult to solve with usual Matlab functions (num2str).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 keep an eye on time...\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":2340,"title":"Numbers spiral diagonals (Part 1)","description":"Inspired by Project Euler n°28 et 58.\r\n\r\nA n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.\r\n\r\nFor exemple with n=5, the spiral matrix is :\r\n\r\n                       21 22 23 24 25\r\n                       20  7  8  9 10\r\n                       19  6  1  2 11\r\n                       18  5  4  3 12\r\n                       17 16 15 14 13\r\n\r\nIn this example, the sum of the numbers on the diagonals is 101.\r\n\r\nWhat is the sum of the numbers on the diagonals in any n by n spiral (n always odd) ?\r\n\r\nHINTS: You want the diagonals, not the whole matrix.","description_html":"\u003cp\u003eInspired by Project Euler n°28 et 58.\u003c/p\u003e\u003cp\u003eA n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.\u003c/p\u003e\u003cp\u003eFor exemple with n=5, the spiral matrix is :\u003c/p\u003e\u003cpre\u003e                       21 22 23 24 25\r\n                       20  7  8  9 10\r\n                       19  6  1  2 11\r\n                       18  5  4  3 12\r\n                       17 16 15 14 13\u003c/pre\u003e\u003cp\u003eIn this example, the sum of the numbers on the diagonals is 101.\u003c/p\u003e\u003cp\u003eWhat is the sum of the numbers on the diagonals in any n by n spiral (n always odd) ?\u003c/p\u003e\u003cp\u003eHINTS: You want the diagonals, not the whole matrix.\u003c/p\u003e","function_template":"function y = spiral_nb(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = 25;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 101;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 9;\r\ny_correct = 537;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 501;\r\ny_correct = 83960501;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 5001;\r\ny_correct = 83395855001;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 10001;\r\ny_correct = 666916710001;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 10003;\r\ny_correct = 667316890025;\r\nassert(isequal(spiral_nb(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":296,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":31,"created_at":"2014-05-30T22:02:51.000Z","updated_at":"2026-02-01T14:00:50.000Z","published_at":"2014-05-30T22:03:01.000Z","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\u003eInspired by Project Euler n°28 et 58.\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 n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise 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\u003eFor exemple with n=5, the spiral matrix 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[                       21 22 23 24 25\\n                       20  7  8  9 10\\n                       19  6  1  2 11\\n                       18  5  4  3 12\\n                       17 16 15 14 13]]\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\u003eIn this example, the sum of the numbers on the diagonals is 101.\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\u003eWhat is the sum of the numbers on the diagonals in any n by n spiral (n always odd) ?\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\u003eHINTS: You want the diagonals, not the whole matrix.\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":44732,"title":"Highly divisible triangular number (inspired by Project Euler 12)","description":"Triangular numbers can be calculated by the sum from 1 to n. For example, the first 10 triangular numbers are:\r\n\r\n 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...\r\n\r\nAll divisors for each of these numbers are listed below\r\n\r\n 1: 1\r\n 3: 1,3\r\n 6: 1,2,3,6\r\n 10: 1,2,5,10\r\n 15: 1,3,5,15\r\n 21: 1,3,7,21\r\n 28: 1,2,4,7,14,28\r\n 36: 1,2,3,4,6,9,12,18,36\r\n 45: 1,3,5,9,15,45\r\n 55: 1,5,11,55\r\n\r\nYour challenge is to write a function that will return the value of the first triangular number to have over d divisors (d will be passed to your function).","description_html":"\u003cp\u003eTriangular numbers can be calculated by the sum from 1 to n. For example, the first 10 triangular numbers are:\u003c/p\u003e\u003cpre\u003e 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...\u003c/pre\u003e\u003cp\u003eAll divisors for each of these numbers are listed below\u003c/p\u003e\u003cpre\u003e 1: 1\r\n 3: 1,3\r\n 6: 1,2,3,6\r\n 10: 1,2,5,10\r\n 15: 1,3,5,15\r\n 21: 1,3,7,21\r\n 28: 1,2,4,7,14,28\r\n 36: 1,2,3,4,6,9,12,18,36\r\n 45: 1,3,5,9,15,45\r\n 55: 1,5,11,55\u003c/pre\u003e\u003cp\u003eYour challenge is to write a function that will return the value of the first triangular number to have over d divisors (d will be passed to your function).\u003c/p\u003e","function_template":"function y = div_tri_n(d)\r\n y = d;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp', 'regexpi', 'str2num'},'FileName','div_tri_n.m')\r\n\r\n%%\r\nassert(isequal(div_tri_n(2),6))\r\n\r\n%%\r\nassert(isequal(div_tri_n(4),28))\r\n\r\n%%\r\nassert(isequal(div_tri_n(8),36))\r\n\r\n%%\r\nassert(isequal(div_tri_n(10),120))\r\n\r\n%%\r\nassert(isequal(div_tri_n(20),630))\r\n\r\n%%\r\nassert(isequal(div_tri_n(25),2016))\r\n\r\n%%\r\nassert(isequal(div_tri_n(39),3240))\r\n\r\n%%\r\nassert(isequal(div_tri_n(40),5460))\r\n\r\n%%\r\nassert(isequal(div_tri_n(50),25200))\r\n\r\n%%\r\nassert(isequal(div_tri_n(70),25200))\r\n\r\n%%\r\nassert(isequal(div_tri_n(80),25200))\r\n\r\n%%\r\nassert(isequal(div_tri_n(100),73920))\r\n\r\n%%\r\nassert(isequal(div_tri_n(115),157080))\r\n\r\n%%\r\nassert(isequal(div_tri_n(120),157080))\r\n\r\n%%\r\nassert(isequal(div_tri_n(130),437580))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":164,"test_suite_updated_at":"2018-08-20T16:04:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-20T15:15:06.000Z","updated_at":"2026-01-05T00:21:49.000Z","published_at":"2018-08-20T16:04:49.000Z","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\u003eTriangular numbers can be calculated by the sum from 1 to n. For example, the first 10 triangular numbers are:\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, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...]]\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\u003eAll divisors for each of these numbers are listed below\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: 1\\n 3: 1,3\\n 6: 1,2,3,6\\n 10: 1,2,5,10\\n 15: 1,3,5,15\\n 21: 1,3,7,21\\n 28: 1,2,4,7,14,28\\n 36: 1,2,3,4,6,9,12,18,36\\n 45: 1,3,5,9,15,45\\n 55: 1,5,11,55]]\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 challenge is to write a function that will return the value of the first triangular number to have over d divisors (d will be passed to your function).\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":42673,"title":"Longest Collatz Sequence","description":"Inspired by Projet Euler n°14.\r\n\r\nThe Collatz iterative sequence (See Cody problem n° 2103 and 211) is defined for the set of positive integers:\r\n\r\n* n → n/2 (n is even)\r\n* n → 3n + 1 (n is odd)\r\n\r\nUsing the rule above and starting with 13, we generate the following sequence:\r\n\r\n13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1\r\n\r\nIt can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.\r\n\r\nWhich starting number, under number given in input, produces the longest chain?\r\n\r\nBe smart because numbers can be big...\r\n","description_html":"\u003cp\u003eInspired by Projet Euler n°14.\u003c/p\u003e\u003cp\u003eThe Collatz iterative sequence (See Cody problem n° 2103 and 211) is defined for the set of positive integers:\u003c/p\u003e\u003cul\u003e\u003cli\u003en → n/2 (n is even)\u003c/li\u003e\u003cli\u003en → 3n + 1 (n is odd)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eUsing the rule above and starting with 13, we generate the following sequence:\u003c/p\u003e\u003cp\u003e13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1\u003c/p\u003e\u003cp\u003eIt can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.\u003c/p\u003e\u003cp\u003eWhich starting number, under number given in input, produces the longest chain?\u003c/p\u003e\u003cp\u003eBe smart because numbers can be big...\u003c/p\u003e","function_template":"function y = euler14(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 10;\r\nassert(isequal(euler14(x),9))\r\n%%\r\nx = 100;\r\nassert(isequal(euler14(x),97))\r\n%%\r\nx = 96;\r\nassert(isequal(euler14(x),73))\r\n%%\r\nx = 1000;\r\nassert(isequal(euler14(x),871))\r\n%%\r\nx = 870;\r\nassert(isequal(euler14(x),703))\r\n%%\r\nassert(isequal(euler14(871),871))\r\n%%\r\nx = 77030;\r\nassert(isequal(euler14(x),52527))\r\n%%\r\nx = 77031;\r\nassert(isequal(euler14(x),77031))\r\n%%\r\nassert(isequal(euler14(500000),410011))\r\n%%\r\nz = 900000;\r\ny_correct=837799;\r\nassert(isequal(euler14(z),y_correct))\r\n%% Projet Euler n°14 solution with x=1000000\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":137,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-10-28T10:14:25.000Z","updated_at":"2026-01-05T00:24:55.000Z","published_at":"2015-10-28T10:15:11.000Z","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 Projet Euler n°14.\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 Collatz iterative sequence (See Cody problem n° 2103 and 211) is defined for the set of positive integers:\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\u003en → n/2 (n is even)\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\u003en → 3n + 1 (n is odd)\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\u003eUsing the rule above and starting with 13, we generate the following 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\u003e13 → 40 → 20 → 10 → 5 → 16 → 8 → 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 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\u003eWhich starting number, under number given in input, produces the longest chain?\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\u003eBe smart because numbers can be big...\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":252,"title":"Project Euler: Problem 16, Sums of Digits of Powers of Two","description":"2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.\r\n\r\nWhat is the sum of the digits of the number 2^N?\r\n\r\nThanks to \u003chttp://projecteuler.net/problem=16 Project Euler Problem 16\u003e.","description_html":"\u003cp\u003e2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.\u003c/p\u003e\u003cp\u003eWhat is the sum of the digits of the number 2^N?\u003c/p\u003e\u003cp\u003eThanks to \u003ca href=\"http://projecteuler.net/problem=16\"\u003eProject Euler Problem 16\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = pow2_sumofdigits(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 1;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 1;\r\ny_correct = 2;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 15;\r\ny_correct = 26;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 345;\r\ny_correct = 521;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 999;\r\ny_correct = 1367;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 2000;\r\ny_correct = 2704;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":178,"test_suite_updated_at":"2012-02-04T07:44:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-03T20:15:41.000Z","updated_at":"2026-01-15T22:21:41.000Z","published_at":"2012-02-04T07:53:38.000Z","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\u003e2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.\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\u003eWhat is the sum of the digits of the number 2^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\u003eThanks 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://projecteuler.net/problem=16\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProject Euler Problem 16\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":273,"title":"Recurring Cycle Length (Inspired by Project Euler Problem 26)","description":"Preface: This problem is inspired by Project Euler Problem 26 and uses text from that question to explain what a recurring cycle is.\r\nDescription\r\nA unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:\r\n1/2  =   0.5\r\n1/3  =  0.(3)\r\n1/4  =   0.25\r\n1/5  =   0.2\r\n1/6  =   0.1(6)\r\n1/7  =   0.(142857)\r\n1/8  =   0.125\r\n1/9  =   0.(1)\r\n1/10 =   0.1\r\nWhere 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.\r\nCreate a function that can determine the length of the recurring cycle of 1/d given d.","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: 377.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 188.95px; transform-origin: 407px 188.95px; 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: 113px 8px; transform-origin: 113px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePreface: This problem is inspired by\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProject Euler Problem 26\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: 190px 8px; transform-origin: 190px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and uses text from that question to explain what a recurring cycle 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: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\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: 382px 8px; transform-origin: 382px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:\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: 404px 91.95px; transform-origin: 404px 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: 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: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/2  =   0.5\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/3  =  0.(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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/4  =   0.25\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: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/5  =   0.2\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: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/6  =   0.1(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: 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: 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; \"\u003e1/7  =   0.(142857)\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: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/8  =   0.125\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: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/9  =   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: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/10 =   0.1\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: 374.5px 8px; transform-origin: 374.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.\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: 264.5px 8px; transform-origin: 264.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate a function that can determine the length of the recurring cycle of 1/d given d.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = recurring_cycle(d)\r\n    L = d;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 1;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 1;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = 6;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 1;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = 16;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 19;\r\ny_correct = 18;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 29;\r\ny_correct = 28;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 19;\r\ny_correct = 18;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 109;\r\ny_correct = 108;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 197;\r\ny_correct = 98;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 223;\r\ny_correct = 222;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 2^randi(10);\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 1977;\r\ny_correct = 658;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 12345;\r\ny_correct = 822;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = randi(6)*3;\r\ny_correct = 1;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":134,"edited_by":223089,"edited_at":"2023-02-02T10:48:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":161,"test_suite_updated_at":"2023-02-02T10:48:13.000Z","rescore_all_solutions":false,"group_id":44,"created_at":"2012-02-06T22:59:19.000Z","updated_at":"2026-01-05T00:27:32.000Z","published_at":"2012-02-23T17:44:12.000Z","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\u003ePreface: This problem is inspired 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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProject Euler Problem 26\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and uses text from that question to explain what a recurring cycle 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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:\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  =   0.5\\n1/3  =  0.(3)\\n1/4  =   0.25\\n1/5  =   0.2\\n1/6  =   0.1(6)\\n1/7  =   0.(142857)\\n1/8  =   0.125\\n1/9  =   0.(1)\\n1/10 =   0.1]]\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\u003eWhere 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 a function that can determine the length of the recurring cycle of 1/d given d.\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":44733,"title":"Large Sum (inspired by Project Euler 13)","description":"Your function will be provided an arbitrary number of numbers of arbitrary sizes as a cell array of strings. Some numbers will be very large. The function must return the first eight digits of the sum of all the numbers as an integer.","description_html":"\u003cp\u003eYour function will be provided an arbitrary number of numbers of arbitrary sizes as a cell array of strings. Some numbers will be very large. The function must return the first eight digits of the sum of all the numbers as an integer.\u003c/p\u003e","function_template":"function y = sum_large_n(c)\r\n y = sum(c);\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp', 'regexpi'},'FileName','sum_large_n.m')\r\n\r\n%%\r\nfiletext = fileread('sum_large_n.m');\r\nassert(isempty(strfind(filetext, 'java')),'java forbidden')\r\n\r\n%%\r\nc = {'12345678'};\r\nassert(isequal(sum_large_n(c),12345678))\r\n\r\n%%\r\nc = {'1234567890','9'};\r\nassert(isequal(sum_large_n(c),12345678))\r\n\r\n%%\r\nc = {'11223344','11223344'};\r\nassert(isequal(sum_large_n(c),22446688))\r\n\r\n%%\r\nc = {'1000000000','99','1'};\r\nassert(isequal(sum_large_n(c),10000001))\r\n\r\n%%\r\nc = {'100000000000000000000000000000000000000000','9999','9999','9999'};\r\nassert(isequal(sum_large_n(c),10000000))\r\n\r\n%%\r\nc = {'15934672','34627951','63195472','98416599','13652729','32167958','32368197'};\r\nassert(isequal(sum_large_n(c),29036357))\r\n\r\n%%\r\nc = {'65281492489834938429841293654542962328498421794427152995741538492824984','37812654179574152749152791584279521794471529572419527149652719458479854'};\r\nassert(isequal(sum_large_n(c),10309414))\r\n\r\n%%\r\nc = {'64854985662353823234394299423463672233451381975635955356744918981347271658799472175596688623815297551711518872659685481224881454663419214254991734594937657622921687245928642452634633638974619883614322', ...\r\n     '41657761135648795316841323455859693737713378487164915457385127524627393723167546676927326556746488366583329656565759211145476799227155854775426317347474774134328484748742893748728958622478835122752521', ...\r\n     '86976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189'};\r\nassert(isequal(sum_large_n(c),19348963))\r\n\r\n%%\r\nc = {'64854985662353823234394299423463672233451381975635955356744918981347271658799472175596688623815297551711518872659685481224881454663419214254991734594937657622921687245928642452634633638974619883614322', ...\r\n     '41657761135648795316841323455859693737713378487164915457385127524627393723167546676927326556746488366583329656565759211145476799227155854775426317347474774134328484748742893748728958622478835122752521', ...\r\n     '86976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189', ...\r\n     '72712636767379814476842172453652813351412836947746192385743174561377221146751622122233239762219763269234174946242784735864354467442133699537777175218226957295718725354423196929864373177764483888569418', ...\r\n     '64936642142748762939341621746461987846653353891518919178589622211694499797463375467656517949485422378718971477337563287912152911673242596141549859249976492768478359536474579387914633766614537837282648', ...\r\n     '55845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396', ...\r\n     '56852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122', ...\r\n     '74731539941789156776746219369224943244241616835615628985373966213897736849135176588835711359733896318691638244872327622595118548457836916433792829847584169247197625598974953476799592136595457182534623', ...\r\n     '22385429486488589446974795531215196112521748441116388952357456927648426638992316148542492581793279692744286781957782569896681841722633444622137377883353886373545979351768994152231775485994546872814784', ...\r\n     '79323439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878125985417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),62027779))\r\n\r\n%%\r\nc = {'6475498566235382323439429942346367223345138697688918695583596876361667997696128582561641522222163575552588326642911226619771899885242193335618684512639295793457812415422975917762632291314192135193313157611795184371176577837641846712559871118981975635955356744918981347271658799472175596688623815297551711518872659685481224881454663419214254991734594937657622921687245928642452634633638974619883614322', ...\r\n     '2165776113564879531684132345585969373771337848716491545738512752462739372316754667692732655674648836658332965656575921114547679922715585477542793234391628259412443979491683978683336834869287354681884467774496836691551984826358235489237499684696975682494699611669765395175193323361338476829815363666515415558781259854175242749186567181329166686317347474774134328484748742893748728958622478835122752521', ...\r\n     '8697688918695583596876361667997696128582561641522222163575552588326642911226619771899885242193335618684512635685254967745626748745477479871465138181752627611214865819152617899531567165296496585574368424348444231433425738141212232269925453142194971776527349843699638491572423451533329987242137654357767625412292957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189', ...\r\n     '7271263676737981447684217245365281335141283694774619238574317456137722114675162212223323976221976326923417494624278473586435446744213369953777717521822695729571872535442319692986437317776445584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239683888569418', ...\r\n     '6293664214274876293934162174646198784665335389151891917858962221169449979746337546765651794948542237871897147733756328791215291167324259614154985568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573814121223226992545314219497177652734984369963849157242345153332998724213765435776762541229249976492768478359536474579387914633766614537837282648', ...\r\n     '5584591927674681196342333231512689695428194147857913127786198359784563737624373984578663575632548872163993896895761565857499845388949884689726131512689695479857499845388966295297837624373984578632571235635787174428334456445697482112331512689695388949884689761479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239687232762259511854845785534518148468892396', ...\r\n     '5685254967745626748745477479871465138181752627611214865819152617899531567165296496585574368424348444231433425738793234391628259412443979491683978683336834869287354681884467774496836691551984826358235489237499684696975682494699611669765395175193323361338476829815363666515415558781259854175242749186567181329166681412122322699254531421949717765273498436996384915724234515333299872421376543577676254122', ...\r\n     '7873153994178915677674621936922494324424161683561562898537396621389773684913517658883571135973389631869163824455845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457836916433792829847584169247197625598974953476799592136595457182534623', ...\r\n     '2238542948648858944697479553121519611252174844111638895235745692764842663899231614854249258179327969274428678195778256989668184172263355845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396444622137377883353886373545979351768994152231775485994546872814784', ...\r\n     '7392343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587815584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239625985417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),59677779))\r\n\r\n%%\r\nc = {'69754985662353823234394299423463672233451386976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189819756359553567449189813472716587994721755966886238152975517115188726596854812248814546634192142549917345949376576229223854294864885894469747955312151961125217484411163889523574569276484266389923161485424925817932796927442867819577825698966818417226335584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239644462213737788335388637354597935176899415223177548599454687281478421687245928642452634633638974619883614322', ...\r\n     '51057761135648795316841323455859693737713378487164915457385127524627393723167546676927326556746488366583329656565759211145476799227155854775427932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291686976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783764184671255987111896686317347474774134328484748742893748728958622478835122752521', ...\r\n     '76976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783767392343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587815584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239625985417524274918656718132916668418467125598711189', ...\r\n     '72712636767379814476842172453652813351412836947746192385743174561377221146751622122233239762219763269234174946242784735864354467442133699537777175218226957295718725354423196929864373177764455845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534586976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783764184671255987111891814846889239683888569418', ...\r\n     '62936642142748762939341621746461987846653353891518919178589622211694499797463375467656517949485422378718971477337563287912152911673242596141549855685254967745626748745477479871465138181752627611214865819152617899531567165296496585574368424348444231433425738141212232269925453142194971776527349843699638491572423451533568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573879323439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878125985417524274918656718132916668141212232269925453142194971776527349843699638491572423451533329987242137654357767625412232998724213765435776762541229249976492768478359536474579387914633766614537837282648', ...\r\n     '55845919276746811963423332315126896954281941478579131277861983597845637376243739845786635756325488721639938968957615658574998453889498846897261315126896954798574998453889662952978376243739845786325712356357871744283344564456974821123315126896953889498846897614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457855345181484688956852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435776762541222396', ...\r\n     '50852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435755845919276746811963423332315126896954281941478579131277861983597845637376243739845786635756325488721639938968957615658574998453889498846897261315126896954798574998453889662952978376243739845786325712356357871744283344564456974821123315126896953889498846897614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457855345181484688923967676254122', ...\r\n     '18731539941789156776746219369224943244241616835615628985373966213897736849135176588835711359733896318691638244558459192767468119634233324281941478579131277861983597845637563254887216399389689576156549884689726147985749984538896629529783762437398457866357871744283344564456974821123315126896955345181484688923968726293664214274876293934162174646198784665335389151891917858962221169449979746337546765651794948542237871897147733756328791215291167324259614154985568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573814121223226992545314219497177652734984369963849157242345153332998724213765435776762541229249976492768478359536474579387914633766614537837282648327622595118548457836916433792829847584169247197625598974953476799592136595457182534623', ...\r\n     '24185429486488589446974795531215196112521748441116388952357456927648426638992316148542492581793279692744286781957782569896681841722633558459192767468119634233324281941478579131277861983597845637563254887216399389689576156549884689726147985749984538896629529783762437398457866357871744283344564456974821123315126896955345181484688923964446221373778833538863735464754985662353823234394299423463672233451386976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189819756359553567449189813472716587994721755966886238152975517115188726596854812248814546634192142549917345949376576229216872459286424526346336389746198836143225979351768994152231775485994546872814784', ...\r\n     '73923439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878155845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435776762541223151268969553451814846889239625985417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),55697779))\r\n\r\n%%\r\nc = {'169754985662353823234394299423463672233451386976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189819756359553567449189813472716587994721755966886238152975517115188726596854812248814546634192142549917345949376576229223854294864885894469747955312151961125217484411163889523574569276484266389923161485424925817932796927442867819577825698966818417226335584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239644462213737788335388637354597935176899415223177548599454687281478421687245928642452634633638974619883614322', ...\r\n     '51057761135648795316841323455859693737713378487164915457385127524627393723167546676927326556746488366583329656565759211145476799227155854775427932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291686976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783764184671255987111896686317347474774134328484748742893748728958622478835122752521', ...\r\n     '476976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783767392343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587815584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239625985417524274918656718132916668418467125598711189', ...\r\n     '72712636767379814476842172453652813351412836947746192385743174561377221146751622122233239762219763269234174946242784735864354467442133699537777175218226957295718725354423196929864373177764455845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534586976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783764184671255987111891814846889239683888569418', ...\r\n     '562936642142748762939341621746461987846653353891518919178589622211694499797463375467656517949485422378718971477337563287912152911673242596141549855685254967745626748745477479871465138181752627611214865819152617899531567165296496585574368424348444231433425738141212232269925453142194971776527349843699638491572423451533568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573879323439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878125985417524274918656718132916668141212232269925453142194971776527349843699638491572423451533329987242137654357767625412232998724213765435776762541229249976492768478359536474579387914633766614537837282648', ...\r\n     '755845919276746811963423332315126896954281941478579131277861983597845637376243739845786635756325488721639938968957615658574998453889498846897261315126896954798574998453889662952978376243739845786325712356357871744283344564456974821123315126896953889498846897614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457855345181484688956852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435776762541222396', ...\r\n     '50852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435755845919276746811963423332315126896954281941478579131277861983597845637376243739845786635756325488721639938968957615658574998453889498846897261315126896954798574998453889662952978376243739845786325712356357871744283344564456974821123315126896953889498846897614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457855345181484688923967676254122', ...\r\n     '8731539941789156776746219369224943244241616835615628985373966213897736849135176588835711359733896318691638244558459192767468119634233324281941478579131277861983597845637563254887216399389689576156549884689726147985749984538896629529783762437398457866357871744283344564456974821123315126896955345181484688923968726293664214274876293934162174646198784665335389151891917858962221169449979746337546765651794948542237871897147733756328791215291167324259614154985568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573814121223226992545314219497177652734984369963849157242345153332998724213765435776762541229249976492768478359536474579387914633766614537837282648327622595118548457836916433792829847584169247197625598974953476799592136595457182534623', ...\r\n     '24185429486488589446974795531215196112521748441116388952357456927648426638992316148542492581793279692744286781957782569896681841722633558459192767468119634233324281941478579131277861983597845637563254887216399389689576156549884689726147985749984538896629529783762437398457866357871744283344564456974821123315126896955345181484688923964446221373778833538863735464754985662353823234394299423463672233451386976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189819756359553567449189813472716587994721755966886238152975517115188726596854812248814546634192142549917345949376576229216872459286424526346336389746198836143225979351768994152231775485994546872814784', ...\r\n     '973923439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878155845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435776762541223151268969553451814846889239625985417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),31469777))\r\n\r\n%%\r\nc = {'16975498566235382323439429942346367223345138697688', ...\r\n     '91869558359687636166799769612858256164152222216357', ...\r\n     '55525883266429112266197718998852421933356186845126', ...\r\n     '39295793457812415422975917762632291314192135193313', ...\r\n     '15761179518437117657783764184671255987111898197563', ...\r\n     '59553567449189813472716587994721755966886238152975', ...\r\n     '51711518872659685481224881454663419214254991734594', ...\r\n     '93765762292238542948648858944697479553121519611252', ...\r\n     '17484411163889523574569276484266389923161485424925', ...\r\n     '81793279692744286781957782569896681841722633558459', ...\r\n     '19276746811963423332428194147857913127786198359784', ...\r\n     '56375632548872163993896895761565498846897261479857', ...\r\n     '49984538896629529783762437398457866357871744283344', ...\r\n     '56445697482112331512689695534518148468892396444622', ...\r\n     '13737788335388637354597935176899415223177548599454', ...\r\n     '68728147842168724592864245263463363897461988361432', ...\r\n     '51057761135648795316841323455859693737713378487164', ...\r\n     '91545738512752462739372316754667692732655674648836', ...\r\n     '65833296565657592111454767992271558547754279323439', ...\r\n     '16282594124439794916839786833368348692873546818844', ...\r\n     '67774496836691551984826358235489237499684696975682', ...\r\n     '49469961166976539517519332336133847682981536366651', ...\r\n     '54155587812598541752427491865671813291686976889186', ...\r\n     '95583596876361667997696128582561641522222163575552', ...\r\n     '58832664291122661977189988524219333561868451263568', ...\r\n     '52549677456267487454774798714651381817526276112148', ...\r\n     '65819152617899531567165296496585574368424348444231', ...\r\n     '43342573814121223226992545314219497177652734984369', ...\r\n     '96384915724234515333299872421376543577676254122929', ...\r\n     '57934578124154229759177626322913141921351933131576', ...\r\n     '11795184371176577837641846712559871118966863173474', ...\r\n     '74774134328484748742893748728958622478835122752521', ...\r\n     '47697688918695583596876361667997696128582561641522', ...\r\n     '22216357555258832664291122661977189988524219333561', ...\r\n     '86845126356852549677456267487454774798714651381817', ...\r\n     '52627611214865819152617899531567165296496585574368', ...\r\n     '42434844423143342573814121223226992545314219497177', ...\r\n     '65273498436996384915724234515333299872421376543577', ...\r\n     '67625412292957934578124154229759177626322913141921', ...\r\n     '35193313157611795184371176577837673923439162825941', ...\r\n     '24439794916839786833368348692873546818844677744968', ...\r\n     '36691551984826358235489237499684696975682494699611', ...\r\n     '66976539517519332336133847682981536366651541555878', ...\r\n     '15584591927674681196342333242819414785791312778619', ...\r\n     '83597845637563254887216399389689576156549884689726', ...\r\n     '14798574998453889662952978376243739845786635787174', ...\r\n     '42833445644569748211233151268969553451814846889239', ...\r\n     '62598541752427491865671813291666841846712559871189', ...\r\n     '72712636767379814476842172453652813351412836947746', ...\r\n     '19238574317456137722114675162212223323976221976326', ...\r\n     '92341749462427847358643544674421336995377771752182', ...\r\n     '26957295718725354423196929864373177764455845919276', ...\r\n     '74681196342333242819414785791312778619835978456375', ...\r\n     '63254887216399389689576156549884689726147985749984', ...\r\n     '53889662952978376243739845786635787174428334456445', ...\r\n     '69748211233151268969553458697688918695583596876361', ...\r\n     '66799769612858256164152222216357555258832664291122', ...\r\n     '66197718998852421933356186845126356852549677456267', ...\r\n     '48745477479871465138181752627611214865819152617899', ...\r\n     '53156716529649658557436842434844423143342573814121', ...\r\n     '22322699254531421949717765273498436996384915724234', ...\r\n     '51533329987242137654357767625412292957934578124154', ...\r\n     '22975917762632291314192135193313157611795184371176', ...\r\n     '57783764184671255987111891814846889239683888569418', ...\r\n     '56293664214274876293934162174646198784665335389151', ...\r\n     '89191785896222116944997974633754676565179494854223', ...\r\n     '78718971477337563287912152911673242596141549855685', ...\r\n     '25496774562674874547747987146513818175262761121486', ...\r\n     '58191526178995315671652964965855743684243484442314', ...\r\n     '33425738141212232269925453142194971776527349843699', ...\r\n     '63849157242345153356852549677456267487454774798714', ...\r\n     '65138181752627611214865819152617899531567165296496', ...\r\n     '58557436842434844423143342573879323439162825941244', ...\r\n     '39794916839786833368348692873546818844677744968366', ...\r\n     '91551984826358235489237499684696975682494699611669', ...\r\n     '76539517519332336133847682981536366651541555878125', ...\r\n     '98541752427491865671813291666814121223226992545314', ...\r\n     '21949717765273498436996384915724234515333299872421', ...\r\n     '37654357767625412232998724213765435776762541229249', ...\r\n     '97649276847835953647457987914633766614537837282648', ...\r\n     '75584591927674681196342333231512689695428194147857', ...\r\n     '91312778619835978456373762437398457866357563254887', ...\r\n     '21639938968957615658574998453889498846897261315126', ...\r\n     '89695479857499845388966295297837624373984578632571', ...\r\n     '23563578717442833445644569748211233151268969538894', ...\r\n     '98846897614798574998453889662952978376243739845786', ...\r\n     '63578717442833445644569748211233151268969553451814', ...\r\n     '84688923968723276225951185484578553451814846889568', ...\r\n     '52549677456267487454774798714651381817526276112148', ...\r\n     '65819152617899531567165296496585574368424348444231', ...\r\n     '43342573879323439162825941244397949168397868333683', ...\r\n     '48692873546818844677744968366915519848263582354892', ...\r\n     '37499684696975682494699611669765395175193323361338', ...\r\n     '47682981536366651541555878125985417524274918656718', ...\r\n     '13291666814121223226992545314219497177652734984369', ...\r\n     '96384915724234515333299872421376543577676541222396', ...\r\n     '50852549677456267487454774798714651381817526276112', ...\r\n     '14865819152617899531567165296496585574368424348444', ...\r\n     '23143342573879323439162825941244397949168397868333', ...\r\n     '68348692873546818844677744968366915519848263582354', ...\r\n     '89237499684696975682494699611669765395175193323361', ...\r\n     '33847682981536366651541555878125985417524274918656', ...\r\n     '71813291666814121223226992545314219497177652734984', ...\r\n     '36996384915724234515333299872421376543575584591927', ...\r\n     '67468119634233323151268969542819414785791312778619', ...\r\n     '83597845637376243739845786635756325488721639938968', ...\r\n     '95761565857499845388949884689726131512689695479857', ...\r\n     '49984538896629529783762437398457863257123563578717', ...\r\n     '44283344564456974821123315126896953889498846897614', ...\r\n     '79857499845388966295297837624373984578663578717442', ...\r\n     '83344564456974821123315126896955345181484688923968', ...\r\n     '72327622595118548457855345181484688923967676254122', ...\r\n     '87315399417891567767462193692249432442416168356156', ...\r\n     '28985373966213897736849135176588835711359733896318', ...\r\n     '69163824455845919276746811963423332428194147857913', ...\r\n     '12778619835978456375632548872163993896895761565498', ...\r\n     '84689726147985749984538896629529783762437398457866', ...\r\n     '35787174428334456445697482112331512689695534518148', ...\r\n     '46889239687262936642142748762939341621746461987846', ...\r\n     '65335389151891917858962221169449979746337546765651', ...\r\n     '79494854223787189714773375632879121529116732425961', ...\r\n     '41549855685254967745626748745477479871465138181752', ...\r\n     '62761121486581915261789953156716529649658557436842', ...\r\n     '43484442314334257381412122322699254531421949717765', ...\r\n     '27349843699638491572423451533329987242137654357767', ...\r\n     '62541229249976492768478359536474579387914633766614', ...\r\n     '53783728264832762259511854845783691643379282984758', ...\r\n     '41692471976255989749534767995921365954570182534623', ...\r\n     '24185429486488589446974795531215196112521748441116', ...\r\n     '38895235745692764842663899231614854249258179327969', ...\r\n     '27442867819577825698966818417226335584591927674681', ...\r\n     '19634233324281941478579131277861983597845637563254', ...\r\n     '88721639938968957615654988468972614798574998453889', ...\r\n     '66295297837624373984578663578717442833445644569748', ...\r\n     '21123315126896955345181484688923964446221373778833', ...\r\n     '53886373546475498566235382323439429942346367223345', ...\r\n     '13869768891869558359687636166799769612858256164152', ...\r\n     '22221635755525883266429112266197718998852421933356', ...\r\n     '18684512639295793457812415422975917762632291314192', ...\r\n     '13519331315761179518437117657783764184671255987111', ...\r\n     '89819756359553567449189813472716587994721755966886', ...\r\n     '23815297551711518872659685481224881454663419214254', ...\r\n     '99173459493765762292168724592864245263463363897461', ...\r\n     '98836143225979351768994152231775485994546872814784', ...\r\n     '97392343916282594124439794916839786833368348692873', ...\r\n     '54681884467774496836691551984826358235489237499684', ...\r\n     '69697568249469961166976539517519332336133847682981', ...\r\n     '53636665154155587815584591927674681196342333242819', ...\r\n     '41478579131277861983597845637563254887216399389689', ...\r\n     '57615654988468972614798574998453889662952978376243', ...\r\n     '73984578663578717442833445644569748211235685254967', ...\r\n     '74562674874547747987146513818175262761121486581915', ...\r\n     '26178995315671652964965855743684243484442314334257', ...\r\n     '38793234391628259412443979491683978683336834869287', ...\r\n     '35468188446777449683669155198482635823548923749968', ...\r\n     '46969756824946996116697653951751933233613384768298', ...\r\n     '15363666515415558781259854175242749186567181329166', ...\r\n     '68141212232269925453142194971776527349843699638491', ...\r\n     '57242345153332998724213765435776762541223151268969', ...\r\n     '55345181484688923962585417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),87139239))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":114,"test_suite_updated_at":"2018-08-20T17:27:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-20T17:18:24.000Z","updated_at":"2026-01-05T00:23:53.000Z","published_at":"2018-08-20T17:18:24.000Z","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\",\"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\u003eYour function will be provided an arbitrary number of numbers of arbitrary sizes as a cell array of strings. Some numbers will be very large. The function must return the first eight digits of the sum of all the numbers as an 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":2323,"title":"Pandigital number n°3 (Inspired by Project Euler 32)","description":"After Problem 2319 and 2320.\r\n\r\nAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\r\n\r\nThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\r\n\r\nFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\r\n\r\nHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\r\n\r\nHINT2: All in good time...  \r\n\r\n","description_html":"\u003cp\u003eAfter Problem 2319 and 2320.\u003c/p\u003e\u003cp\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/p\u003e\u003cp\u003eThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\u003c/p\u003e\u003cp\u003eFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\u003c/p\u003e\u003cp\u003eHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\u003c/p\u003e\u003cp\u003eHINT2: All in good time...\u003c/p\u003e","function_template":"function y = pandigital_sum(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [];\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 4;\r\ny_correct = 12;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 52;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 6;\r\ny_correct = 162;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = []; % Strange no ?\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 13458;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n\r\n\r\n%% You obtain the Project Euler n°32 solution with n=9\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2019-10-23T23:21:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-15T10:08:43.000Z","updated_at":"2025-12-19T11:41:31.000Z","published_at":"2014-05-15T10:20:54.000Z","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\u003eAfter Problem 2319 and 2320.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT2: All in good time...\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":2342,"title":"Numbers spiral diagonals (Part 2)","description":"Inspired by Project Euler n°28 and 58.\r\nA n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.\r\nFor example with n=5, the spiral matrix is :\r\n                       21 22 23 24 25\r\n                       20  7  8  9 10\r\n                       19  6  1  2 11\r\n                       18  5  4  3 12\r\n                       17 16 15 14 13\r\nThe sum of the numbers on the diagonals is 101 (See problem 2340) and you have 5 primes (3, 5, 7, 13, 17) out of the 9 numbers lying along both diagonals. So the prime ratio is 5/9 ≈ 55%.\r\nWith a 7x7 spiral matrix, the ratio is 62% (8 primes out of the 13 diagonal numbers).\r\nWhat is the side length (always odd and greater than 1) of the square spiral for which the ratio of primes along both diagonals FIRST falls below p% ? (0\u003cp\u003c1)","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: 326.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 163.083px; transform-origin: 407px 163.083px; 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: 120px 8px; transform-origin: 120px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Project Euler n°28 and 58.\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: 341px 8px; transform-origin: 341px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.\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: 131.5px 8px; transform-origin: 131.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example with n=5, the spiral matrix is :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; 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 51.0833px; transform-origin: 404px 51.0833px; 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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       21 22 23 24 25\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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       20  7  8  9 10\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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       19  6  1  2 11\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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       18  5  4  3 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: 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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       17 16 15 14 13\u003c/span\u003e\u003c/span\u003e\u003c/div\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: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; 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: 382.5px 8px; transform-origin: 382.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sum of the numbers on the diagonals is 101 (See problem 2340) and you have 5 primes (3, 5, 7, 13, 17) out of the 9 numbers lying along both diagonals. So the prime ratio is 5/9 ≈ 55%.\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: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWith a 7x7 spiral matrix, the ratio is 62% (8 primes out of the 13 diagonal numbers).\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: 364.5px 8px; transform-origin: 364.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"perspective-origin: 74px 8px; transform-origin: 74px 8px; \"\u003eWhat is the side length \u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; perspective-origin: 2.5px 8.5px; transform-origin: 2.5px 8.5px; \"\u003e(\u003c/span\u003e\u003cspan style=\"perspective-origin: 96px 8px; transform-origin: 96px 8px; \"\u003ealways odd and greater than 1\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; perspective-origin: 2.5px 8.5px; transform-origin: 2.5px 8.5px; \"\u003e)\u003c/span\u003e\u003cspan style=\"perspective-origin: 189.5px 8px; transform-origin: 189.5px 8px; \"\u003e of the square spiral for which the ratio of primes along both diagonals FIRST falls below p% ? (0\u0026lt;p\u0026lt;1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function res=spiral_ratio(pourcentage)\r\nres=pourcentage*2;\r\nend","test_suite":"%%\r\nx = 0.8;\r\ny_correct = 3;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.5;\r\ny_correct = 11;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.4;\r\ny_correct = 31;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.3;\r\ny_correct = 49;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.25;\r\ny_correct = 99;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.2;\r\ny_correct = 309;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.15;\r\ny_correct = 981;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.14;\r\ny_correct = 1883;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.13;\r\ny_correct = 3593;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.12;\r\ny_correct = 6523;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.11;\r\ny_correct = 12201;\r\nassert(isequal(spiral_ratio(x),y_correct))","published":true,"deleted":false,"likes_count":7,"comments_count":5,"created_by":5390,"edited_by":223089,"edited_at":"2022-09-26T17:42:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":197,"test_suite_updated_at":"2022-07-09T19:28:50.000Z","rescore_all_solutions":false,"group_id":31,"created_at":"2014-05-31T18:36:25.000Z","updated_at":"2026-04-17T12:45:31.000Z","published_at":"2014-05-31T18:53:35.000Z","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\u003eInspired by Project Euler n°28 and 58.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example with n=5, the spiral matrix 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[                       21 22 23 24 25\\n                       20  7  8  9 10\\n                       19  6  1  2 11\\n                       18  5  4  3 12\\n                       17 16 15 14 13]]\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 sum of the numbers on the diagonals is 101 (See problem 2340) and you have 5 primes (3, 5, 7, 13, 17) out of the 9 numbers lying along both diagonals. So the prime ratio is 5/9 ≈ 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\u003eWith a 7x7 spiral matrix, the ratio is 62% (8 primes out of the 13 diagonal numbers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 is the side length (always odd and greater than 1) of the square spiral for which the ratio of primes along both diagonals FIRST falls below p% ? (0\u0026lt;p\u0026lt;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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":2319,"title":"Pandigital number n°1 (Inspired by Project Euler 32)","description":"A little warm-up to begin...\r\n\r\nAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\r\n\r\nFor example, the 5-digit number 15234, is 1 through 5 pandigital.\r\n\r\nGiven a positive integer find whether it is a pandigital number.\r\n\r\n","description_html":"\u003cp\u003eA little warm-up to begin...\u003c/p\u003e\u003cp\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\u003c/p\u003e\u003cp\u003eFor example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/p\u003e\u003cp\u003eGiven a positive integer find whether it is a pandigital number.\u003c/p\u003e","function_template":"function flag = is_pandigital(x)\r\nflag=2;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = true;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 0;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 123;\r\ny_correct = true;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 1203;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 5432;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 54321;\r\ny_correct = true;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 2361457879;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 1234567809;\r\ny_correct = false;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n%%\r\nx = 987654321;\r\ny_correct = true;\r\nassert(isequal(is_pandigital(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":114,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-13T22:49:33.000Z","updated_at":"2026-03-09T20:20:18.000Z","published_at":"2014-05-13T22:55:20.000Z","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\u003eA little warm-up to begin...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 positive integer find whether it is a pandigital number.\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":52639,"title":"Determine whether a number is unprimeable","description":"The number 204 is unprimeable because no single digit can be changed to make it prime. In contrast, the number 207 is not unprimeable because changing the first digit to 0, 1, 3, 6, or 9 or the second digit to 2, 5, or 7 would make it prime. \r\nWrite a function to determine whether the input number is unprimeable. ","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: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; 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: 384px 8.05px; transform-origin: 384px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 204 is unprimeable because no single digit can be changed to make it prime. In contrast, the number 207 is not unprimeable because changing the first digit to 0, 1, 3, 6, or 9 or the second digit to 2, 5, or 7 would make it 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; 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: 221.983px 8.05px; transform-origin: 221.983px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the input number is unprimeable. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isUnprimeable(n)\r\n   tf = f(n)\r\nend","test_suite":"%%\r\nn = randi(199);\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 200;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 202;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 207;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 322;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 845;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 848;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 3505;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 5454;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 6002;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 14610;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 14617;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 28725;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 28735;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 39998;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 40005;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\ndn = [0 2 4 5 6 8];\r\nn = 47000+dn(randi(6));\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nn = 55545;\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = 55555;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nk = randi(100000);\r\nn = 2310*k+510;\r\nassert(isUnprimeable(n))\r\n\r\n%%\r\nd = [1 3 7 9];\r\nk = randi(21214);\r\nn = 10*k+d(randi(4));\r\nassert(~isUnprimeable(n))\r\n\r\n%%\r\nn = [595631 1203623 872897 212159];\r\nassert(all(arrayfun(@isUnprimeable,n)))\r\n\r\n%%\r\nfiletext = fileread('isUnprimeable.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-29T15:22:09.000Z","updated_at":"2025-11-29T20:38:34.000Z","published_at":"2021-08-29T15:24:50.000Z","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 number 204 is unprimeable because no single digit can be changed to make it prime. In contrast, the number 207 is not unprimeable because changing the first digit to 0, 1, 3, 6, or 9 or the second digit to 2, 5, or 7 would make it 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 to determine whether the input number is unprimeable. \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":2337,"title":"Sum of big primes without primes","description":"Inspired by Project Euler n°10 (I am quite obviously a fan).\r\nWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\r\nFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\r\nBut how to proceed (in time) with big number and WITHOUT the primes function ?\r\nHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\r\nhttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes","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: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; 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: 183px 8px; transform-origin: 183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Project Euler n°10 (I am quite obviously a fan).\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: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\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: 208px 8px; transform-origin: 208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\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: 255.5px 8px; transform-origin: 255.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut how to proceed (in time) with big number and WITHOUT the primes function ?\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: 288.5px 8px; transform-origin: 288.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\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\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = big_euler10(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('big_euler10.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'primes'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = 17;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = 1060;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000;\r\ny_correct = 76127;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 10000;\r\ny_correct = 5736396;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 100000;\r\ny_correct = 454396537;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000000;\r\ny_correct = 37550402023;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000000-100;\r\ny_correct = 37542402433;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 2000000-1000;\r\ny_correct = 142781862782;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%% Solution of Project Euler 10 with n=2000000\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":5390,"edited_by":223089,"edited_at":"2023-06-05T10:25:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":239,"test_suite_updated_at":"2023-06-05T10:25:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-27T21:25:58.000Z","updated_at":"2026-03-29T22:02:38.000Z","published_at":"2014-05-27T21:51:18.000Z","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 Project Euler n°10 (I am quite obviously a fan).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input 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\u003eFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 how to proceed (in time) with big number and WITHOUT the primes function ?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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":2320,"title":"Pandigital number n°2 (Inspired by Project Euler 32)","description":"After Problem 2319.\r\nAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\r\nFor example, the 5-digit number 15234, is 1 through 5 pandigital.\r\nFind the number of pandigital numbers in a given interval [xlower,xupper] (inclusive if it is not explicit enough).\r\nThe test suite is simple here, but how to compute this number with BIG interval (pandigital number length \u003e 7) in Cody time?\r\nFor example, between 58755 and 99899923?","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: 192px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 96px; transform-origin: 407px 96px; 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: 15px 8px; transform-origin: 15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblem 2319\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\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: 257px 8px; transform-origin: 257px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\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: 204.5px 8px; transform-origin: 204.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the 5-digit number 15234, is 1 through 5 pandigital.\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: 343px 8px; transform-origin: 343px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the number of pandigital numbers in a given interval [xlower,xupper] (inclusive if it is not explicit enough).\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: 370.5px 8px; transform-origin: 370.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe test suite is simple here, but how to compute this number with BIG interval (pandigital number length \u0026gt; 7) in Cody time?\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: 143.5px 8px; transform-origin: 143.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, between 58755 and 99899923?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pandigital_nb(xlower, xupper)\r\n  y=xupper-xlower;\r\nend","test_suite":"%%\r\nxl = 1;\r\nxu = 10\r\ny_correct = 1;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 10;\r\nxu = 99;\r\ny_correct = 2;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 100;\r\nxu = 999;\r\ny_correct = 6;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 1000;\r\nxu = 9999;\r\ny_correct = 24;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 10000;\r\nxu = 99999;\r\ny_correct = 120;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 1;\r\nxu = 999;\r\ny_correct = 9;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 1;\r\nxu = 9999;\r\ny_correct = 33;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))\r\n%%\r\nxl = 100000;\r\nxu = 999999;\r\ny_correct = 720;\r\nassert(isequal(pandigital_nb(xl,xu),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":5390,"edited_by":223089,"edited_at":"2022-08-09T08:36:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":68,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-14T08:11:36.000Z","updated_at":"2026-03-10T00:41:57.000Z","published_at":"2014-05-14T08:12:54.000Z","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\u003eAfter\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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2319\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:r\u003e\u003cw:t\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of pandigital numbers in a given interval [xlower,xupper] (inclusive if it is not explicit enough).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 test suite is simple here, but how to compute this number with BIG interval (pandigital number length \u0026gt; 7) in Cody 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:r\u003e\u003cw:t\u003eFor example, between 58755 and 99899923?\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":52881,"title":"List the cuban primes","description":"The number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \r\nWrite a function to list the cuban primes less than or equal to the input number. \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: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; 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: 295.108px 8.05px; transform-origin: 295.108px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \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: 245.3px 8.05px; transform-origin: 245.3px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the cuban primes less than or equal to the input number. \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 8.05px; transform-origin: 0px 8.05px; 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 q = cubanPrimes(n)\r\n  q = n^3;\r\nend","test_suite":"%%\r\nn = 100;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 1000;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61 127 271 331 397 547 631 919];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 10000;\r\nq = cubanPrimes(n);\r\nq_correct = [7 19 37 61 127 271 331 397 547 631 919 1657 1801 1951 2269 2437 2791 3169 3571 4219 4447 5167 5419 6211 7057 7351 8269 9241];\r\nassert(isequal(q,q_correct))\r\n\r\n%%\r\nn = 100000;\r\nq = cubanPrimes(n);\r\nqhi_correct = [10267 11719 12097 13267 13669 16651 19441 19927 22447 23497 24571 25117 26227 27361 33391 35317 42841 45757 47251 49537 50311 55897 59221 60919 65269 70687 73477 74419 75367 81181 82171 87211 88237 89269 92401 96661];\r\nassert(isequal(q(q\u003e10000),qhi_correct))\r\n\r\n%%\r\nn = 1e6;\r\nq = cubanPrimes(n);\r\nqhi_correct = [102121 103231 104347 110017 112327 114661 115837 126691 129169 131671 135469 140617 144541 145861 151201 155269 163567 169219 170647 176419 180811 189757 200467 202021 213067 231019 234361 241117 246247 251431 260191 263737 267307 276337 279991 283669 285517 292969 296731 298621 310087 329677 333667 337681 347821 351919 360187 368551 372769 374887 377011 383419 387721 398581 407377 423001 436627 452797 459817 476407 478801 493291 522919 527941 553411 574219 584767 590077 592741 595411 603457 608851 611557 619711 627919 650071 658477 666937 689761 692641 698419 707131 733591 742519 760537 769627 772669 784897 791047 812761 825301 837937 847477 863497 879667 886177 895987 909151 915769 925741 929077 932419 939121 952597 972991 976411 986707 990151 997057];\r\nassert(isequal(q(q\u003e100000),qhi_correct))\r\n\r\n%%\r\nn = 1e7;\r\nq = cubanPrimes(n);\r\nqhi = q(q\u003e1e6);\r\nqhi26_correct = [1021417 1570357 2129419 2676241 3483019 4476187 5382781 6138991 7073281 8401807 9779491];\r\nassert(isequal(qhi(1:26:end),qhi26_correct))\r\n\r\n%%\r\nn = 1e8;\r\nq = cubanPrimes(n);\r\nlen_correct = 1200;\r\nqhi20_correct = [67987081 71282251 74326519 77892361 81510469 84891241 88210519 92991169 95954041 99896011];\r\nassert(isequal(q(1020:20:end),qhi20_correct) \u0026\u0026 isequal(length(q),len_correct))\r\n\r\n%%\r\nn = 1e9;\r\nq = cubanPrimes(n);\r\ns = sum(q(primes(length(q))));\r\ns_correct = 127462233426;\r\nqmax_correct = 999461269;\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(max(q),qmax_correct))\r\n\r\n%%\r\nfiletext = fileread('cubanPrimes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assignin') || contains(filetext, 'persistent');\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2021-10-10T13:54:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-10T13:40:55.000Z","updated_at":"2025-12-14T17:50:30.000Z","published_at":"2021-10-10T13:52:53.000Z","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 number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 list the cuban primes less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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\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":42377,"title":"Bouncy numbers","description":"Inspired by Project Euler n°112.\r\n\r\nWorking from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number. For example: 134468.\r\n\r\nSimilarly if no digit is exceeded by the digit to its right it is called a decreasing number. For example: 66420.\r\nWe shall call a positive integer that is neither increasing nor decreasing a bouncy number. For example, 155349.\r\nClearly there cannot be any bouncy numbers below one-hundred, but surprisingly, these numbers become more and more common after.\r\nFind the least number for which the proportion of bouncy numbers is exactly p%.\r\nAs always this type of problem is difficult to solve with usual Matlab functions (num2str).\r\nSo keep an eye on time...","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: 315.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 157.583px; transform-origin: 407px 157.583px; 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: 99.5px 8px; transform-origin: 99.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Project Euler n°112.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.167px; 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 51.0833px; transform-origin: 391px 51.0833px; 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\u003c/li\u003e\u003cli style=\"block-size: 40.8667px; 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 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 256.5px 8px; transform-origin: 256.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWorking from left-to-right if no digit is exceeded by the digit to its left it is called an\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 66px 8px; transform-origin: 66px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eincreasing number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example: 134468.\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\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: 204.5px 8px; transform-origin: 204.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSimilarly if no digit is exceeded by the digit to its right it is called a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edecreasing\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number. For example: 66420.\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: 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: 230.5px 8px; transform-origin: 230.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe shall call a positive integer that is neither increasing nor decreasing a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.5px 8px; transform-origin: 25.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ebouncy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.5px 8px; transform-origin: 98.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e number. For example, 155349.\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: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eClearly there cannot be any bouncy numbers below one-hundred, but surprisingly, these numbers become more and more common after.\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: 252.5px 8px; transform-origin: 252.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the least number for which the proportion of bouncy numbers is exactly p%.\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: 273.5px 8px; transform-origin: 273.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs always this type of problem is difficult to solve with usual Matlab functions (num2str).\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: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSo keep an eye on time...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bouncy_numbers(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 0.01;\r\ny_correct = 102;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.05;\r\ny_correct = 106;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.1;\r\ny_correct = 132;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.2;\r\ny_correct = 175;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.5;\r\ny_correct = 538;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.8;\r\ny_correct = 4770;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.9;\r\ny_correct = 21780;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.95;\r\ny_correct = 63720;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.96;\r\ny_correct = 152975;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.97;\r\ny_correct = 208200;\r\nassert(isequal(bouncy_numbers(x),y_correct))\r\n%%\r\nx = 0.98;\r\ny_correct = 377650;\r\nassert(isequal(bouncy_numbers(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":"2021-07-22T06:29:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-14T23:04:12.000Z","updated_at":"2026-03-16T15:11:37.000Z","published_at":"2015-06-14T23:09:36.000Z","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\u003eInspired by Project Euler n°112.\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\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\u003eWorking from left-to-right if no digit is exceeded by the digit to its left it is called an\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\u003eincreasing number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. For example: 134468.\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\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\u003eSimilarly if no digit is exceeded by the digit to its right it is called a\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\u003edecreasing\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number. For example: 66420.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe shall call a positive integer that is neither increasing nor decreasing a\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\u003ebouncy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number. For example, 155349.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eClearly there cannot be any bouncy numbers below one-hundred, but surprisingly, these numbers become more and more common after.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the least number for which the proportion of bouncy numbers is exactly p%.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs always this type of problem is difficult to solve with usual Matlab functions (num2str).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 keep an eye on time...\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":2340,"title":"Numbers spiral diagonals (Part 1)","description":"Inspired by Project Euler n°28 et 58.\r\n\r\nA n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.\r\n\r\nFor exemple with n=5, the spiral matrix is :\r\n\r\n                       21 22 23 24 25\r\n                       20  7  8  9 10\r\n                       19  6  1  2 11\r\n                       18  5  4  3 12\r\n                       17 16 15 14 13\r\n\r\nIn this example, the sum of the numbers on the diagonals is 101.\r\n\r\nWhat is the sum of the numbers on the diagonals in any n by n spiral (n always odd) ?\r\n\r\nHINTS: You want the diagonals, not the whole matrix.","description_html":"\u003cp\u003eInspired by Project Euler n°28 et 58.\u003c/p\u003e\u003cp\u003eA n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.\u003c/p\u003e\u003cp\u003eFor exemple with n=5, the spiral matrix is :\u003c/p\u003e\u003cpre\u003e                       21 22 23 24 25\r\n                       20  7  8  9 10\r\n                       19  6  1  2 11\r\n                       18  5  4  3 12\r\n                       17 16 15 14 13\u003c/pre\u003e\u003cp\u003eIn this example, the sum of the numbers on the diagonals is 101.\u003c/p\u003e\u003cp\u003eWhat is the sum of the numbers on the diagonals in any n by n spiral (n always odd) ?\u003c/p\u003e\u003cp\u003eHINTS: You want the diagonals, not the whole matrix.\u003c/p\u003e","function_template":"function y = spiral_nb(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = 25;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 101;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 9;\r\ny_correct = 537;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 501;\r\ny_correct = 83960501;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 5001;\r\ny_correct = 83395855001;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 10001;\r\ny_correct = 666916710001;\r\nassert(isequal(spiral_nb(x),y_correct))\r\n%%\r\nx = 10003;\r\ny_correct = 667316890025;\r\nassert(isequal(spiral_nb(x),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":296,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":31,"created_at":"2014-05-30T22:02:51.000Z","updated_at":"2026-02-01T14:00:50.000Z","published_at":"2014-05-30T22:03:01.000Z","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\u003eInspired by Project Euler n°28 et 58.\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 n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise 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\u003eFor exemple with n=5, the spiral matrix 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[                       21 22 23 24 25\\n                       20  7  8  9 10\\n                       19  6  1  2 11\\n                       18  5  4  3 12\\n                       17 16 15 14 13]]\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\u003eIn this example, the sum of the numbers on the diagonals is 101.\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\u003eWhat is the sum of the numbers on the diagonals in any n by n spiral (n always odd) ?\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\u003eHINTS: You want the diagonals, not the whole matrix.\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":44732,"title":"Highly divisible triangular number (inspired by Project Euler 12)","description":"Triangular numbers can be calculated by the sum from 1 to n. For example, the first 10 triangular numbers are:\r\n\r\n 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...\r\n\r\nAll divisors for each of these numbers are listed below\r\n\r\n 1: 1\r\n 3: 1,3\r\n 6: 1,2,3,6\r\n 10: 1,2,5,10\r\n 15: 1,3,5,15\r\n 21: 1,3,7,21\r\n 28: 1,2,4,7,14,28\r\n 36: 1,2,3,4,6,9,12,18,36\r\n 45: 1,3,5,9,15,45\r\n 55: 1,5,11,55\r\n\r\nYour challenge is to write a function that will return the value of the first triangular number to have over d divisors (d will be passed to your function).","description_html":"\u003cp\u003eTriangular numbers can be calculated by the sum from 1 to n. For example, the first 10 triangular numbers are:\u003c/p\u003e\u003cpre\u003e 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...\u003c/pre\u003e\u003cp\u003eAll divisors for each of these numbers are listed below\u003c/p\u003e\u003cpre\u003e 1: 1\r\n 3: 1,3\r\n 6: 1,2,3,6\r\n 10: 1,2,5,10\r\n 15: 1,3,5,15\r\n 21: 1,3,7,21\r\n 28: 1,2,4,7,14,28\r\n 36: 1,2,3,4,6,9,12,18,36\r\n 45: 1,3,5,9,15,45\r\n 55: 1,5,11,55\u003c/pre\u003e\u003cp\u003eYour challenge is to write a function that will return the value of the first triangular number to have over d divisors (d will be passed to your function).\u003c/p\u003e","function_template":"function y = div_tri_n(d)\r\n y = d;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp', 'regexpi', 'str2num'},'FileName','div_tri_n.m')\r\n\r\n%%\r\nassert(isequal(div_tri_n(2),6))\r\n\r\n%%\r\nassert(isequal(div_tri_n(4),28))\r\n\r\n%%\r\nassert(isequal(div_tri_n(8),36))\r\n\r\n%%\r\nassert(isequal(div_tri_n(10),120))\r\n\r\n%%\r\nassert(isequal(div_tri_n(20),630))\r\n\r\n%%\r\nassert(isequal(div_tri_n(25),2016))\r\n\r\n%%\r\nassert(isequal(div_tri_n(39),3240))\r\n\r\n%%\r\nassert(isequal(div_tri_n(40),5460))\r\n\r\n%%\r\nassert(isequal(div_tri_n(50),25200))\r\n\r\n%%\r\nassert(isequal(div_tri_n(70),25200))\r\n\r\n%%\r\nassert(isequal(div_tri_n(80),25200))\r\n\r\n%%\r\nassert(isequal(div_tri_n(100),73920))\r\n\r\n%%\r\nassert(isequal(div_tri_n(115),157080))\r\n\r\n%%\r\nassert(isequal(div_tri_n(120),157080))\r\n\r\n%%\r\nassert(isequal(div_tri_n(130),437580))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":164,"test_suite_updated_at":"2018-08-20T16:04:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-20T15:15:06.000Z","updated_at":"2026-01-05T00:21:49.000Z","published_at":"2018-08-20T16:04:49.000Z","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\u003eTriangular numbers can be calculated by the sum from 1 to n. For example, the first 10 triangular numbers are:\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, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...]]\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\u003eAll divisors for each of these numbers are listed below\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: 1\\n 3: 1,3\\n 6: 1,2,3,6\\n 10: 1,2,5,10\\n 15: 1,3,5,15\\n 21: 1,3,7,21\\n 28: 1,2,4,7,14,28\\n 36: 1,2,3,4,6,9,12,18,36\\n 45: 1,3,5,9,15,45\\n 55: 1,5,11,55]]\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 challenge is to write a function that will return the value of the first triangular number to have over d divisors (d will be passed to your function).\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":42673,"title":"Longest Collatz Sequence","description":"Inspired by Projet Euler n°14.\r\n\r\nThe Collatz iterative sequence (See Cody problem n° 2103 and 211) is defined for the set of positive integers:\r\n\r\n* n → n/2 (n is even)\r\n* n → 3n + 1 (n is odd)\r\n\r\nUsing the rule above and starting with 13, we generate the following sequence:\r\n\r\n13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1\r\n\r\nIt can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.\r\n\r\nWhich starting number, under number given in input, produces the longest chain?\r\n\r\nBe smart because numbers can be big...\r\n","description_html":"\u003cp\u003eInspired by Projet Euler n°14.\u003c/p\u003e\u003cp\u003eThe Collatz iterative sequence (See Cody problem n° 2103 and 211) is defined for the set of positive integers:\u003c/p\u003e\u003cul\u003e\u003cli\u003en → n/2 (n is even)\u003c/li\u003e\u003cli\u003en → 3n + 1 (n is odd)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eUsing the rule above and starting with 13, we generate the following sequence:\u003c/p\u003e\u003cp\u003e13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1\u003c/p\u003e\u003cp\u003eIt can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.\u003c/p\u003e\u003cp\u003eWhich starting number, under number given in input, produces the longest chain?\u003c/p\u003e\u003cp\u003eBe smart because numbers can be big...\u003c/p\u003e","function_template":"function y = euler14(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 10;\r\nassert(isequal(euler14(x),9))\r\n%%\r\nx = 100;\r\nassert(isequal(euler14(x),97))\r\n%%\r\nx = 96;\r\nassert(isequal(euler14(x),73))\r\n%%\r\nx = 1000;\r\nassert(isequal(euler14(x),871))\r\n%%\r\nx = 870;\r\nassert(isequal(euler14(x),703))\r\n%%\r\nassert(isequal(euler14(871),871))\r\n%%\r\nx = 77030;\r\nassert(isequal(euler14(x),52527))\r\n%%\r\nx = 77031;\r\nassert(isequal(euler14(x),77031))\r\n%%\r\nassert(isequal(euler14(500000),410011))\r\n%%\r\nz = 900000;\r\ny_correct=837799;\r\nassert(isequal(euler14(z),y_correct))\r\n%% Projet Euler n°14 solution with x=1000000\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":1,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":137,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-10-28T10:14:25.000Z","updated_at":"2026-01-05T00:24:55.000Z","published_at":"2015-10-28T10:15:11.000Z","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 Projet Euler n°14.\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 Collatz iterative sequence (See Cody problem n° 2103 and 211) is defined for the set of positive integers:\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\u003en → n/2 (n is even)\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\u003en → 3n + 1 (n is odd)\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\u003eUsing the rule above and starting with 13, we generate the following 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\u003e13 → 40 → 20 → 10 → 5 → 16 → 8 → 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 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\u003eWhich starting number, under number given in input, produces the longest chain?\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\u003eBe smart because numbers can be big...\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":252,"title":"Project Euler: Problem 16, Sums of Digits of Powers of Two","description":"2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.\r\n\r\nWhat is the sum of the digits of the number 2^N?\r\n\r\nThanks to \u003chttp://projecteuler.net/problem=16 Project Euler Problem 16\u003e.","description_html":"\u003cp\u003e2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.\u003c/p\u003e\u003cp\u003eWhat is the sum of the digits of the number 2^N?\u003c/p\u003e\u003cp\u003eThanks to \u003ca href=\"http://projecteuler.net/problem=16\"\u003eProject Euler Problem 16\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = pow2_sumofdigits(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 1;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 1;\r\ny_correct = 2;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 15;\r\ny_correct = 26;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 345;\r\ny_correct = 521;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 999;\r\ny_correct = 1367;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))\r\n\r\n%%\r\nx = 2000;\r\ny_correct = 2704;\r\nassert(isequal(pow2_sumofdigits(x),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":178,"test_suite_updated_at":"2012-02-04T07:44:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-03T20:15:41.000Z","updated_at":"2026-01-15T22:21:41.000Z","published_at":"2012-02-04T07:53:38.000Z","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\u003e2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.\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\u003eWhat is the sum of the digits of the number 2^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\u003eThanks 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://projecteuler.net/problem=16\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProject Euler Problem 16\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":273,"title":"Recurring Cycle Length (Inspired by Project Euler Problem 26)","description":"Preface: This problem is inspired by Project Euler Problem 26 and uses text from that question to explain what a recurring cycle is.\r\nDescription\r\nA unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:\r\n1/2  =   0.5\r\n1/3  =  0.(3)\r\n1/4  =   0.25\r\n1/5  =   0.2\r\n1/6  =   0.1(6)\r\n1/7  =   0.(142857)\r\n1/8  =   0.125\r\n1/9  =   0.(1)\r\n1/10 =   0.1\r\nWhere 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.\r\nCreate a function that can determine the length of the recurring cycle of 1/d given d.","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: 377.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 188.95px; transform-origin: 407px 188.95px; 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: 113px 8px; transform-origin: 113px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePreface: This problem is inspired by\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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 = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProject Euler Problem 26\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: 190px 8px; transform-origin: 190px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and uses text from that question to explain what a recurring cycle 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: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDescription\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: 382px 8px; transform-origin: 382px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:\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: 404px 91.95px; transform-origin: 404px 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: 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: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/2  =   0.5\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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/3  =  0.(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: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/4  =   0.25\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: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/5  =   0.2\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: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/6  =   0.1(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: 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: 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; \"\u003e1/7  =   0.(142857)\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: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/8  =   0.125\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: 56px 8.5px; tab-size: 4; transform-origin: 56px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/9  =   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: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1/10 =   0.1\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: 374.5px 8px; transform-origin: 374.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.\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: 264.5px 8px; transform-origin: 264.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate a function that can determine the length of the recurring cycle of 1/d given d.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function L = recurring_cycle(d)\r\n    L = d;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 1;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 1;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = 6;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 1;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = 16;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 19;\r\ny_correct = 18;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 29;\r\ny_correct = 28;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 19;\r\ny_correct = 18;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 109;\r\ny_correct = 108;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 197;\r\ny_correct = 98;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 223;\r\ny_correct = 222;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 2^randi(10);\r\ny_correct = 0;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 1977;\r\ny_correct = 658;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = 12345;\r\ny_correct = 822;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n\r\n%%\r\nx = randi(6)*3;\r\ny_correct = 1;\r\nassert(isequal(recurring_cycle(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":134,"edited_by":223089,"edited_at":"2023-02-02T10:48:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":161,"test_suite_updated_at":"2023-02-02T10:48:13.000Z","rescore_all_solutions":false,"group_id":44,"created_at":"2012-02-06T22:59:19.000Z","updated_at":"2026-01-05T00:27:32.000Z","published_at":"2012-02-23T17:44:12.000Z","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\u003ePreface: This problem is inspired 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=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProject Euler Problem 26\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and uses text from that question to explain what a recurring cycle 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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:\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  =   0.5\\n1/3  =  0.(3)\\n1/4  =   0.25\\n1/5  =   0.2\\n1/6  =   0.1(6)\\n1/7  =   0.(142857)\\n1/8  =   0.125\\n1/9  =   0.(1)\\n1/10 =   0.1]]\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\u003eWhere 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 a function that can determine the length of the recurring cycle of 1/d given d.\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":44733,"title":"Large Sum (inspired by Project Euler 13)","description":"Your function will be provided an arbitrary number of numbers of arbitrary sizes as a cell array of strings. Some numbers will be very large. The function must return the first eight digits of the sum of all the numbers as an integer.","description_html":"\u003cp\u003eYour function will be provided an arbitrary number of numbers of arbitrary sizes as a cell array of strings. Some numbers will be very large. The function must return the first eight digits of the sum of all the numbers as an integer.\u003c/p\u003e","function_template":"function y = sum_large_n(c)\r\n y = sum(c);\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp', 'regexpi'},'FileName','sum_large_n.m')\r\n\r\n%%\r\nfiletext = fileread('sum_large_n.m');\r\nassert(isempty(strfind(filetext, 'java')),'java forbidden')\r\n\r\n%%\r\nc = {'12345678'};\r\nassert(isequal(sum_large_n(c),12345678))\r\n\r\n%%\r\nc = {'1234567890','9'};\r\nassert(isequal(sum_large_n(c),12345678))\r\n\r\n%%\r\nc = {'11223344','11223344'};\r\nassert(isequal(sum_large_n(c),22446688))\r\n\r\n%%\r\nc = {'1000000000','99','1'};\r\nassert(isequal(sum_large_n(c),10000001))\r\n\r\n%%\r\nc = {'100000000000000000000000000000000000000000','9999','9999','9999'};\r\nassert(isequal(sum_large_n(c),10000000))\r\n\r\n%%\r\nc = {'15934672','34627951','63195472','98416599','13652729','32167958','32368197'};\r\nassert(isequal(sum_large_n(c),29036357))\r\n\r\n%%\r\nc = {'65281492489834938429841293654542962328498421794427152995741538492824984','37812654179574152749152791584279521794471529572419527149652719458479854'};\r\nassert(isequal(sum_large_n(c),10309414))\r\n\r\n%%\r\nc = {'64854985662353823234394299423463672233451381975635955356744918981347271658799472175596688623815297551711518872659685481224881454663419214254991734594937657622921687245928642452634633638974619883614322', ...\r\n     '41657761135648795316841323455859693737713378487164915457385127524627393723167546676927326556746488366583329656565759211145476799227155854775426317347474774134328484748742893748728958622478835122752521', ...\r\n     '86976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189'};\r\nassert(isequal(sum_large_n(c),19348963))\r\n\r\n%%\r\nc = {'64854985662353823234394299423463672233451381975635955356744918981347271658799472175596688623815297551711518872659685481224881454663419214254991734594937657622921687245928642452634633638974619883614322', ...\r\n     '41657761135648795316841323455859693737713378487164915457385127524627393723167546676927326556746488366583329656565759211145476799227155854775426317347474774134328484748742893748728958622478835122752521', ...\r\n     '86976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189', ...\r\n     '72712636767379814476842172453652813351412836947746192385743174561377221146751622122233239762219763269234174946242784735864354467442133699537777175218226957295718725354423196929864373177764483888569418', ...\r\n     '64936642142748762939341621746461987846653353891518919178589622211694499797463375467656517949485422378718971477337563287912152911673242596141549859249976492768478359536474579387914633766614537837282648', ...\r\n     '55845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396', ...\r\n     '56852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122', ...\r\n     '74731539941789156776746219369224943244241616835615628985373966213897736849135176588835711359733896318691638244872327622595118548457836916433792829847584169247197625598974953476799592136595457182534623', ...\r\n     '22385429486488589446974795531215196112521748441116388952357456927648426638992316148542492581793279692744286781957782569896681841722633444622137377883353886373545979351768994152231775485994546872814784', ...\r\n     '79323439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878125985417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),62027779))\r\n\r\n%%\r\nc = {'6475498566235382323439429942346367223345138697688918695583596876361667997696128582561641522222163575552588326642911226619771899885242193335618684512639295793457812415422975917762632291314192135193313157611795184371176577837641846712559871118981975635955356744918981347271658799472175596688623815297551711518872659685481224881454663419214254991734594937657622921687245928642452634633638974619883614322', ...\r\n     '2165776113564879531684132345585969373771337848716491545738512752462739372316754667692732655674648836658332965656575921114547679922715585477542793234391628259412443979491683978683336834869287354681884467774496836691551984826358235489237499684696975682494699611669765395175193323361338476829815363666515415558781259854175242749186567181329166686317347474774134328484748742893748728958622478835122752521', ...\r\n     '8697688918695583596876361667997696128582561641522222163575552588326642911226619771899885242193335618684512635685254967745626748745477479871465138181752627611214865819152617899531567165296496585574368424348444231433425738141212232269925453142194971776527349843699638491572423451533329987242137654357767625412292957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189', ...\r\n     '7271263676737981447684217245365281335141283694774619238574317456137722114675162212223323976221976326923417494624278473586435446744213369953777717521822695729571872535442319692986437317776445584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239683888569418', ...\r\n     '6293664214274876293934162174646198784665335389151891917858962221169449979746337546765651794948542237871897147733756328791215291167324259614154985568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573814121223226992545314219497177652734984369963849157242345153332998724213765435776762541229249976492768478359536474579387914633766614537837282648', ...\r\n     '5584591927674681196342333231512689695428194147857913127786198359784563737624373984578663575632548872163993896895761565857499845388949884689726131512689695479857499845388966295297837624373984578632571235635787174428334456445697482112331512689695388949884689761479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239687232762259511854845785534518148468892396', ...\r\n     '5685254967745626748745477479871465138181752627611214865819152617899531567165296496585574368424348444231433425738793234391628259412443979491683978683336834869287354681884467774496836691551984826358235489237499684696975682494699611669765395175193323361338476829815363666515415558781259854175242749186567181329166681412122322699254531421949717765273498436996384915724234515333299872421376543577676254122', ...\r\n     '7873153994178915677674621936922494324424161683561562898537396621389773684913517658883571135973389631869163824455845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457836916433792829847584169247197625598974953476799592136595457182534623', ...\r\n     '2238542948648858944697479553121519611252174844111638895235745692764842663899231614854249258179327969274428678195778256989668184172263355845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396444622137377883353886373545979351768994152231775485994546872814784', ...\r\n     '7392343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587815584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239625985417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),59677779))\r\n\r\n%%\r\nc = {'69754985662353823234394299423463672233451386976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189819756359553567449189813472716587994721755966886238152975517115188726596854812248814546634192142549917345949376576229223854294864885894469747955312151961125217484411163889523574569276484266389923161485424925817932796927442867819577825698966818417226335584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239644462213737788335388637354597935176899415223177548599454687281478421687245928642452634633638974619883614322', ...\r\n     '51057761135648795316841323455859693737713378487164915457385127524627393723167546676927326556746488366583329656565759211145476799227155854775427932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291686976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783764184671255987111896686317347474774134328484748742893748728958622478835122752521', ...\r\n     '76976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783767392343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587815584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239625985417524274918656718132916668418467125598711189', ...\r\n     '72712636767379814476842172453652813351412836947746192385743174561377221146751622122233239762219763269234174946242784735864354467442133699537777175218226957295718725354423196929864373177764455845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534586976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783764184671255987111891814846889239683888569418', ...\r\n     '62936642142748762939341621746461987846653353891518919178589622211694499797463375467656517949485422378718971477337563287912152911673242596141549855685254967745626748745477479871465138181752627611214865819152617899531567165296496585574368424348444231433425738141212232269925453142194971776527349843699638491572423451533568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573879323439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878125985417524274918656718132916668141212232269925453142194971776527349843699638491572423451533329987242137654357767625412232998724213765435776762541229249976492768478359536474579387914633766614537837282648', ...\r\n     '55845919276746811963423332315126896954281941478579131277861983597845637376243739845786635756325488721639938968957615658574998453889498846897261315126896954798574998453889662952978376243739845786325712356357871744283344564456974821123315126896953889498846897614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457855345181484688956852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435776762541222396', ...\r\n     '50852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435755845919276746811963423332315126896954281941478579131277861983597845637376243739845786635756325488721639938968957615658574998453889498846897261315126896954798574998453889662952978376243739845786325712356357871744283344564456974821123315126896953889498846897614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457855345181484688923967676254122', ...\r\n     '18731539941789156776746219369224943244241616835615628985373966213897736849135176588835711359733896318691638244558459192767468119634233324281941478579131277861983597845637563254887216399389689576156549884689726147985749984538896629529783762437398457866357871744283344564456974821123315126896955345181484688923968726293664214274876293934162174646198784665335389151891917858962221169449979746337546765651794948542237871897147733756328791215291167324259614154985568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573814121223226992545314219497177652734984369963849157242345153332998724213765435776762541229249976492768478359536474579387914633766614537837282648327622595118548457836916433792829847584169247197625598974953476799592136595457182534623', ...\r\n     '24185429486488589446974795531215196112521748441116388952357456927648426638992316148542492581793279692744286781957782569896681841722633558459192767468119634233324281941478579131277861983597845637563254887216399389689576156549884689726147985749984538896629529783762437398457866357871744283344564456974821123315126896955345181484688923964446221373778833538863735464754985662353823234394299423463672233451386976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189819756359553567449189813472716587994721755966886238152975517115188726596854812248814546634192142549917345949376576229216872459286424526346336389746198836143225979351768994152231775485994546872814784', ...\r\n     '73923439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878155845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435776762541223151268969553451814846889239625985417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),55697779))\r\n\r\n%%\r\nc = {'169754985662353823234394299423463672233451386976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189819756359553567449189813472716587994721755966886238152975517115188726596854812248814546634192142549917345949376576229223854294864885894469747955312151961125217484411163889523574569276484266389923161485424925817932796927442867819577825698966818417226335584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239644462213737788335388637354597935176899415223177548599454687281478421687245928642452634633638974619883614322', ...\r\n     '51057761135648795316841323455859693737713378487164915457385127524627393723167546676927326556746488366583329656565759211145476799227155854775427932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291686976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783764184671255987111896686317347474774134328484748742893748728958622478835122752521', ...\r\n     '476976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783767392343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587815584591927674681196342333242819414785791312778619835978456375632548872163993896895761565498846897261479857499845388966295297837624373984578663578717442833445644569748211233151268969553451814846889239625985417524274918656718132916668418467125598711189', ...\r\n     '72712636767379814476842172453652813351412836947746192385743174561377221146751622122233239762219763269234174946242784735864354467442133699537777175218226957295718725354423196929864373177764455845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112331512689695534586976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257381412122322699254531421949717765273498436996384915724234515333299872421376543577676254122929579345781241542297591776263229131419213519331315761179518437117657783764184671255987111891814846889239683888569418', ...\r\n     '562936642142748762939341621746461987846653353891518919178589622211694499797463375467656517949485422378718971477337563287912152911673242596141549855685254967745626748745477479871465138181752627611214865819152617899531567165296496585574368424348444231433425738141212232269925453142194971776527349843699638491572423451533568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573879323439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878125985417524274918656718132916668141212232269925453142194971776527349843699638491572423451533329987242137654357767625412232998724213765435776762541229249976492768478359536474579387914633766614537837282648', ...\r\n     '755845919276746811963423332315126896954281941478579131277861983597845637376243739845786635756325488721639938968957615658574998453889498846897261315126896954798574998453889662952978376243739845786325712356357871744283344564456974821123315126896953889498846897614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457855345181484688956852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435776762541222396', ...\r\n     '50852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435755845919276746811963423332315126896954281941478579131277861983597845637376243739845786635756325488721639938968957615658574998453889498846897261315126896954798574998453889662952978376243739845786325712356357871744283344564456974821123315126896953889498846897614798574998453889662952978376243739845786635787174428334456445697482112331512689695534518148468892396872327622595118548457855345181484688923967676254122', ...\r\n     '8731539941789156776746219369224943244241616835615628985373966213897736849135176588835711359733896318691638244558459192767468119634233324281941478579131277861983597845637563254887216399389689576156549884689726147985749984538896629529783762437398457866357871744283344564456974821123315126896955345181484688923968726293664214274876293934162174646198784665335389151891917858962221169449979746337546765651794948542237871897147733756328791215291167324259614154985568525496774562674874547747987146513818175262761121486581915261789953156716529649658557436842434844423143342573814121223226992545314219497177652734984369963849157242345153332998724213765435776762541229249976492768478359536474579387914633766614537837282648327622595118548457836916433792829847584169247197625598974953476799592136595457182534623', ...\r\n     '24185429486488589446974795531215196112521748441116388952357456927648426638992316148542492581793279692744286781957782569896681841722633558459192767468119634233324281941478579131277861983597845637563254887216399389689576156549884689726147985749984538896629529783762437398457866357871744283344564456974821123315126896955345181484688923964446221373778833538863735464754985662353823234394299423463672233451386976889186955835968763616679976961285825616415222221635755525883266429112266197718998852421933356186845126392957934578124154229759177626322913141921351933131576117951843711765778376418467125598711189819756359553567449189813472716587994721755966886238152975517115188726596854812248814546634192142549917345949376576229216872459286424526346336389746198836143225979351768994152231775485994546872814784', ...\r\n     '973923439162825941244397949168397868333683486928735468188446777449683669155198482635823548923749968469697568249469961166976539517519332336133847682981536366651541555878155845919276746811963423332428194147857913127786198359784563756325488721639938968957615654988468972614798574998453889662952978376243739845786635787174428334456445697482112356852549677456267487454774798714651381817526276112148658191526178995315671652964965855743684243484442314334257387932343916282594124439794916839786833368348692873546818844677744968366915519848263582354892374996846969756824946996116697653951751933233613384768298153636665154155587812598541752427491865671813291666814121223226992545314219497177652734984369963849157242345153332998724213765435776762541223151268969553451814846889239625985417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),31469777))\r\n\r\n%%\r\nc = {'16975498566235382323439429942346367223345138697688', ...\r\n     '91869558359687636166799769612858256164152222216357', ...\r\n     '55525883266429112266197718998852421933356186845126', ...\r\n     '39295793457812415422975917762632291314192135193313', ...\r\n     '15761179518437117657783764184671255987111898197563', ...\r\n     '59553567449189813472716587994721755966886238152975', ...\r\n     '51711518872659685481224881454663419214254991734594', ...\r\n     '93765762292238542948648858944697479553121519611252', ...\r\n     '17484411163889523574569276484266389923161485424925', ...\r\n     '81793279692744286781957782569896681841722633558459', ...\r\n     '19276746811963423332428194147857913127786198359784', ...\r\n     '56375632548872163993896895761565498846897261479857', ...\r\n     '49984538896629529783762437398457866357871744283344', ...\r\n     '56445697482112331512689695534518148468892396444622', ...\r\n     '13737788335388637354597935176899415223177548599454', ...\r\n     '68728147842168724592864245263463363897461988361432', ...\r\n     '51057761135648795316841323455859693737713378487164', ...\r\n     '91545738512752462739372316754667692732655674648836', ...\r\n     '65833296565657592111454767992271558547754279323439', ...\r\n     '16282594124439794916839786833368348692873546818844', ...\r\n     '67774496836691551984826358235489237499684696975682', ...\r\n     '49469961166976539517519332336133847682981536366651', ...\r\n     '54155587812598541752427491865671813291686976889186', ...\r\n     '95583596876361667997696128582561641522222163575552', ...\r\n     '58832664291122661977189988524219333561868451263568', ...\r\n     '52549677456267487454774798714651381817526276112148', ...\r\n     '65819152617899531567165296496585574368424348444231', ...\r\n     '43342573814121223226992545314219497177652734984369', ...\r\n     '96384915724234515333299872421376543577676254122929', ...\r\n     '57934578124154229759177626322913141921351933131576', ...\r\n     '11795184371176577837641846712559871118966863173474', ...\r\n     '74774134328484748742893748728958622478835122752521', ...\r\n     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'55345181484688923962585417524274918656718132916668'};\r\nassert(isequal(sum_large_n(c),87139239))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":114,"test_suite_updated_at":"2018-08-20T17:27:20.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-20T17:18:24.000Z","updated_at":"2026-01-05T00:23:53.000Z","published_at":"2018-08-20T17:18:24.000Z","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\",\"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\u003eYour function will be provided an arbitrary number of numbers of arbitrary sizes as a cell array of strings. Some numbers will be very large. The function must return the first eight digits of the sum of all the numbers as an 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":2323,"title":"Pandigital number n°3 (Inspired by Project Euler 32)","description":"After Problem 2319 and 2320.\r\n\r\nAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\r\n\r\nThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\r\n\r\nFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\r\n\r\nHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\r\n\r\nHINT2: All in good time...  \r\n\r\n","description_html":"\u003cp\u003eAfter Problem 2319 and 2320.\u003c/p\u003e\u003cp\u003eAn n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/p\u003e\u003cp\u003eThe product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\u003c/p\u003e\u003cp\u003eFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\u003c/p\u003e\u003cp\u003eHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\u003c/p\u003e\u003cp\u003eHINT2: All in good time...\u003c/p\u003e","function_template":"function y = pandigital_sum(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 3;\r\ny_correct = [];\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 4;\r\ny_correct = 12;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 52;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 6;\r\ny_correct = 162;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = []; % Strange no ?\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 13458;\r\nassert(isequal(pandigital_sum(x),y_correct))\r\n\r\n\r\n%% You obtain the Project Euler n°32 solution with n=9\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":5390,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":"2019-10-23T23:21:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-15T10:08:43.000Z","updated_at":"2025-12-19T11:41:31.000Z","published_at":"2014-05-15T10:20:54.000Z","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\u003eAfter Problem 2319 and 2320.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 n-digit number is pandigital if it makes use of all the digits 1 to n exactly ONCE. For example, the 5-digit number 15234, is 1 through 5 pandigital.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital ([391867254]).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through n pandigital (n is given in input).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT1: Some products can be obtained in more than one way so be sure to only include it once in your sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT2: All in good time...\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":2342,"title":"Numbers spiral diagonals (Part 2)","description":"Inspired by Project Euler n°28 and 58.\r\nA n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.\r\nFor example with n=5, the spiral matrix is :\r\n                       21 22 23 24 25\r\n                       20  7  8  9 10\r\n                       19  6  1  2 11\r\n                       18  5  4  3 12\r\n                       17 16 15 14 13\r\nThe sum of the numbers on the diagonals is 101 (See problem 2340) and you have 5 primes (3, 5, 7, 13, 17) out of the 9 numbers lying along both diagonals. So the prime ratio is 5/9 ≈ 55%.\r\nWith a 7x7 spiral matrix, the ratio is 62% (8 primes out of the 13 diagonal numbers).\r\nWhat is the side length (always odd and greater than 1) of the square spiral for which the ratio of primes along both diagonals FIRST falls below p% ? (0\u003cp\u003c1)","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: 326.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 163.083px; transform-origin: 407px 163.083px; 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: 120px 8px; transform-origin: 120px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Project Euler n°28 and 58.\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: 341px 8px; transform-origin: 341px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise direction.\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: 131.5px 8px; transform-origin: 131.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example with n=5, the spiral matrix is :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; 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 51.0833px; transform-origin: 404px 51.0833px; 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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       21 22 23 24 25\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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       20  7  8  9 10\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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       19  6  1  2 11\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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       18  5  4  3 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: 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: 148px 8.5px; tab-size: 4; transform-origin: 148px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e                       17 16 15 14 13\u003c/span\u003e\u003c/span\u003e\u003c/div\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: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; 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: 382.5px 8px; transform-origin: 382.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe sum of the numbers on the diagonals is 101 (See problem 2340) and you have 5 primes (3, 5, 7, 13, 17) out of the 9 numbers lying along both diagonals. So the prime ratio is 5/9 ≈ 55%.\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: 262px 8px; transform-origin: 262px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWith a 7x7 spiral matrix, the ratio is 62% (8 primes out of the 13 diagonal numbers).\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: 364.5px 8px; transform-origin: 364.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"perspective-origin: 74px 8px; transform-origin: 74px 8px; \"\u003eWhat is the side length \u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; perspective-origin: 2.5px 8.5px; transform-origin: 2.5px 8.5px; \"\u003e(\u003c/span\u003e\u003cspan style=\"perspective-origin: 96px 8px; transform-origin: 96px 8px; \"\u003ealways odd and greater than 1\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; perspective-origin: 2.5px 8.5px; transform-origin: 2.5px 8.5px; \"\u003e)\u003c/span\u003e\u003cspan style=\"perspective-origin: 189.5px 8px; transform-origin: 189.5px 8px; \"\u003e of the square spiral for which the ratio of primes along both diagonals FIRST falls below p% ? (0\u0026lt;p\u0026lt;1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function res=spiral_ratio(pourcentage)\r\nres=pourcentage*2;\r\nend","test_suite":"%%\r\nx = 0.8;\r\ny_correct = 3;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.5;\r\ny_correct = 11;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.4;\r\ny_correct = 31;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.3;\r\ny_correct = 49;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.25;\r\ny_correct = 99;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.2;\r\ny_correct = 309;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.15;\r\ny_correct = 981;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.14;\r\ny_correct = 1883;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.13;\r\ny_correct = 3593;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.12;\r\ny_correct = 6523;\r\nassert(isequal(spiral_ratio(x),y_correct))\r\n%%\r\nx = 0.11;\r\ny_correct = 12201;\r\nassert(isequal(spiral_ratio(x),y_correct))","published":true,"deleted":false,"likes_count":7,"comments_count":5,"created_by":5390,"edited_by":223089,"edited_at":"2022-09-26T17:42:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":197,"test_suite_updated_at":"2022-07-09T19:28:50.000Z","rescore_all_solutions":false,"group_id":31,"created_at":"2014-05-31T18:36:25.000Z","updated_at":"2026-04-17T12:45:31.000Z","published_at":"2014-05-31T18:53:35.000Z","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\u003eInspired by Project Euler n°28 and 58.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 n x n spiral matrix is obtained by starting with the number 1 and moving to the right in a clockwise 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example with n=5, the spiral matrix 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[                       21 22 23 24 25\\n                       20  7  8  9 10\\n                       19  6  1  2 11\\n                       18  5  4  3 12\\n                       17 16 15 14 13]]\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 sum of the numbers on the diagonals is 101 (See problem 2340) and you have 5 primes (3, 5, 7, 13, 17) out of the 9 numbers lying along both diagonals. So the prime ratio is 5/9 ≈ 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\u003eWith a 7x7 spiral matrix, the ratio is 62% (8 primes out of the 13 diagonal numbers).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 is the side length (always odd and greater than 1) of the square spiral for which the ratio of primes along both diagonals FIRST falls below p% ? 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