{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","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":"2025-12-14T00:00:00.000Z","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":42976,"title":"iteration of N blank spot","description":"we have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8","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: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.5px 8px; transform-origin: 372.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewe have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 32;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 256;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 2048;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 16;\r\ny_correct = 65536;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":86389,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":59,"test_suite_updated_at":"2021-06-17T14:24:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-02T16:46:32.000Z","updated_at":"2026-02-26T11:42:20.000Z","published_at":"2016-09-02T16:46:32.000Z","restored_at":"2022-02-16T22:15:33.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewe have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8\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":42583,"title":"Find smallest number to leave a remainder of 1","description":"given a vector of numbers, find the smallest number to be divisible by all of them with a remainder of 1. Note: input numbers will always be greater than 1 ","description_html":"\u003cp\u003egiven a vector of numbers, find the smallest number to be divisible by all of them with a remainder of 1. Note: input numbers will always be greater than 1\u003c/p\u003e","function_template":"function num = OneDirection(vec)\r\n  num = vec;\r\nend","test_suite":"%%\r\nvec = [2,4];\r\ny_correct = 5;\r\nassert(isequal(OneDirection(vec),y_correct))\r\n%%\r\nvec = [16:18];\r\ny_correct = 2449;\r\nassert(isequal(OneDirection(vec),y_correct))\r\n%%\r\nvec = [2:6];\r\ny_correct = 61;\r\nassert(isequal(OneDirection(vec),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":15602,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2015-09-02T15:00:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-09-01T17:44:12.000Z","updated_at":"2026-03-31T12:48:56.000Z","published_at":"2015-09-01T17:53:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven a vector of numbers, find the smallest number to be divisible by all of them with a remainder of 1. Note: input numbers will always be greater than 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43216,"title":"Encode Me From The Past","description":"Given this input\r\n\r\n x = 2, 5, 1, 2, 4, 1, 1, 3\r\n\r\noutput should be (Five 2's, Two 1's, One 4, Three 1's)\r\n\r\n [2 2 2 2 2 1 1 4 1 1 1]","description_html":"\u003cp\u003eGiven this input\u003c/p\u003e\u003cpre\u003e x = 2, 5, 1, 2, 4, 1, 1, 3\u003c/pre\u003e\u003cp\u003eoutput should be (Five 2's, Two 1's, One 4, Three 1's)\u003c/p\u003e\u003cpre\u003e [2 2 2 2 2 1 1 4 1 1 1]\u003c/pre\u003e","function_template":"function y = encodeThePast(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [2, 5, 1, 2, 4, 1, 1, 3];\r\ny_correct = [2 2 2 2 2 1 1 4 1 1 1];\r\nassert(isequal(encodeThePast(x),y_correct))\r\n%%\r\nx = [2 3 4 3];\r\ny_correct = [2 2 2 4 4 4];\r\nassert(isequal(encodeThePast(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":0,"created_by":13865,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":"2016-10-29T16:40:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-08T10:22:58.000Z","updated_at":"2026-01-04T08:18:44.000Z","published_at":"2016-10-08T10:25:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven this input\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = 2, 5, 1, 2, 4, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput should be (Five 2's, Two 1's, One 4, Three 1's)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ [2 2 2 2 2 1 1 4 1 1 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44530,"title":"Are you more familiar with iteration methods or Linear Algebra? Let's see together.","description":"Given a sum result *_x_* value of a *_N_* number of addends, build an array of _*N*_ elements _*y*_ such that the following equality is satisfied: _sum(y) = x_ .\r\n\r\nFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\r\n\r\nMore formally if x = a and N = n it results: \r\n\r\ny = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\r\n\r\nImportant notice: All the elements in y must be *different from zero* and *different from each other* . On the other hand I will not take into account if they are _integers or decimal numbers_ .\r\n\r\nHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\r\n\r\nGood luck and enjoy with the solution ;)\r\n","description_html":"\u003cp\u003eGiven a sum result \u003cb\u003e\u003ci\u003ex\u003c/i\u003e\u003c/b\u003e value of a \u003cb\u003e\u003ci\u003eN\u003c/i\u003e\u003c/b\u003e number of addends, build an array of \u003ci\u003e\u003cb\u003eN\u003c/b\u003e\u003c/i\u003e elements \u003ci\u003e\u003cb\u003ey\u003c/b\u003e\u003c/i\u003e such that the following equality is satisfied: \u003ci\u003esum(y) = x\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\u003c/p\u003e\u003cp\u003eMore formally if x = a and N = n it results:\u003c/p\u003e\u003cp\u003ey = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\u003c/p\u003e\u003cp\u003eImportant notice: All the elements in y must be \u003cb\u003edifferent from zero\u003c/b\u003e and \u003cb\u003edifferent from each other\u003c/b\u003e . On the other hand I will not take into account if they are \u003ci\u003eintegers or decimal numbers\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/p\u003e\u003cp\u003eGood luck and enjoy with the solution ;)\u003c/p\u003e","function_template":"function y = buildSumArray(x,N)\r\n  y = sum(1:N);\r\nend","test_suite":"%% Test Case 1\r\nx = 6;\r\nN = 3;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n%% Test Case 2\r\nx = 13;\r\nN = 5;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n\r\n%% Test Case 3\r\nx = 78;\r\nN = 11;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n\r\n%% Test Case 4\r\nx = 2689;\r\nN = 245;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":181340,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2018-02-24T12:07:13.000Z","rescore_all_solutions":false,"group_id":677,"created_at":"2018-02-24T11:21:15.000Z","updated_at":"2026-04-02T13:09:38.000Z","published_at":"2018-02-24T11:49:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sum result\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e value of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number of addends, build an array of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the following equality is satisfied:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum(y) = x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or [8 2].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore formally if x = a and N = n it results:\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\u003ey = [y_1 y_2 y_3 ... y_n] where: y_1 + y_2 + y_3 +...+ y_n = a\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\u003eImportant notice: All the elements in y must be\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\u003edifferent from zero\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from each other\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . On the other hand I will not take into account if they are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegers or decimal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck and enjoy with the solution ;)\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":61091,"title":"Slicing a 4-pointed star polygon","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the area, A_r, of the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \r\nGiven (A,h), find the 9×2 matrix, M = [A1 a1; A2 a2; ...; A8 a8; A_r/π n], where\r\nin the first row (i=1), A1 stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and a1 stands for the logical 1 if A1 does not exceed the circle's area, A_r, or a1 stands for the logical 0 otherwise;\r\nin the second row (i=2), A2 stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and a2 has the same previous false-true meaning relative to the areas A2 and A_r;\r\nand so on, until last slice of the 4-pointed star polygon;\r\nin the last row (i=9), A_r is the area of the circle, and n stands for the maximum number of slices that their cumulative area does not exceed the circle area.\r\nHint: The slices of the 4-pointed star polygon are not congruent among each other.\r\ninput: (A, h)\r\noutput: M = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 840.862px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 420.425px; transform-origin: 408px 420.431px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2L\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the vertices, consider the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,h)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 143.062px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 71.525px; transform-origin: 391px 71.5312px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e does not exceed the circle's area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e otherwise;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand so on, until last slice of the 4-pointed star polygon;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=9)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the circle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, h)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlkAAAHfCAIAAADsm1pIAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6QwDECUuAtncXQAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAwMy1EZWMtMjAyNSAxNjozNzo0NjdgV3gAACAASURBVHic7d1/dFTlnfjxJ2QSJjIJBBwFcrWa4ApsbRCFmW9BFE9b5Sgty1AF3NPiSu2uFkfOGvW4ba2uPQoB90xZf6FrT1cX/EGoreuy/uh20bA7I7aCKK78tHiHRAMkZAYzhiH5/vHI3dlJMjNJ5v6Yed6vs8cjk5B5tuPMO/dznztT0tvbKwAAUNgIuxcAAIDNcmrhnj17li9fPnny5Nra2q9//etPPvlkV1dX5r/S1NQUDofzsUIAAMyVvYXNzc2BQGDr1q3Tp0+/7rrrysrKHnzwwR/+8IexWCzD39q0aVM0Gs3fOgEAMIsr85fj8fijjz568uTJX/ziF/PmzRNCdHV1/eQnP/n1r3/9n//5n/Pnz7dkkQAAmCjLceHnn38ejUanTZt22WWXyVsqKiquvvrq3t7e//qv/zJ/eQAAmC5LC0tKSlwuV0dHR+oJwng8LoQYN26cuUsDAMASWVp45plnXn/99Xv37n3wwQfb29t7e3vffffdhx9+eNy4cVdffbU1SwQAwFRZzheWlJTcdNNNo0ePvvfee1966SV5Y319/UMPPXThhReavzwAAExXkvla+97e3t/97nd33313PB6fM2fO2LFjt2/ffvDgwdmzZ69du9br9Q70F5csWdJ3H+mbb76Zn1UDAJA/WY4L33///b/9278966yzXnzxxfPPP18IcerUqfXr169Zs+b+++9/+OGHy8rKBvq7gUDA5/Pleb0AAORblha++uqrsVjsvvvukyEUQpSWli5btiwSiUQikY8//viCCy4Y6O9qmub3+/O5WAAATJBl70xra6sQwuPxpN5YUVFx5plnfvHFF4lEwsSlAQBgiSwtHD9+vBDi8OHDqTd2dXUdOXLE5XKVlpaauDQAACyRpYVz5871eDzPPPPMwYMH5S29vb2vvPJKOBy+5JJLjMEpAACFK8v5wunTp69YsWL16tXz5s2bMWNGTU3NH//4x/3799fU1Nx2220VFRXWrBIAAPNkv75w+fLl9fX1a9eu3b59+7Zt28aNG3fTTTf99V//9dixY61ZIgAApsrSQiFESUnJzJkzn3/+eQtWAwCA9fgsXwCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoLqcWtjZ2blq1aoZM2bU1tZedNFFd999dzQaNXtlAABYI3sLDx8+/P3vf/+JJ56oqqq67rrramtrX3zxxWXLlpFDAEBxyNLC3t7ep5566r333mtoaHjttdceeuihl1566a677jpw4MBTTz1lzRIBADBVlhbu27fvX//1Xy+77LJly5aVlpYKIUpKSubPn3/uuefu3bu3s7PTkkUCAGAiV+Yv79u378iRIwsWLKioqDBunDBhwu9//3uTFwYAgEWyHBfu37/f4/F85Stf2bJly7e+9a26ujr2zgAAikyWFn788cdCiMcff/z2228fNWrUd7/73bPOOuuFF15g7wwAoGiU9Pb2ZvjyHXfcsXnz5vLy8n/4h3+YN2+eEOLUqVPr169fs2bNtddeu3btWper/ynrkiVLIpFI2o0HDhzI17oBAMiXLOcLpcWLF1999dXy30tLS5cuXfraa6+98847hw8fPvfccwf6W8FgMBAI5GeZAACYJksLy8rKhBAXXHBBSUmJcePo0aPr6uoOHDhw/PjxDH9X0zRN0/KySgAAzJPlfOGkSZOEEIlEIvXG3t7enp4eExcFAICFsrTwa1/7mtvtfuutt7q6uowbjxw5snv37rFjx5555pkmLw8AANNlaeGUKVOmTZsWDodfeeUVucvm1KlTmzZt2rt379y5c8ePH2/JIgEAMFGW84Uej+eee+655ZZb7rrrrmeeeWbKlCnbt28/ePDg1KlTly9fnnoSEQCAApX9vbm/+tWvbty48bvf/e6hQ4deeOGFzs7OH/7whxs2bJg4caIF6wMAwGxZri8csiVLlixatIhrKgAAzsdn+QIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqG1wLT5482dDQUF9fv2vXLpMWBACAxQbXwpdffnnz5s0mLQUAAFsMooV79uxZtWpVb2+veasBAMB6ubawq6trzZo11dXVM2fONHVBAABYLNcWPvvss83NzXfccYemaaYuCAAAi+XUwh07dqxfv37hwoVXXHGFyesBAMBqrqzfEYvFHn74Ya/XGwwGXa7s3w8ASKPreiQSCYfDfr8/EAjYvRyky9K23t7ejRs3vvPOO0888YTX6x3Uj9Z1Xdf11FuYr5pK/q+t63o0Gk39Y9q3pT4KmqbV1NRomsZDA5hB1/WmpqZwOByJROQtTU1NNTU1fr/f3oUhTZYW7tix45FHHlm8ePHs2bMH+6NDoVAoFEq95cCBA4P9IRiI/FUjGo2Gw2H5L32zJ2maNtCX0r5NCOHz+fx+P89VYDj6JjBVKBTi+eU0mVrY3t5+//3319bWrlixoqSkZLA/urGxkVFAHsmeyTFLJBIx8paaOk3zCCFqakZVVfXIo8NRo04mkx+MG9dj/By32y2EiMVKa2pqOjtHRKMndD0uUo4jm5qajJ8soygDadn/p0CBypxAw1axtba2VtO0QCAQDAYtWx4yKMlwveCuXbv+8i//MhaL9fvVysrKZ5999qKLLur3q0uWLFm0aBEtHD7jNIORKIOmeXy+s4UQfv/4mhqP3392Z2enrusffvjhoUOHkslkMpns7u7u+zNHjBhRXl7udrurqqqmTJk6deqUzs4RQohI5FNdj8v/i0Q+TftbsoiBQICBKpAqxwQa2oPtHcEOd9jtjrirQ9VE0QkytVDX9aeffjqRSKTeGA6Ho9Ho3LlzJ06c+Fd/9VcDvSzSwmHq99kl42eUz7g9xwT21TeKVVVVKWuINzXtl/9M/VvyqcvBIhSXYwLPKEmOG5H4vNd1tMctb5EtNL6BKDpBphb264477nj99dczHBFKtHBo+j67NM1TUzPK7x/v841P7Z8YRgL7yhxFcbqL4XBr6vGifOpypAilDCqB57pi40YkhBDvdns/OeWRX0proYEo2ohrJBxBDkI3bdqUmkB5CBgI1KV9cx4TaOjp6UkkEolEorOz87PPPotEwmlR1DRPMFgfDNbrelzXT0QiraHQTl3X5Q4pnrooekNL4KAk/ImEP9ER7GgJt+yK7ArV8syyDi20mXyCNTU1pe5/CQbrrUlgX7lEUdM8fv/ZwWB9KLTz9BxVD4VCTU1NPG9RZCxIYF9E0XqDnpHmiBlpVvI5Zlx2ommeQKAuEKiTe0EN1iQwgxzHp6HQTuOWYDDI4BQFLe8JzGVGmgHjU7PRQhv0W8FgsD71e2xPYF9ZoyiLKK/QEBQRBci8o8BhttBAFE1CCy3Vt4KrV8/Ky45QK2XdfRoK7TS2ngaDQZ6ucDgLBqH5aqGBKOYXLbRI2nnBtAoWRAL7yhBFigjns/JcYN5baCCKeUELraDr+tKlS40KGltjCjSBfQ0URV2PNzRsk5dhaJq2evVqLkmE7WzZDmNeCw1EcThooblSh6LGecGiSWBf/UYxHP70zju3yfOIgUCgsbHR7mVCRbYk0GBBCw1EcQhooYlkBXVdlxW88cbzizWBffWN4i9/edDYa8rIFJaxN4EGK1toIIq5o4WmSD0crKrqCQa/UlV1TIUE9pUaxaqqc3/5y/bduz8XQvh8vo0bN9q9OhQthyTQYEsLDUQxK661zz/j7GBVVc+UKV/MnPn5kSNtra1qJdCQevF+efln3/ymu7LSHYlURCKROXPmcAYR+eW0BDoEF+9nRQvzzPjURo8nOX9++xlndHd2qpjAvowoTp06orbW/dZb4+QvDcxLMXwkMEdEcSDMSPMj7Q1F6+vbp02zdAZSiHbsGLNzZ7XgPb4xVAWUQHtnpBkwPpVo4bD0fU9tjydZVxcjhDlqbXW/+uoE449EEbkooAQaHNtCg+JRpIVDYSRw27Zt8vMdPR6PEMLjSV51VYvHk7R7gYUkHndt2+ZtbXULIdra2lwuV3V1NVFEX4WYQIPzW2hQM4q0cBDSEtjV1RWPx8eMGVNdXS0I4fC8+uoEmcP29vaOjg6Xy+XxeIgiRIEn0FBALTQoFUVamF2/CZRfMkLICcLhM04fxuPxtrY2eSNRVFZxJNBQiC00qBBF9pEOKEMCJUKYX9OmdXg8yW3bvB6Px+VytbS0CCGSyWRHR0dHR8cnn3yya9cu43ODiWKxKrIEFgcVdp9yXJguawIlQmgSYzdNIpGQOUzDkWJRKvoEFvRxYV/Fd6RIC7+UYwIlGUK2jJokaw4lolgEij6BhiJroaFooqh6CweVQIkQWiDHHEpEseCok0BDsbbQUOhRVLSFQ0igRAgtM6gcSkTR4RRMoKHoW2go0Ciq1cIhJ1DiHKHFjBym7izNBVF0FJUTaFCnhYbCiqISLRxmAiWPx+P1egUhtJaRw7a2tiE8akTRRiQwlYItNBREFIv5moq8JFByuVyE0Bbjxyfq69t37qz2er3JZFK+y0/uuCTDeiQQaQrikowibGEeEyi5XK4JEyYIISZNihNC602b1nHiRNm+fR6v19vW1jbYHEpE0WwkEFk5OYrF08K8J1CSR4Qul8vjSc6aNYhTVsijWbPa4nFXa6vb6/V+8sknw/lRRDG/SCCGwIFRLOzzhbquCyHMSKDB2DjKe43arqnpnHjclfu20hz1Paeo6zqfMJyLpqamhoaGDN9AAg0qny/MRd9ziuFw2MqnYQG3MBwOL1261PhjfhNo8Hg8VVU9c+cenziRj+S12eHD5b/5TbUQIpFIJJP5/73E5XK53W7578FgkCPFzHRdnzNnTr9f8pT2nD0yWTuya1yp6gk0ROKjDya+/K+LFmZgRFEI0djYaNkGzEKdkeq6HgqFfInEoljMrLtwuZoqK3Uhbjz/+DfP+lxwTGi7s5LnXS5CW6vdbncgHvd3deX/LmIxIcSmyko5O+UAcSC6rmc4IrymInZtaVz0CNFj5aIcreVUz0G711AQklpSREQyqSWTNZs2baKFWUQikUgk4hMiYM7hoO5ybfJ6dZdL8ySD0zoEx4TOMPW87vBHFZFWd8TtbhzMFYeDEq6oiAgRDocbGxtNuotCJ5+AA331+fjot0pG3VzWPr/UlKdnIarq4feCLFy6y9PkqVx7USwWaIkHkklt69YloVDImpOIIyy4j7zTdX3lypXt7e3m3UXE7Y643ZonueGqfJ6awvBtvKpF8ySFEA1er3n30tbWJreEmHcXhSvtoLBmZE/NyPQX+sO9rp91e+cnznn59EkyYCAu3TUmNGbC1/+f+NnPWlo2dHQEk0lNCNHW1hgKhax5GhZeC+XzMBaLDW1vfU534XLJ19lgfbvGfhnnWT2rTXe5mjye8OnTe2ZoaWm58847zfv5BSothJUV4oYpJ1+7+PgtWhdFxGANVEEpmdTa24OhUMiClRReCyORyLZt2zo6zDrzbITQNz4RmMSEx4n8px+aO808NEwkEvv27cu8T1JBadPRs8f0TBwrhBC3agmKiNxlrqChoyO4dauwIIcF1kI5HR3UW1MOljEdbeRqQgdrnNWmeZK6yxUaM8a8e2lpaWFSmirtoHDUyB7/Bf9nBxNFRFY5VtBgzaS0kFrIdBSpVs9qE0KEqquZlFqjbwhn1p3o9zspIvo12ApK1kxKC6mFZk9HhRCh6mohhOZJMh11Pv/4hG98Qpx+1EzCpNSQNh31ViW9VZl+X6SIMAytggYLJqUF00ILpqNyO4Y4fcAB55Nz7IjbbfahIZPS3A8K01BExQ2zggazJ6WF0UILpqPi9B79wKS4fzxvllEYNE8yWN8uTN5EI5SflA45hAaKqKB8VVAye1JaGC20YDoaPr1lRr62olAEp3XITTTymN4kik9KBzsdHQhFVER+K2gwdVJaAC20YDoqTp9z8o1PsGWm4MhfX0w9aygUnpQO/6AwDUUsYiZV0GDepNTpLbRmOspBYUELTIpbcGgolJyU5j2EBopYZMyuoGTepNTpLbRgOio4KCx88pcYU9+VTSg5Kc3XdHQgFLEIWFNBg0mTUke30JrpKAeFRUAeGgohLDg0VGdSat5BYRqKWKAsrqDBjEmpc1tozXRUcFBYLOSvMpsqK82+I0UmpZaF0EARC4hdFZTMmJQ6t4XWTEd1l0seFAbqzPocRFhDvj2C2dcaCmUmpWZPRwdCER3O3goa8j4pdWgLrZmOitMHhTWeJNcUFgEjh2bfUdFPSq0/KExDER3IIRU05HdS6sQWWjYdNXYecqawOMjHsamyUneZ/iHVRTwptT2EBoroEE6roJTfSakTW2jNdFScPoDQOCgsFpon6RufsODiClHUk1K7pqMDoYg2cmYFDXmclDquhZZNR8XpfRacKSwmi+piwvzr7qWinJQ656AwDUW0mMMraMjXpNRZLbRsOipSds34OCgsIsYHjJi9g0YqskmpY0NooIgWKJQKSvmalDqrhZZNR8XpC9HYNVN8ZA6bzL+4QhTdpNRp09GBUESTFFYFDXmZlDqohVZOR4UQ4YoKcXqkhmLiP7tLmH/RvaFoJqXOPyhMQxHzqEAraBj+pNQpLbRyOipSLyvkM3uLjvEeNNaMSUVRTEoLLoQGijhMhV5BafiT0pxauGfPnuXLl0+ePLm2tvbiiy++++67o9HokO+yX1ZOR8XpHaQ1vNFMkZLngK0Zk4qimJQWynR0IBRxCIqjgoZhTkqzt3DLli3f/va3t27dOn369Ouuu27s2LEvvPDCsmXL8phDi6ej4vQOUjlMQ/GRj6wFF90bCnpSWrgHhWkoYo6KrIKG4UxKs7Swra1t3bp1lZWVzz333IYNGx566KHXXnutoaHhwIEDq1evTibz8JujxdNRIYTuckVdLnH66AHFR46+dZfLgovuDQU6KS2aEBooYgbFWkFpOJPSLC18//33P/roo2uuuWb69OnyltLS0uuvv/7CCy/csWPHsWPHhnCXaSyejorTL5FcYl/c5C86Vh4aFuiktNCnowOhiGmKu4KGIU9Ks7Tw8OHDVVVV06ZNKykpMW4sLy+vqqoa9Br7Y/10VJx+feSgsLjJMancLWyZgpuUFt9BYRqKKJSpoGFok9IsLbzhhhvefffdBQsWpN740Ucf7d69u6am5owzzhj0MlNYPx2V5OsjbzdT3Kz5OMO+CmhSWvQhNChbRNUqKA1tUjroaypisVgoFDpx4sSiRYs8w3uhsX46Kk5fTWHlPcIWxtUyVp4yFAU1KS3W6ehAlCqimhU0DGFSOriXiXg8fu+99zY3Ny9evHj+/PmZv1nX9bSjVL/fn/pV66ej4vQrIycLVaB5kqJDRNxuLW7pVaRyUhoIBFL/g3cadQ4K09yqJW7VEo/o7t+0jYx+8X8OBmQR15dU31zWPr+0UK88dukuT5Oncu1FsVigJR5QKoGp2toaQ6E5Pp8vx6fhIFrY3t5+++23v/XWWwsWLLjnnnvKysoyf3/fEyfGmuyajgquLFSJb3yiKe4JV1QErG2hOD0pffPNNy2+3xwpG0JDURaRCqYyJqV5buHevXtXrFixd+/e5cuXNzQ0ZA2hECIYDAYCgX6/ZMt0VJInC7myUAX+s7ua9tkz8jImpY2NjbYsIDPVpqMDKZoiUsF+dXQEt24Nh0KhYDCY9ZtzOl/Y3Ny8dOnSjz/++Mc//vFdd92VSwgzsGs6mopNpCqosWn7jOTYPaUcFKYp6POIip8XzCr3PaXZW7hjx46VK1d2d3c/+uijN954Y2lp6XBWZuN0VDI+v9eWe4eVjFPCFm+fMThwTykhHEjBFZEK5iL3PaVZWhiNRuUz5+mnn77yyiuHvzIbp6MiZeMMLVSEfKDtaqED95QyHc2sIIpIBQclxz2lWV4jXnzxxf3795eXl99+++2pl9sLISZOnLhu3Tqv15v7mmyfjtr1mgi7+MYn9H2eqH2Pu6P2lHJQmCPHnkfkvODQ5LKnNNNrRDwef/vtt4UQ3d3dfd+Ju6SkpLe3N/fV2D4dFULI10Q2karG3t+BHLKnlBAOlqOKSAWHI5c9pZleIzwez4YNG/K1Gnuno5J8TWQTqTrkVlJ9eLu9hskhe0qZjg6N7UWkgnmRdU+pRZ/la/t09Mtl2PqaCLvYPhu3fU8pB4XDZMt5RM4L5lfmPaVWtNAJ09FUbJxRh5yH23i+0GDjnlJCmC+WFZEKmiHznlIrWuiE6aikc75QMfbuI01l455SpqP5ZWoRqaCpMuwpNb2FDpmOSk44PoCVHDUDsGVSykGhSfJeRCpojYEmpea20GnTUeP6QrsXAkVZPCklhGbLSxGpoJUGmpSa20LnTEehOCeMSYXlk1Kmo9bIpYh/6Onno+KooC36nZSa+AKh6/ratWsdMh1NxXEhbGTZ1fdpB4VCiD/Xuk58kedff784JaLlI6L5/rGFaIG3e4G3+1G9Ynunq+/VF2nfzJUS9up79b2JLQyFQs6ZjkJZmiepxx1xUGiw5ur7vkefr7w72qT7ahRm/eSiVNlUSQXt1ffqexNfI5LJpKOmow6ZkgEWXH0fDodTp6Nwlo/PSyR8QgiPp8nupSgtEokYV9+b20LzfvgQaA5bD1Rm9rOj75smwjlmJff5T+6yexVO11RZ+T+JxMmTJ036+WVlZcmkW9d1+UcTW+h2u8eMGeOoQ0PACTwez+TJk019S7ZAILBp0yYODR1ISyY3trTYvYoCEK6o2G7mWba0p6GJLQwGg6FQKJFIcMoQNnLayUKXy1VdXb169Wqz76ixsXHOnDmpt5x79PK834vL5bqgvPxbn3+e959ciI6M6Pqw/FizO3qktJ83PdaSyWB7eyBu9adboC+Xy3XxxRenPg1NfJnQNC0YDK5atarFYb8E6XEXW0lhl+rq6uuvv96Cj3CST8DUjeMxd7T6xKT83kt5abn3lOvMU4P4yJqidKS063/Kjv161D4q6Hwul8vr9abt5TZ3J3QwGLz88svHjBlj6r0AWTnkbLEF09FUwWDQ5/MZf2wfta+r7Jg1d62OI6Vdze7og2PefrJqV98QaslkY1vbm598Qgidw+12T5o0Ke0DK0y/KqixsbG6utrt7uc6U+s55AURlnHUgNSy6WiqtO62VbFlI2+oYCHqOx2VTG+hHNRUV1ebfUe5c9TrIyzgkN+BLJuOppJPQOOPydKu9lH7rFxAUaKCBarf6ahkxbtFOGdSWpNMCiGitFAZzvm9x+LpaCompXlEBQtav9NRyaJ3TnLIpFQeHzjn9RHWqLH7uNCW6WgqJqXDRwUL3UDTUcmiFjpkUqqdPCmE0E/w6faqiLQ64kS1LdPRVExKh4MKFoEM01HJunfUdcKk1CHnjWAxf1c/29wtY+N0NBWT0iGggkUjw3RUsvTd5R0yKXXIsQIsEP60Qtj6O5Dt09FUTEpzRwWLSebpqGRpC22flPoSCcH5QsVoyaSN5wttn46mYlKaCypYZLJORyWrP3XM3kmpcXxADlWgx12RVrfuctl1XOiQ6WgqJqUZUMGilHU6KtnwCZz2TkrlyyJjUnVoyaQtLXTUdDQVk9K+qGCxymU6KtnQQnsnpYxJ1SEfZbsGpI6ajqZiUpqKChaxHKejkg0tFLZOSuWWQi6rUIE8+rdlE6kDp6OpmJQKKqiAHKejkj0tFHZPSpv2eWy5X1hJbiL1Wf6RYY6djqZSeVJKBVWQ+3RUsq2Fdk1Kjf++GZMWN7lxxpa7dux0NJWak1IqqIhBTUcl21oo7JuUsn1GBfJ3HV8i4bf2uNDh09FUSk1KqaBSBjUdlexsobBpUiqHZnKAhmJly+86BTEdTaXCpJQKqmaw01HJ5hbaMimVmyk4ZVjc5O86i2IxK++0IKajqYp7UkoFFTSE6ahkcwuFHZNSThkWPeNkoZUXVBTQdDRVUU5KqaCyhjAdlexvobBjUirHpJwyLFbytxwtmbTsZGHBTUdTFdOklAqqbGjTUckRLbR+UipHZ5wyLFahndVCiICFA9KCm46mKo5JKRVU3JCno5IjWigsn5TK50PTPg9j0uJjDEgtu7KwQKejqQp6UkoFIYYxHZWc0kJh+aSUMWmxsnhAWtDT0VSFOCmlgpCGMx2VHNRCiyeljEmLVdP+SmHhQWFBT0dTFdaklArCMMzpqOSgFgprJ6WBeFxLJhmTFhk97pJXy1hzsrAIpqOpCmJSSgWRZpjTUclZLRTWTkpreAOaomPlgLRopqOpnDwppYLoa/jTUclxLbRyUirHpA3bvBbcF6xh5Q7SopmOpnLmpJQKol95mY5KjmuhsHBSajxzwhwaFgW5g1RLJi04WVhk09FUjpqUUkFkkJfpqOTEFgoLJ6VfXlyxv9LsO4IF5EFhjfkDA+ndigAAGEBJREFU0qKcjqZywqSUCiKzfE1HJYe20LJJabC9XXChYVEwds3Ix9RURTkdTWXvpJQKIqs8Tkclh7ZQWDUpNeZp8pAChUvugbJg10wRT0dT2TIppYLIUR6no5JzWyismpRyaFgE9LhL/jZj9kFh0U9HU1k5KaWCyF1+p6OSo1tozaTUn0jIQ0M+xalwRVrdetylJZNmv1YW/XQ0lTWTUiqIQcn7dFRydAuFVZNSeXEFY9ICZdlBoSLT0VSmTkqpIIYg79NRyektFJZMSgPxuDw05FrDQmTNQaFS09FUZkxKqSCGxozpqFQALbRmUspZwwJl2UGhUtPRVPmdlFJBDJlJ01GpAFooLJmUGmcNmZQWFvnri9kHhQpOR1PlZVJKBTFMJk1HpcJoobBkUmocGvI2NIXCOChc3dZm3r0oOx1NNZxJKRXE8Jk3HZVyamE0Gl2xYsXkyZNra2tnz579z//8zydPnjRpQQOxYFLqTyTks5FDw0Ihz+/6EglTrylUdjqaamiTUiqIvDB1Oiplb+Hu3bsXLlz47//+79OnT1+4cGEymfzZz3527733Wp9DCyaljW1tQohIq5vrK5wv3OqW7z5q6plCxaejqQY1KaWCyCNTp6NSlhaePHnyscceO378+C9+8YsNGzasWbPm9ddfnz179ubNm8PhsHnLGogFk1KZw4ZtXjbROJked91p/kEh09E0uUxKqSDyy+zpqJSlhQcOHAiHw36//4orrpC3VFZWBoPB8vLy3/72t729vaYuri8LJqVcX1EQjC0zjWaeKWQ6mibzpJQKIu8smI5KWVr44YcfHj169NJLL62oqDBuPP/88zVN++CDD9rNfxPkvqyclLKJxpnCrW4LtswwHe1X2qT007LdsRGfUUGYxILpqJSlha2trUKIyZMnp95YXl4+ZsyY48ePx236L9vsSalxCmrpqxOYlDqNMR0NxONMR22R9vvBtpF/oIIwgzXTUSlLC//0pz/1vXHUqFHjx4+Px+PHjx83Z1VZyEFNZaWJHzoY7OhgUupMoZ3VFkxHKysrmY4OJG1SeqS0iwrCDNZMR6UsBz39bhYtKSkZMSL7BtS+m2sCgUDuK8ssGAyGw+Hotm1NHrM2fPq7uiJud6TV/ffvjQ1cyvPZESL/8+UWX18iYd5Dr7tcLpfL7/fLk+Um3UtBk0/ASCTS71d9iYR8j1/zHiMoQtM0a56GWVpYVlbW98be3t6enp6sP1rX9bQc5rGFQohgMBgSoiESEUIkk8mEGeOyeNzj8fzy3dHHzu2ZOLE7/z8fgxGPu555a5wQIh6P/0qIX6Wcwx4+12lCHvcEAjU1NYQwg8bGxjlz5qTdKM+b/E6I3+X10YEiXC6XcfJLPg19Pp+maVbcdeYvf+UrX+l744kTJ1pbWz0ez+jRozP83UWLFuU3fmn8fr/f79d1vampKRwOb9u2LRaLJZPJvJ/F9Hg8v/lNdSDwiceTzO9PRu7icderr44TQrS3t3d0dOTrx8r+VVZWut1uTdMCgYDP5yOBudA0rbGxsaGhQf57IBBoamr6+OOPY7FYIpEw5XdTFCmZwIqKCuNpGAgErEng/64h85dlC/ft2/eNb3zDuLG7u7ujo2P06NEeBwxA5KmLYDBoUhTb2trk4/TqqxMCgU+G/wMxBPG4a9s2bzzuSiaTeQmhkUCPx0MCh0z+76bruvyfzngaEkXkwkig8TS0PoGGkszXCO7du/eGG26YOnXqY489ZlxWsX379u9///vXXHPN6tWrS0pK+v2LS5YsMfu4cCB5j6LL5TrnnHOEEOPHJ666qiVPy8Qg7NgxZufO6mQy2dbWNpzXVhJoGaKIgTgqgYYsLezq6goGg2+++WZjY+O1115bUlISi8VuvfXWt99++8knn7zssssG+os2ttCQxyi63e4JEyYIISZNis+aZeL2RfRlhLC9vX1ojyAJtBFRhOTMBBqytFAIsWPHjh/84AcdHR0zZsyYOHFic3PzZ599tnjx4vvuu6/fnTWSE1poyEsUjRzOmtU2aRLbSi2yb59n2zavGNJpQhLoKERRTQ5PoCF7C4UQBw8e/PnPf97c3Nzd3T1x4sSbb755yZIlGUIoHNZCwzCj6PF4vF6vIIdWGVoISaDDEUUVFEoCDTm1cAic2ULDkKPo9XrljqGrrmoZP54nsInicVdT0zlCiHg83pbDZfUksOAQxeJTcAk0KNpCwxCiSA4tkHsISWARIIqFrnATaFC9hYZBRZEcmiqXEJLAokQUC0sRJNBAC9PlGEUjh5w7zC/jHGG/ISSBiiCKTlZMCTTQwgFljaKRw/r69mnT8vZOKCqTl0+IPiEkgcoiis5RlAk00MLsMkRxzJgx8oOFue5w+IwQGrtGSSAMRNEuxZ1AAy0chH6jaFxowbvSDFk87tq3z2OEMB6Pk0AMhChaQ5EEGmjhUKRFsaysTA5LPZ7krFlt7KYZlHjc9eqrE+JxlxAikUgkk0kSiFwQRTOolkADLRwWI4qpH+TGbprctba6X311gvFHEoghIIrDp2wCDbQwP4xno67rgtOHOUidi5JA5AVRHCwSaKCFeRYKhUKhkBDC40lefnn7xInd3d18CPD/GjFixIgRIxIJ98svj+vsHCGEkB+5Zfe6UFSIYmYksC9amH/hcPjOO++UB4g+X9fMmZ93d3f39PSoHEWZwPLy8vLy8nDYHYlUiNOHg4QQ5iGKqUhgBrTQFLquNzQ0yJOIVVU9N95YrWnJQ4cOqRbF1ARWVVVVVZ0bCv1J111CCJ/Pt3HjRrsXCFWoHEUSmAtaaKJwOLx06VL578Fg/Y03nr9794fRqF70UUxL4JQpU4UYE4kkQqGdgsNB2EqdKJLAQaGF5pJPPHkGUdM8gUBdMFjf2dlZlFHsm0BNq9E0ralpfyi0U9fjQgifz9fY2MgTErYr1iiSwKGhhVbQdX3p0qXyDKKmeVavnuX3ny2EKI4oDpRAIYSuxxsatkUinwoh5DZRDgfhNMURRRI4TLTQOsYWU/F/iygKM4oZEiiE0PV4KLSzqWm/YCiKAlGIUSSB+UILLZU6MhVCaJonGKwPBOqMb3B+FDMnUPRXQZ6cKCzOjyIJzDtaaIO+RZTnEVO/x2lRzCWBkcinmzbtkxNRTdN8Pl8wGOT5icLltCiSQPPQQtv0W8RAoE7TPKnfZm8UsyZQCKHr8aam/U1N++XuGCqI4mNvFEmgBWihzdKKKAY4TBTWRjHHBEYin4bDrXIcKpiIQgFWRpEEWokWOkU4HJbPMeMWn+9sv3+8lVEcWgKFEJqmBYNBHm6ow7wokkBb0EJnSXuPb0keKfp84419p1K+oph7Ao3TgacXxntqQ3X5iiIJtBctdKh+Pw1K0zw1NaP8/vFpXRxaFLNeFCGE6HsIKE6fEQwEAiQQMAwtiiTQIWih0/UbRUnTPD7f2Zrm0TRPTY3H7z87lyj2m0Ahxggh5DFfONwqjwL/731pNTU1fr+fo0Ags1yiSAKdhhYWEvkck/8c6HvksWMsFhOio7LyVFoOZQVjsVIhRGVlpRBjotET8hCwvx+l+Xw++U/6BwxW3ygmk0kS6Ey0sFDpuq7rujxYlEeNmqalnmUcLHnkp2ma3++X/8JTFMiL1H0AJNCZaGFRkYGMRqPy340b075NPgnlP8keALjsXgDyiaoBwBCMsHsBAADYjBYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKC6nFq4Z8+e5cuXT548uba29uKLL7777ruj0ajZKwMAwBrZW7hly5Zvf/vbW7dunT59+nXXXTd27NgXXnhh2bJl5BAAUBxcmb/c1ta2bt26ysrKxx9//JJLLhFCnDp1av369WvWrFm9evXatWtdriw/AQAAh8tyXPj+++9/9NFH11xzzfTp0+UtpaWl119//YUXXrhjx45jx46Zv0IAAMyVpYWHDx+uqqqaNm1aSUmJcWN5eXlVVZXJCwMAwCJZJpw33HDDDTfckHbjRx99tHv37q9+9atnnHGGaQsDAMAig76mIhaLhUKhEydOLFq0yOPxmLEmAACsNLidL/F4/N57721ubl68ePH8+fMzf3M4HNZ1PfWWYDA46AUCAGCyQRwXtre333rrrS+99NKCBQvuueeesrKyzN+fFkIAAJzpy+PCeDx+8803h8Nh4wt+v3/9+vXGFHTv3r0rVqzYu3fv8uXLGxoasoZQCLFo0aJAIGDGogEAyKOcZqTNzc0rV66MxWI//vGPv/e975WWlpq9LAAALPNlCz0ez4YNG/r9jh07dqxcubK7u/vRRx+98sorLVwbAABWyHJcGI1GGxoahBBPP/20fN8ZAACKTJYWvvjii/v37y8vL7/99ttTL7cXQkycOHHdunVer9fM5QEAYLpMLYzH42+//bYQoru7u+87cZeUlPT29pq4NAAALJGphRlOIgIAUDT4LF8AgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKC6wbXw5MmTDQ0N9fX1u3btMmlBAABYbHAtfPnllzdv3mzSUgAAsMUgWrhnz55Vq1b19vaatxoAAKyXawu7urrWrFlTXV09c+ZMUxcEAIDFcm3hs88+29zcfMcdd2iaZuqCAACwWE4t3LFjx/r16xcuXHjFFVeYvB4AAKyWvYWxWOzhhx/2er3BYNDlclmwJgAArJSlbb29vRs3bnznnXeeeOIJr9c7qB+9adOmcDicektjY+OgFwgAgMmytHDHjh2PPPLI4sWLZ8+ePdgfrWma3+8f6sIAALDIly2Mx+M333xz6mGc3+9fvXr1/fffX1tbu2LFipKSksH+aL/fHwgE8rZSAADMkem48PDhwwcOHIjFYpdccknal77zne9UVlY+++yzF110kZnLAwDAdF+20OPxbNiwIe1ruq4HAoFEIpF6Yzgcjkajc+fOnThxYnV1tUXLBADANJmOCzVN++lPf5p24x133HH06NFbb72VI0IAQHHgcyoAAKqjhQAA1Q362vk1a9aYsQ4AAOzCcSEAQHW0EACgOloIAFAdLQQAqI4WAgBURwsBAKqjhQAA1dFCAIDqaCEAQHW0EACgOloIAFAdLQQAqI4WAgBURwsBAKqjhQAA1dFCAIDqaCEAQHW0EACgOloIAFAdLQQAqI4WAgBURwsBAKqjhQAA1dFCAIDqaCEAQHUF3EJd13Vdt3sVsJSu6+Fw2O5VwGo86Aqy+EEv7BY2NDTYvQpYbenSpXYvAVZbunQpv/iqJhQKWZnDAm4hAAB5QQsBAKqjhQAA1dFCAIDqXOb96HA4bOrpbl3Xo9FoKBQy7y7gTDzoCmpqarJ7CbBUNBptamqKRCKm3oumaYFAQAhR0tvba8YdNDU1se8LAOBkprcQAIBCwflCAIDqaCEAQHW0EACgOloIAFAdLQQAqI4WAgBURwsBAKqjhQAA1dFCAIDqCrKFe/bsWbx48QUXXFBXV/etb31ry5YtvHtOcdu7d+/MmTNr+3j88cftXhpM8f7778+YMeONN95Iu/3UqVO//e1vZ8+eXVtbO3ny5OXLlx88eNCWFSLvBnrQ/+Vf/qXvc7++vn7Xrl15vHcT35vbJG+88cbKlStPnjw5d+7ckSNHbt269Uc/+tFdd931gx/8oKSkxO7VwRS6rh89enT06NGVlZWpt6f9EcWhvb191apVR48eTbs9mUw+8MADzzzzjNfrXbhw4eHDh7du3bpz584nn3xy2rRptiwV+TLQgy6EeP/990tKSrxeb3l5uXFjZWWly5XPfhVYC9vb2x955BG32/3MM8/I//qj0eiyZcv+6Z/+6YorrvizP/szuxcIUxw4cEAI8fDDD8+dO9futcBcuq6vWLFi586dfb/0hz/8YfPmzbNmzXrkkUfkr0FbtmxZuXLlo48+GgqFKioqLF8s8iPDg37ixIloNHreeec999xzXq/XvDUU2Iz0vffe27179zXXXFNfXy9vqampue22244cOfIf//Ef9q4N5vnwww/HjBlz9tln270QmEjOPxcsWLBv376pU6emfbW3t3fLli1ffPHFTTfdZMwDvvnNb1511VWRSGTfvn2Wrxd5kPlBF0KcOHHiT3/6U01NzRlnnGHqSgqshdu3bz958qTP50sdh06ePHncuHHvvPPOF198YePaYJJ4PK7r+tlnnz1+/Hi71wIT7d69+yc/+UlpaekTTzxx7bXXpn21s7Nz586dZ5111gUXXGDc6HK5Zs6cGYvF3nvvPWsXi/zI/KALIVpaWtrb2+vq6kaNGmXqSgqsha2trZWVlZqmpd44evToioqKo0ePJhIJuxYG83R2dkaj0crKynXr1s2YMaO2tnbGjBmrVq3q7Oy0e2nIp9LS0u9973uvv/7617/+9b5f/eKLL44dO3bOOedUVVWl3i6nBS0tLRatEnmV+UEXQhw+fDgej/f09Cxfvnzy5Mlyv+Qrr7xy6tSp/K6kkM4Xnjhx4rPPPut7+xlnnDFhwoSWlhaOC4tSNBo9evRoNBo9cOCA3+8fOXJkc3PzE088sXXr1ieffLKmpsbuBSI/pk6d2u+UTDpy5Eg8Hu97u9fr9Xg8ra2tZi4NZsn8oAshPvjgAyHEs88+W1dXt2DBgmPHjr355pu33XbbkiVL7r333rKysnytpJBa2Nvbm0wm+/3SiBEFdoCL3B0/fnzkyJHf+c53fvrTn8r9EV1dXffff//zzz//j//4j3//93+f3+1kcKZTp071+/QfMWIEG8iL1alTpzo7Oz0ez89//vNrr71WPtAHDx68+eabX3zxxVmzZs2bNy9f91VICSkpKRnoVa+np8fixcAy3/jGN959990HH3zQ2ChYUVFxyy231NTUNDc39zsqQPEpLS3t9+nf09PD5cXFqrS09P7773/vvffmz59v/MZz/vnn33bbbclk8vXXX8/jQ19ILRw1atRZZ53V9/bPP/+8paVl7NixI0eOtH5VsEV1dfU555zT2dnZ7wVJKD5nnnmmx+Ppe3tbW1s8HmdflVLOO+88ORg/ceJEvn5mIbVQCHHeeefFYrFPP/009cbjx493dXWNGzfO7XbbtTCYKhaLnTx5su/tLpertLTU+vXAenJbQDQa/fzzz1Nvl68GEyZMsGldMNepU6eOHz/e7/Gfy+XK43i8wFo4bdq0srKy5ubm1P9pPvjggyNHjlx66aUcFxafZDL5ox/9aNq0aVu3bk29PRqN7t27lwst1OHxeKZMmdLa2vrhhx8aNyaTyf/+7/+urKz82te+ZuPaYJJDhw7NmTNnwYIFaXuj3n333Vgslt8LLQqshRdeeGFdXd0rr7zyxz/+Ud4SjUYfeeQRr9d75ZVX2rs2mMHlcl111VVCiF/96lft7e3yxvb29gceeODYsWN/8Rd/MXbsWFsXCOtceeWVJSUlTz31lPFfwuuvv/7GG2/4fL5JkybZuzaYYeLEiZdeeumhQ4deeukl4yKKP/zhD+vWrRs3blwgEMjjfRXYBjyv17tixYqVK1fecMMNc+bMke9HeuLEibvuuiv1ClwUk6uvvvr6669/7rnnLr/88ssvv1wIsXXr1ng8vmDBgiVLlti9OljH7/cvXLjwueeemzdv3uzZsw8fPrx9+/YxY8bccsstvAFbUXK5XHfeeefu3bsbGxs3bdo0Y8aMQ4cObd++vbS09IEHHvjzP//zfN5XHn+WNebNm3fmmWeuXr3697//fU9PT11d3cqVK6+++mr2VRersrKy++67b8aMGY899ti//du/CSHq6ur+5m/+5tprr83j1UVwPvlfwuTJk9evX7958+by8vLLL7/87/7u784//3y7lwaz1NTUPP/8848//vivf/3rF154QT7oK1asMN6GM19K2I4MAFBcgZ0vBAAg7/4/dKSOP0LtKKgAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_star(A,h)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [3 1; 6.75 1; 10.5 1; 13.5 1; 16.5 1; 20.25 0; 24 0; 27 0; 6.25 5];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [3.75 1; 9 1; 14.25 1; 18 1; 21.75 1; 27 1; 32.25 1; 36 1; 12.25 8];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('slicing_star.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [7.75 1; 17 1; 26.25 1; 34 1; 41.75 1; 51 0; 60.25 0; 68 0; 13.69 5];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [9.5 1; 22.25 1; 35 1; 44.5 1; 54 1; 66.75 1; 79.5 1; 89 0; 26.01 7];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-08T13:42:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-03T13:58:16.000Z","updated_at":"2025-12-19T15:03:36.000Z","published_at":"2025-12-08T13:42:41.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not exceed the circle's area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e otherwise;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on, until last slice of the 4-pointed star polygon;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=9)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the circle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, h)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi 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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"479\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"601\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlkAAAHfCAIAAADsm1pIAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6QwDECUuAtncXQAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAwMy1EZWMtMjAyNSAxNjozNzo0NjdgV3gAACAASURBVHic7d1/dFTlnfjxJ2QSJjIJBBwFcrWa4ApsbRCFmW9BFE9b5Sgty1AF3NPiSu2uFkfOGvW4ba2uPQoB90xZf6FrT1cX/EGoreuy/uh20bA7I7aCKK78tHiHRAMkZAYzhiH5/vHI3dlJMjNJ5v6Yed6vs8cjk5B5tuPMO/dznztT0tvbKwAAUNgIuxcAAIDNcmrhnj17li9fPnny5Nra2q9//etPPvlkV1dX5r/S1NQUDofzsUIAAMyVvYXNzc2BQGDr1q3Tp0+/7rrrysrKHnzwwR/+8IexWCzD39q0aVM0Gs3fOgEAMIsr85fj8fijjz568uTJX/ziF/PmzRNCdHV1/eQnP/n1r3/9n//5n/Pnz7dkkQAAmCjLceHnn38ejUanTZt22WWXyVsqKiquvvrq3t7e//qv/zJ/eQAAmC5LC0tKSlwuV0dHR+oJwng8LoQYN26cuUsDAMASWVp45plnXn/99Xv37n3wwQfb29t7e3vffffdhx9+eNy4cVdffbU1SwQAwFRZzheWlJTcdNNNo0ePvvfee1966SV5Y319/UMPPXThhReavzwAAExXkvla+97e3t/97nd33313PB6fM2fO2LFjt2/ffvDgwdmzZ69du9br9Q70F5csWdJ3H+mbb76Zn1UDAJA/WY4L33///b/9278966yzXnzxxfPPP18IcerUqfXr169Zs+b+++9/+OGHy8rKBvq7gUDA5/Pleb0AAORblha++uqrsVjsvvvukyEUQpSWli5btiwSiUQikY8//viCCy4Y6O9qmub3+/O5WAAATJBl70xra6sQwuPxpN5YUVFx5plnfvHFF4lEwsSlAQBgiSwtHD9+vBDi8OHDqTd2dXUdOXLE5XKVlpaauDQAACyRpYVz5871eDzPPPPMwYMH5S29vb2vvPJKOBy+5JJLjMEpAACFK8v5wunTp69YsWL16tXz5s2bMWNGTU3NH//4x/3799fU1Nx2220VFRXWrBIAAPNkv75w+fLl9fX1a9eu3b59+7Zt28aNG3fTTTf99V//9dixY61ZIgAApsrSQiFESUnJzJkzn3/+eQtWAwCA9fgsXwCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoLqcWtjZ2blq1aoZM2bU1tZedNFFd999dzQaNXtlAABYI3sLDx8+/P3vf/+JJ56oqqq67rrramtrX3zxxWXLlpFDAEBxyNLC3t7ep5566r333mtoaHjttdceeuihl1566a677jpw4MBTTz1lzRIBADBVlhbu27fvX//1Xy+77LJly5aVlpYKIUpKSubPn3/uuefu3bu3s7PTkkUCAGAiV+Yv79u378iRIwsWLKioqDBunDBhwu9//3uTFwYAgEWyHBfu37/f4/F85Stf2bJly7e+9a26ujr2zgAAikyWFn788cdCiMcff/z2228fNWrUd7/73bPOOuuFF15g7wwAoGiU9Pb2ZvjyHXfcsXnz5vLy8n/4h3+YN2+eEOLUqVPr169fs2bNtddeu3btWper/ynrkiVLIpFI2o0HDhzI17oBAMiXLOcLpcWLF1999dXy30tLS5cuXfraa6+98847hw8fPvfccwf6W8FgMBAI5GeZAACYJksLy8rKhBAXXHBBSUmJcePo0aPr6uoOHDhw/PjxDH9X0zRN0/KySgAAzJPlfOGkSZOEEIlEIvXG3t7enp4eExcFAICFsrTwa1/7mtvtfuutt7q6uowbjxw5snv37rFjx5555pkmLw8AANNlaeGUKVOmTZsWDodfeeUVucvm1KlTmzZt2rt379y5c8ePH2/JIgEAMFGW84Uej+eee+655ZZb7rrrrmeeeWbKlCnbt28/ePDg1KlTly9fnnoSEQCAApX9vbm/+tWvbty48bvf/e6hQ4deeOGFzs7OH/7whxs2bJg4caIF6wMAwGxZri8csiVLlixatIhrKgAAzsdn+QIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqo4UAANXRQgCA6mghAEB1tBAAoDpaCABQHS0EAKiOFgIAVEcLAQCqG1wLT5482dDQUF9fv2vXLpMWBACAxQbXwpdffnnz5s0mLQUAAFsMooV79uxZtWpVb2+veasBAMB6ubawq6trzZo11dXVM2fONHVBAABYLNcWPvvss83NzXfccYemaaYuCAAAi+XUwh07dqxfv37hwoVXXHGFyesBAMBqrqzfEYvFHn74Ya/XGwwGXa7s3w8ASKPreiQSCYfDfr8/EAjYvRyky9K23t7ejRs3vvPOO0888YTX6x3Uj9Z1Xdf11FuYr5pK/q+t63o0Gk39Y9q3pT4KmqbV1NRomsZDA5hB1/WmpqZwOByJROQtTU1NNTU1fr/f3oUhTZYW7tix45FHHlm8ePHs2bMH+6NDoVAoFEq95cCBA4P9IRiI/FUjGo2Gw2H5L32zJ2maNtCX0r5NCOHz+fx+P89VYDj6JjBVKBTi+eU0mVrY3t5+//3319bWrlixoqSkZLA/urGxkVFAHsmeyTFLJBIx8paaOk3zCCFqakZVVfXIo8NRo04mkx+MG9dj/By32y2EiMVKa2pqOjtHRKMndD0uUo4jm5qajJ8soygDadn/p0CBypxAw1axtba2VtO0QCAQDAYtWx4yKMlwveCuXbv+8i//MhaL9fvVysrKZ5999qKLLur3q0uWLFm0aBEtHD7jNIORKIOmeXy+s4UQfv/4mhqP3392Z2enrusffvjhoUOHkslkMpns7u7u+zNHjBhRXl7udrurqqqmTJk6deqUzs4RQohI5FNdj8v/i0Q+TftbsoiBQICBKpAqxwQa2oPtHcEOd9jtjrirQ9VE0QkytVDX9aeffjqRSKTeGA6Ho9Ho3LlzJ06c+Fd/9VcDvSzSwmHq99kl42eUz7g9xwT21TeKVVVVKWuINzXtl/9M/VvyqcvBIhSXYwLPKEmOG5H4vNd1tMctb5EtNL6BKDpBphb264477nj99dczHBFKtHBo+j67NM1TUzPK7x/v841P7Z8YRgL7yhxFcbqL4XBr6vGifOpypAilDCqB57pi40YkhBDvdns/OeWRX0proYEo2ohrJBxBDkI3bdqUmkB5CBgI1KV9cx4TaOjp6UkkEolEorOz87PPPotEwmlR1DRPMFgfDNbrelzXT0QiraHQTl3X5Q4pnrooekNL4KAk/ImEP9ER7GgJt+yK7ArV8syyDi20mXyCNTU1pe5/CQbrrUlgX7lEUdM8fv/ZwWB9KLTz9BxVD4VCTU1NPG9RZCxIYF9E0XqDnpHmiBlpVvI5Zlx2ommeQKAuEKiTe0EN1iQwgxzHp6HQTuOWYDDI4BQFLe8JzGVGmgHjU7PRQhv0W8FgsD71e2xPYF9ZoyiLKK/QEBQRBci8o8BhttBAFE1CCy3Vt4KrV8/Ky45QK2XdfRoK7TS2ngaDQZ6ucDgLBqH5aqGBKOYXLbRI2nnBtAoWRAL7yhBFigjns/JcYN5baCCKeUELraDr+tKlS40KGltjCjSBfQ0URV2PNzRsk5dhaJq2evVqLkmE7WzZDmNeCw1EcThooblSh6LGecGiSWBf/UYxHP70zju3yfOIgUCgsbHR7mVCRbYk0GBBCw1EcQhooYlkBXVdlxW88cbzizWBffWN4i9/edDYa8rIFJaxN4EGK1toIIq5o4WmSD0crKrqCQa/UlV1TIUE9pUaxaqqc3/5y/bduz8XQvh8vo0bN9q9OhQthyTQYEsLDUQxK661zz/j7GBVVc+UKV/MnPn5kSNtra1qJdCQevF+efln3/ymu7LSHYlURCKROXPmcAYR+eW0BDoEF+9nRQvzzPjURo8nOX9++xlndHd2qpjAvowoTp06orbW/dZb4+QvDcxLMXwkMEdEcSDMSPMj7Q1F6+vbp02zdAZSiHbsGLNzZ7XgPb4xVAWUQHtnpBkwPpVo4bD0fU9tjydZVxcjhDlqbXW/+uoE449EEbkooAQaHNtCg+JRpIVDYSRw27Zt8vMdPR6PEMLjSV51VYvHk7R7gYUkHndt2+ZtbXULIdra2lwuV3V1NVFEX4WYQIPzW2hQM4q0cBDSEtjV1RWPx8eMGVNdXS0I4fC8+uoEmcP29vaOjg6Xy+XxeIgiRIEn0FBALTQoFUVamF2/CZRfMkLICcLhM04fxuPxtrY2eSNRVFZxJNBQiC00qBBF9pEOKEMCJUKYX9OmdXg8yW3bvB6Px+VytbS0CCGSyWRHR0dHR8cnn3yya9cu43ODiWKxKrIEFgcVdp9yXJguawIlQmgSYzdNIpGQOUzDkWJRKvoEFvRxYV/Fd6RIC7+UYwIlGUK2jJokaw4lolgEij6BhiJroaFooqh6CweVQIkQWiDHHEpEseCok0BDsbbQUOhRVLSFQ0igRAgtM6gcSkTR4RRMoKHoW2go0Ciq1cIhJ1DiHKHFjBym7izNBVF0FJUTaFCnhYbCiqISLRxmAiWPx+P1egUhtJaRw7a2tiE8akTRRiQwlYItNBREFIv5moq8JFByuVyE0Bbjxyfq69t37qz2er3JZFK+y0/uuCTDeiQQaQrikowibGEeEyi5XK4JEyYIISZNihNC602b1nHiRNm+fR6v19vW1jbYHEpE0WwkEFk5OYrF08K8J1CSR4Qul8vjSc6aNYhTVsijWbPa4nFXa6vb6/V+8sknw/lRRDG/SCCGwIFRLOzzhbquCyHMSKDB2DjKe43arqnpnHjclfu20hz1Paeo6zqfMJyLpqamhoaGDN9AAg0qny/MRd9ziuFw2MqnYQG3MBwOL1261PhjfhNo8Hg8VVU9c+cenziRj+S12eHD5b/5TbUQIpFIJJP5/73E5XK53W7578FgkCPFzHRdnzNnTr9f8pT2nD0yWTuya1yp6gk0ROKjDya+/K+LFmZgRFEI0djYaNkGzEKdkeq6HgqFfInEoljMrLtwuZoqK3Uhbjz/+DfP+lxwTGi7s5LnXS5CW6vdbncgHvd3deX/LmIxIcSmyko5O+UAcSC6rmc4IrymInZtaVz0CNFj5aIcreVUz0G711AQklpSREQyqSWTNZs2baKFWUQikUgk4hMiYM7hoO5ybfJ6dZdL8ySD0zoEx4TOMPW87vBHFZFWd8TtbhzMFYeDEq6oiAgRDocbGxtNuotCJ5+AA331+fjot0pG3VzWPr/UlKdnIarq4feCLFy6y9PkqVx7USwWaIkHkklt69YloVDImpOIIyy4j7zTdX3lypXt7e3m3UXE7Y643ZonueGqfJ6awvBtvKpF8ySFEA1er3n30tbWJreEmHcXhSvtoLBmZE/NyPQX+sO9rp91e+cnznn59EkyYCAu3TUmNGbC1/+f+NnPWlo2dHQEk0lNCNHW1hgKhax5GhZeC+XzMBaLDW1vfU534XLJ19lgfbvGfhnnWT2rTXe5mjye8OnTe2ZoaWm58847zfv5BSothJUV4oYpJ1+7+PgtWhdFxGANVEEpmdTa24OhUMiClRReCyORyLZt2zo6zDrzbITQNz4RmMSEx4n8px+aO808NEwkEvv27cu8T1JBadPRs8f0TBwrhBC3agmKiNxlrqChoyO4dauwIIcF1kI5HR3UW1MOljEdbeRqQgdrnNWmeZK6yxUaM8a8e2lpaWFSmirtoHDUyB7/Bf9nBxNFRFY5VtBgzaS0kFrIdBSpVs9qE0KEqquZlFqjbwhn1p3o9zspIvo12ApK1kxKC6mFZk9HhRCh6mohhOZJMh11Pv/4hG98Qpx+1EzCpNSQNh31ViW9VZl+X6SIMAytggYLJqUF00ILpqNyO4Y4fcAB55Nz7IjbbfahIZPS3A8K01BExQ2zggazJ6WF0UILpqPi9B79wKS4fzxvllEYNE8yWN8uTN5EI5SflA45hAaKqKB8VVAye1JaGC20YDoaPr1lRr62olAEp3XITTTymN4kik9KBzsdHQhFVER+K2gwdVJaAC20YDoqTp9z8o1PsGWm4MhfX0w9aygUnpQO/6AwDUUsYiZV0GDepNTpLbRmOspBYUELTIpbcGgolJyU5j2EBopYZMyuoGTepNTpLbRgOio4KCx88pcYU9+VTSg5Kc3XdHQgFLEIWFNBg0mTUke30JrpKAeFRUAeGgohLDg0VGdSat5BYRqKWKAsrqDBjEmpc1tozXRUcFBYLOSvMpsqK82+I0UmpZaF0EARC4hdFZTMmJQ6t4XWTEd1l0seFAbqzPocRFhDvj2C2dcaCmUmpWZPRwdCER3O3goa8j4pdWgLrZmOitMHhTWeJNcUFgEjh2bfUdFPSq0/KExDER3IIRU05HdS6sQWWjYdNXYecqawOMjHsamyUneZ/iHVRTwptT2EBoroEE6roJTfSakTW2jNdFScPoDQOCgsFpon6RufsODiClHUk1K7pqMDoYg2cmYFDXmclDquhZZNR8XpfRacKSwmi+piwvzr7qWinJQ656AwDUW0mMMraMjXpNRZLbRsOipSds34OCgsIsYHjJi9g0YqskmpY0NooIgWKJQKSvmalDqrhZZNR8XpC9HYNVN8ZA6bzL+4QhTdpNRp09GBUESTFFYFDXmZlDqohVZOR4UQ4YoKcXqkhmLiP7tLmH/RvaFoJqXOPyhMQxHzqEAraBj+pNQpLbRyOipSLyvkM3uLjvEeNNaMSUVRTEoLLoQGijhMhV5BafiT0pxauGfPnuXLl0+ePLm2tvbiiy++++67o9HokO+yX1ZOR8XpHaQ1vNFMkZLngK0Zk4qimJQWynR0IBRxCIqjgoZhTkqzt3DLli3f/va3t27dOn369Ouuu27s2LEvvPDCsmXL8phDi6ej4vQOUjlMQ/GRj6wFF90bCnpSWrgHhWkoYo6KrIKG4UxKs7Swra1t3bp1lZWVzz333IYNGx566KHXXnutoaHhwIEDq1evTibz8JujxdNRIYTuckVdLnH66AHFR46+dZfLgovuDQU6KS2aEBooYgbFWkFpOJPSLC18//33P/roo2uuuWb69OnyltLS0uuvv/7CCy/csWPHsWPHhnCXaSyejorTL5FcYl/c5C86Vh4aFuiktNCnowOhiGmKu4KGIU9Ks7Tw8OHDVVVV06ZNKykpMW4sLy+vqqoa9Br7Y/10VJx+feSgsLjJMancLWyZgpuUFt9BYRqKKJSpoGFok9IsLbzhhhvefffdBQsWpN740Ucf7d69u6am5owzzhj0MlNYPx2V5OsjbzdT3Kz5OMO+CmhSWvQhNChbRNUqKA1tUjroaypisVgoFDpx4sSiRYs8w3uhsX46Kk5fTWHlPcIWxtUyVp4yFAU1KS3W6ehAlCqimhU0DGFSOriXiXg8fu+99zY3Ny9evHj+/PmZv1nX9bSjVL/fn/pV66ej4vQrIycLVaB5kqJDRNxuLW7pVaRyUhoIBFL/g3cadQ4K09yqJW7VEo/o7t+0jYx+8X8OBmQR15dU31zWPr+0UK88dukuT5Oncu1FsVigJR5QKoGp2toaQ6E5Pp8vx6fhIFrY3t5+++23v/XWWwsWLLjnnnvKysoyf3/fEyfGmuyajgquLFSJb3yiKe4JV1QErG2hOD0pffPNNy2+3xwpG0JDURaRCqYyJqV5buHevXtXrFixd+/e5cuXNzQ0ZA2hECIYDAYCgX6/ZMt0VJInC7myUAX+s7ua9tkz8jImpY2NjbYsIDPVpqMDKZoiUsF+dXQEt24Nh0KhYDCY9ZtzOl/Y3Ny8dOnSjz/++Mc//vFdd92VSwgzsGs6mopNpCqosWn7jOTYPaUcFKYp6POIip8XzCr3PaXZW7hjx46VK1d2d3c/+uijN954Y2lp6XBWZuN0VDI+v9eWe4eVjFPCFm+fMThwTykhHEjBFZEK5iL3PaVZWhiNRuUz5+mnn77yyiuHvzIbp6MiZeMMLVSEfKDtaqED95QyHc2sIIpIBQclxz2lWV4jXnzxxf3795eXl99+++2pl9sLISZOnLhu3Tqv15v7mmyfjtr1mgi7+MYn9H2eqH2Pu6P2lHJQmCPHnkfkvODQ5LKnNNNrRDwef/vtt4UQ3d3dfd+Ju6SkpLe3N/fV2D4dFULI10Q2karG3t+BHLKnlBAOlqOKSAWHI5c9pZleIzwez4YNG/K1Gnuno5J8TWQTqTrkVlJ9eLu9hskhe0qZjg6N7UWkgnmRdU+pRZ/la/t09Mtl2PqaCLvYPhu3fU8pB4XDZMt5RM4L5lfmPaVWtNAJ09FUbJxRh5yH23i+0GDjnlJCmC+WFZEKmiHznlIrWuiE6aikc75QMfbuI01l455SpqP5ZWoRqaCpMuwpNb2FDpmOSk44PoCVHDUDsGVSykGhSfJeRCpojYEmpea20GnTUeP6QrsXAkVZPCklhGbLSxGpoJUGmpSa20LnTEehOCeMSYXlk1Kmo9bIpYh/6Onno+KooC36nZSa+AKh6/ratWsdMh1NxXEhbGTZ1fdpB4VCiD/Xuk58kedff784JaLlI6L5/rGFaIG3e4G3+1G9Ynunq+/VF2nfzJUS9up79b2JLQyFQs6ZjkJZmiepxx1xUGiw5ur7vkefr7w72qT7ahRm/eSiVNlUSQXt1ffqexNfI5LJpKOmow6ZkgEWXH0fDodTp6Nwlo/PSyR8QgiPp8nupSgtEokYV9+b20LzfvgQaA5bD1Rm9rOj75smwjlmJff5T+6yexVO11RZ+T+JxMmTJ036+WVlZcmkW9d1+UcTW+h2u8eMGeOoQ0PACTwez+TJk019S7ZAILBp0yYODR1ISyY3trTYvYoCEK6o2G7mWba0p6GJLQwGg6FQKJFIcMoQNnLayUKXy1VdXb169Wqz76ixsXHOnDmpt5x79PK834vL5bqgvPxbn3+e959ciI6M6Pqw/FizO3qktJ83PdaSyWB7eyBu9adboC+Xy3XxxRenPg1NfJnQNC0YDK5atarFYb8E6XEXW0lhl+rq6uuvv96Cj3CST8DUjeMxd7T6xKT83kt5abn3lOvMU4P4yJqidKS063/Kjv161D4q6Hwul8vr9abt5TZ3J3QwGLz88svHjBlj6r0AWTnkbLEF09FUwWDQ5/MZf2wfta+r7Jg1d62OI6Vdze7og2PefrJqV98QaslkY1vbm598Qgidw+12T5o0Ke0DK0y/KqixsbG6utrt7uc6U+s55AURlnHUgNSy6WiqtO62VbFlI2+oYCHqOx2VTG+hHNRUV1ebfUe5c9TrIyzgkN+BLJuOppJPQOOPydKu9lH7rFxAUaKCBarf6ahkxbtFOGdSWpNMCiGitFAZzvm9x+LpaCompXlEBQtav9NRyaJ3TnLIpFQeHzjn9RHWqLH7uNCW6WgqJqXDRwUL3UDTUcmiFjpkUqqdPCmE0E/w6faqiLQ64kS1LdPRVExKh4MKFoEM01HJunfUdcKk1CHnjWAxf1c/29wtY+N0NBWT0iGggkUjw3RUsvTd5R0yKXXIsQIsEP60Qtj6O5Dt09FUTEpzRwWLSebpqGRpC22flPoSCcH5QsVoyaSN5wttn46mYlKaCypYZLJORyWrP3XM3kmpcXxADlWgx12RVrfuctl1XOiQ6WgqJqUZUMGilHU6KtnwCZz2TkrlyyJjUnVoyaQtLXTUdDQVk9K+qGCxymU6KtnQQnsnpYxJ1SEfZbsGpI6ajqZiUpqKChaxHKejkg0tFLZOSuWWQi6rUIE8+rdlE6kDp6OpmJQKKqiAHKejkj0tFHZPSpv2eWy5X1hJbiL1Wf6RYY6djqZSeVJKBVWQ+3RUsq2Fdk1Kjf++GZMWN7lxxpa7dux0NJWak1IqqIhBTUcl21oo7JuUsn1GBfJ3HV8i4bf2uNDh09FUSk1KqaBSBjUdlexsobBpUiqHZnKAhmJly+86BTEdTaXCpJQKqmaw01HJ5hbaMimVmyk4ZVjc5O86i2IxK++0IKajqYp7UkoFFTSE6ahkcwuFHZNSThkWPeNkoZUXVBTQdDRVUU5KqaCyhjAdlexvobBjUirHpJwyLFbytxwtmbTsZGHBTUdTFdOklAqqbGjTUckRLbR+UipHZ5wyLFahndVCiICFA9KCm46mKo5JKRVU3JCno5IjWigsn5TK50PTPg9j0uJjDEgtu7KwQKejqQp6UkoFIYYxHZWc0kJh+aSUMWmxsnhAWtDT0VSFOCmlgpCGMx2VHNRCiyeljEmLVdP+SmHhQWFBT0dTFdaklArCMMzpqOSgFgprJ6WBeFxLJhmTFhk97pJXy1hzsrAIpqOpCmJSSgWRZpjTUclZLRTWTkpreAOaomPlgLRopqOpnDwppYLoa/jTUclxLbRyUirHpA3bvBbcF6xh5Q7SopmOpnLmpJQKol95mY5KjmuhsHBSajxzwhwaFgW5g1RLJi04WVhk09FUjpqUUkFkkJfpqOTEFgoLJ6VfXlyxv9LsO4IF5EFhjfkDA+ndigAAGEBJREFU0qKcjqZywqSUCiKzfE1HJYe20LJJabC9XXChYVEwds3Ix9RURTkdTWXvpJQKIqs8Tkclh7ZQWDUpNeZp8pAChUvugbJg10wRT0dT2TIppYLIUR6no5JzWyismpRyaFgE9LhL/jZj9kFh0U9HU1k5KaWCyF1+p6OSo1tozaTUn0jIQ0M+xalwRVrdetylJZNmv1YW/XQ0lTWTUiqIQcn7dFRydAuFVZNSeXEFY9ICZdlBoSLT0VSmTkqpIIYg79NRyektFJZMSgPxuDw05FrDQmTNQaFS09FUZkxKqSCGxozpqFQALbRmUspZwwJl2UGhUtPRVPmdlFJBDJlJ01GpAFooLJmUGmcNmZQWFvnri9kHhQpOR1PlZVJKBTFMJk1HpcJoobBkUmocGvI2NIXCOChc3dZm3r0oOx1NNZxJKRXE8Jk3HZVyamE0Gl2xYsXkyZNra2tnz579z//8zydPnjRpQQOxYFLqTyTks5FDw0Ihz+/6EglTrylUdjqaamiTUiqIvDB1Oiplb+Hu3bsXLlz47//+79OnT1+4cGEymfzZz3527733Wp9DCyaljW1tQohIq5vrK5wv3OqW7z5q6plCxaejqQY1KaWCyCNTp6NSlhaePHnyscceO378+C9+8YsNGzasWbPm9ddfnz179ubNm8PhsHnLGogFk1KZw4ZtXjbROJked91p/kEh09E0uUxKqSDyy+zpqJSlhQcOHAiHw36//4orrpC3VFZWBoPB8vLy3/72t729vaYuri8LJqVcX1EQjC0zjWaeKWQ6mibzpJQKIu8smI5KWVr44YcfHj169NJLL62oqDBuPP/88zVN++CDD9rNfxPkvqyclLKJxpnCrW4LtswwHe1X2qT007LdsRGfUUGYxILpqJSlha2trUKIyZMnp95YXl4+ZsyY48ePx236L9vsSalxCmrpqxOYlDqNMR0NxONMR22R9vvBtpF/oIIwgzXTUSlLC//0pz/1vXHUqFHjx4+Px+PHjx83Z1VZyEFNZaWJHzoY7OhgUupMoZ3VFkxHKysrmY4OJG1SeqS0iwrCDNZMR6UsBz39bhYtKSkZMSL7BtS+m2sCgUDuK8ssGAyGw+Hotm1NHrM2fPq7uiJud6TV/ffvjQ1cyvPZESL/8+UWX18iYd5Dr7tcLpfL7/fLk+Um3UtBk0/ASCTS71d9iYR8j1/zHiMoQtM0a56GWVpYVlbW98be3t6enp6sP1rX9bQc5rGFQohgMBgSoiESEUIkk8mEGeOyeNzj8fzy3dHHzu2ZOLE7/z8fgxGPu555a5wQIh6P/0qIX6Wcwx4+12lCHvcEAjU1NYQwg8bGxjlz5qTdKM+b/E6I3+X10YEiXC6XcfJLPg19Pp+maVbcdeYvf+UrX+l744kTJ1pbWz0ez+jRozP83UWLFuU3fmn8fr/f79d1vampKRwOb9u2LRaLJZPJvJ/F9Hg8v/lNdSDwiceTzO9PRu7icderr44TQrS3t3d0dOTrx8r+VVZWut1uTdMCgYDP5yOBudA0rbGxsaGhQf57IBBoamr6+OOPY7FYIpEw5XdTFCmZwIqKCuNpGAgErEng/64h85dlC/ft2/eNb3zDuLG7u7ujo2P06NEeBwxA5KmLYDBoUhTb2trk4/TqqxMCgU+G/wMxBPG4a9s2bzzuSiaTeQmhkUCPx0MCh0z+76bruvyfzngaEkXkwkig8TS0PoGGkszXCO7du/eGG26YOnXqY489ZlxWsX379u9///vXXHPN6tWrS0pK+v2LS5YsMfu4cCB5j6LL5TrnnHOEEOPHJ666qiVPy8Qg7NgxZufO6mQy2dbWNpzXVhJoGaKIgTgqgYYsLezq6goGg2+++WZjY+O1115bUlISi8VuvfXWt99++8knn7zssssG+os2ttCQxyi63e4JEyYIISZNis+aZeL2RfRlhLC9vX1ojyAJtBFRhOTMBBqytFAIsWPHjh/84AcdHR0zZsyYOHFic3PzZ599tnjx4vvuu6/fnTWSE1poyEsUjRzOmtU2aRLbSi2yb59n2zavGNJpQhLoKERRTQ5PoCF7C4UQBw8e/PnPf97c3Nzd3T1x4sSbb755yZIlGUIoHNZCwzCj6PF4vF6vIIdWGVoISaDDEUUVFEoCDTm1cAic2ULDkKPo9XrljqGrrmoZP54nsInicVdT0zlCiHg83pbDZfUksOAQxeJTcAk0KNpCwxCiSA4tkHsISWARIIqFrnATaFC9hYZBRZEcmiqXEJLAokQUC0sRJNBAC9PlGEUjh5w7zC/jHGG/ISSBiiCKTlZMCTTQwgFljaKRw/r69mnT8vZOKCqTl0+IPiEkgcoiis5RlAk00MLsMkRxzJgx8oOFue5w+IwQGrtGSSAMRNEuxZ1AAy0chH6jaFxowbvSDFk87tq3z2OEMB6Pk0AMhChaQ5EEGmjhUKRFsaysTA5LPZ7krFlt7KYZlHjc9eqrE+JxlxAikUgkk0kSiFwQRTOolkADLRwWI4qpH+TGbprctba6X311gvFHEoghIIrDp2wCDbQwP4xno67rgtOHOUidi5JA5AVRHCwSaKCFeRYKhUKhkBDC40lefnn7xInd3d18CPD/GjFixIgRIxIJ98svj+vsHCGEkB+5Zfe6UFSIYmYksC9amH/hcPjOO++UB4g+X9fMmZ93d3f39PSoHEWZwPLy8vLy8nDYHYlUiNOHg4QQ5iGKqUhgBrTQFLquNzQ0yJOIVVU9N95YrWnJQ4cOqRbF1ARWVVVVVZ0bCv1J111CCJ/Pt3HjRrsXCFWoHEUSmAtaaKJwOLx06VL578Fg/Y03nr9794fRqF70UUxL4JQpU4UYE4kkQqGdgsNB2EqdKJLAQaGF5pJPPHkGUdM8gUBdMFjf2dlZlFHsm0BNq9E0ralpfyi0U9fjQgifz9fY2MgTErYr1iiSwKGhhVbQdX3p0qXyDKKmeVavnuX3ny2EKI4oDpRAIYSuxxsatkUinwoh5DZRDgfhNMURRRI4TLTQOsYWU/F/iygKM4oZEiiE0PV4KLSzqWm/YCiKAlGIUSSB+UILLZU6MhVCaJonGKwPBOqMb3B+FDMnUPRXQZ6cKCzOjyIJzDtaaIO+RZTnEVO/x2lRzCWBkcinmzbtkxNRTdN8Pl8wGOT5icLltCiSQPPQQtv0W8RAoE7TPKnfZm8UsyZQCKHr8aam/U1N++XuGCqI4mNvFEmgBWihzdKKKAY4TBTWRjHHBEYin4bDrXIcKpiIQgFWRpEEWokWOkU4HJbPMeMWn+9sv3+8lVEcWgKFEJqmBYNBHm6ow7wokkBb0EJnSXuPb0keKfp84419p1K+oph7Ao3TgacXxntqQ3X5iiIJtBctdKh+Pw1K0zw1NaP8/vFpXRxaFLNeFCGE6HsIKE6fEQwEAiQQMAwtiiTQIWih0/UbRUnTPD7f2Zrm0TRPTY3H7z87lyj2m0Ahxggh5DFfONwqjwL/731pNTU1fr+fo0Ags1yiSAKdhhYWEvkck/8c6HvksWMsFhOio7LyVFoOZQVjsVIhRGVlpRBjotET8hCwvx+l+Xw++U/6BwxW3ygmk0kS6Ey0sFDpuq7rujxYlEeNmqalnmUcLHnkp2ma3++X/8JTFMiL1H0AJNCZaGFRkYGMRqPy340b075NPgnlP8keALjsXgDyiaoBwBCMsHsBAADYjBYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKC6nFq4Z8+e5cuXT548uba29uKLL7777ruj0ajZKwMAwBrZW7hly5Zvf/vbW7dunT59+nXXXTd27NgXXnhh2bJl5BAAUBxcmb/c1ta2bt26ysrKxx9//JJLLhFCnDp1av369WvWrFm9evXatWtdriw/AQAAh8tyXPj+++9/9NFH11xzzfTp0+UtpaWl119//YUXXrhjx45jx46Zv0IAAMyVpYWHDx+uqqqaNm1aSUmJcWN5eXlVVZXJCwMAwCJZJpw33HDDDTfckHbjRx99tHv37q9+9atnnHGGaQsDAMAig76mIhaLhUKhEydOLFq0yOPxmLEmAACsNLidL/F4/N57721ubl68ePH8+fMzf3M4HNZ1PfWWYDA46AUCAGCyQRwXtre333rrrS+99NKCBQvuueeesrKyzN+fFkIAAJzpy+PCeDx+8803h8Nh4wt+v3/9+vXGFHTv3r0rVqzYu3fv8uXLGxoasoZQCLFo0aJAIGDGogEAyKOcZqTNzc0rV66MxWI//vGPv/e975WWlpq9LAAALPNlCz0ez4YNG/r9jh07dqxcubK7u/vRRx+98sorLVwbAABWyHJcGI1GGxoahBBPP/20fN8ZAACKTJYWvvjii/v37y8vL7/99ttTL7cXQkycOHHdunVer9fM5QEAYLpMLYzH42+//bYQoru7u+87cZeUlPT29pq4NAAALJGphRlOIgIAUDT4LF8AgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKA6WggAUB0tBACojhYCAFRHCwEAqqOFAADV0UIAgOpoIQBAdbQQAKC6wbXw5MmTDQ0N9fX1u3btMmlBAABYbHAtfPnllzdv3mzSUgAAsMUgWrhnz55Vq1b19vaatxoAAKyXawu7urrWrFlTXV09c+ZMUxcEAIDFcm3hs88+29zcfMcdd2iaZuqCAACwWE4t3LFjx/r16xcuXHjFFVeYvB4AAKyWvYWxWOzhhx/2er3BYNDlclmwJgAArJSlbb29vRs3bnznnXeeeOIJr9c7qB+9adOmcDicektjY+OgFwgAgMmytHDHjh2PPPLI4sWLZ8+ePdgfrWma3+8f6sIAALDIly2Mx+M333xz6mGc3+9fvXr1/fffX1tbu2LFipKSksH+aL/fHwgE8rZSAADMkem48PDhwwcOHIjFYpdccknal77zne9UVlY+++yzF110kZnLAwDAdF+20OPxbNiwIe1ruq4HAoFEIpF6Yzgcjkajc+fOnThxYnV1tUXLBADANJmOCzVN++lPf5p24x133HH06NFbb72VI0IAQHHgcyoAAKqjhQAA1Q362vk1a9aYsQ4AAOzCcSEAQHW0EACgOloIAFAdLQQAqI4WAgBURwsBAKqjhQAA1dFCAIDqaCEAQHW0EACgOloIAFAdLQQAqI4WAgBURwsBAKqjhQAA1dFCAIDqaCEAQHW0EACgOloIAFAdLQQAqI4WAgBURwsBAKqjhQAA1dFCAIDqaCEAQHUF3EJd13Vdt3sVsJSu6+Fw2O5VwGo86Aqy+EEv7BY2NDTYvQpYbenSpXYvAVZbunQpv/iqJhQKWZnDAm4hAAB5QQsBAKqjhQAA1dFCAIDqXOb96HA4bOrpbl3Xo9FoKBQy7y7gTDzoCmpqarJ7CbBUNBptamqKRCKm3oumaYFAQAhR0tvba8YdNDU1se8LAOBkprcQAIBCwflCAIDqaCEAQHW0EACgOloIAFAdLQQAqI4WAgBURwsBAKqjhQAA1dFCAIDqCrKFe/bsWbx48QUXXFBXV/etb31ry5YtvHtOcdu7d+/MmTNr+3j88cftXhpM8f7778+YMeONN95Iu/3UqVO//e1vZ8+eXVtbO3ny5OXLlx88eNCWFSLvBnrQ/+Vf/qXvc7++vn7Xrl15vHcT35vbJG+88cbKlStPnjw5d+7ckSNHbt269Uc/+tFdd931gx/8oKSkxO7VwRS6rh89enT06NGVlZWpt6f9EcWhvb191apVR48eTbs9mUw+8MADzzzzjNfrXbhw4eHDh7du3bpz584nn3xy2rRptiwV+TLQgy6EeP/990tKSrxeb3l5uXFjZWWly5XPfhVYC9vb2x955BG32/3MM8/I//qj0eiyZcv+6Z/+6YorrvizP/szuxcIUxw4cEAI8fDDD8+dO9futcBcuq6vWLFi586dfb/0hz/8YfPmzbNmzXrkkUfkr0FbtmxZuXLlo48+GgqFKioqLF8s8iPDg37ixIloNHreeec999xzXq/XvDUU2Iz0vffe27179zXXXFNfXy9vqampue22244cOfIf//Ef9q4N5vnwww/HjBlz9tln270QmEjOPxcsWLBv376pU6emfbW3t3fLli1ffPHFTTfdZMwDvvnNb1511VWRSGTfvn2Wrxd5kPlBF0KcOHHiT3/6U01NzRlnnGHqSgqshdu3bz958qTP50sdh06ePHncuHHvvPPOF198YePaYJJ4PK7r+tlnnz1+/Hi71wIT7d69+yc/+UlpaekTTzxx7bXXpn21s7Nz586dZ5111gUXXGDc6HK5Zs6cGYvF3nvvPWsXi/zI/KALIVpaWtrb2+vq6kaNGmXqSgqsha2trZWVlZqmpd44evToioqKo0ePJhIJuxYG83R2dkaj0crKynXr1s2YMaO2tnbGjBmrVq3q7Oy0e2nIp9LS0u9973uvv/7617/+9b5f/eKLL44dO3bOOedUVVWl3i6nBS0tLRatEnmV+UEXQhw+fDgej/f09Cxfvnzy5Mlyv+Qrr7xy6tSp/K6kkM4Xnjhx4rPPPut7+xlnnDFhwoSWlhaOC4tSNBo9evRoNBo9cOCA3+8fOXJkc3PzE088sXXr1ieffLKmpsbuBSI/pk6d2u+UTDpy5Eg8Hu97u9fr9Xg8ra2tZi4NZsn8oAshPvjgAyHEs88+W1dXt2DBgmPHjr355pu33XbbkiVL7r333rKysnytpJBa2Nvbm0wm+/3SiBEFdoCL3B0/fnzkyJHf+c53fvrTn8r9EV1dXffff//zzz//j//4j3//93+f3+1kcKZTp071+/QfMWIEG8iL1alTpzo7Oz0ez89//vNrr71WPtAHDx68+eabX3zxxVmzZs2bNy9f91VICSkpKRnoVa+np8fixcAy3/jGN959990HH3zQ2ChYUVFxyy231NTUNDc39zsqQPEpLS3t9+nf09PD5cXFqrS09P7773/vvffmz59v/MZz/vnn33bbbclk8vXXX8/jQ19ILRw1atRZZ53V9/bPP/+8paVl7NixI0eOtH5VsEV1dfU555zT2dnZ7wVJKD5nnnmmx+Ppe3tbW1s8HmdflVLOO+88ORg/ceJEvn5mIbVQCHHeeefFYrFPP/009cbjx493dXWNGzfO7XbbtTCYKhaLnTx5su/tLpertLTU+vXAenJbQDQa/fzzz1Nvl68GEyZMsGldMNepU6eOHz/e7/Gfy+XK43i8wFo4bdq0srKy5ubm1P9pPvjggyNHjlx66aUcFxafZDL5ox/9aNq0aVu3bk29PRqN7t27lwst1OHxeKZMmdLa2vrhhx8aNyaTyf/+7/+urKz82te+ZuPaYJJDhw7NmTNnwYIFaXuj3n333Vgslt8LLQqshRdeeGFdXd0rr7zyxz/+Ud4SjUYfeeQRr9d75ZVX2rs2mMHlcl111VVCiF/96lft7e3yxvb29gceeODYsWN/8Rd/MXbsWFsXCOtceeWVJSUlTz31lPFfwuuvv/7GG2/4fL5JkybZuzaYYeLEiZdeeumhQ4deeukl4yKKP/zhD+vWrRs3blwgEMjjfRXYBjyv17tixYqVK1fecMMNc+bMke9HeuLEibvuuiv1ClwUk6uvvvr6669/7rnnLr/88ssvv1wIsXXr1ng8vmDBgiVLlti9OljH7/cvXLjwueeemzdv3uzZsw8fPrx9+/YxY8bccsstvAFbUXK5XHfeeefu3bsbGxs3bdo0Y8aMQ4cObd++vbS09IEHHvjzP//zfN5XHn+WNebNm3fmmWeuXr3697//fU9PT11d3cqVK6+++mr2VRersrKy++67b8aMGY899ti//du/CSHq6ur+5m/+5tprr83j1UVwPvlfwuTJk9evX7958+by8vLLL7/87/7u784//3y7lwaz1NTUPP/8848//vivf/3rF154QT7oK1asMN6GM19K2I4MAFBcgZ0vBAAg7/4/dKSOP0LtKKgAAAAASUVORK5CYII=\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1024,"title":"Doubling elements in a vector","description":"Given the vector A, return B in which all numbers in A are doubling. So for:\r\n\r\nA = [  1   5   8 ]\r\n\r\nthen\r\n\r\nB = [  1   1   5   5   8  8 ]\r\n","description_html":"\u003cp\u003eGiven the vector A, return B in which all numbers in A are doubling. So for:\u003c/p\u003e\u003cp\u003eA = [  1   5   8 ]\u003c/p\u003e\u003cp\u003ethen\u003c/p\u003e\u003cp\u003eB = [  1   1   5   5   8  8 ]\u003c/p\u003e","function_template":"function B = your_fcn_name(A)\r\n  \r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = [1 1];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [0 -1 1 0 0 0 1 2];\r\ny_correct = [0 0 -1 -1 1 1 0 0 0 0 0 0 1 1 2 2];\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":69,"comments_count":13,"created_by":7968,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10270,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-11-03T15:44:34.000Z","updated_at":"2026-04-04T03:51:57.000Z","published_at":"2012-11-03T15:46:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the vector A, return B in which all numbers in A are doubling. So for:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 = [ 1 5 8 ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB = [ 1 1 5 5 8 8 ]\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":46,"title":"Which doors are open?","description":"There are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut these doors in a particular manner:\r\n\r\n* Toggle the state of each door you visit. That is, if the door is shut, open it, and if the door is open, shut it.\r\n* On the i-th trip down the alley, start with door i and visit every i-th door.\r\n\r\nGiven n doors, return the list of open doors.\r\n\r\nExample:\r\n\r\nLet's say n = 3.\r\n\r\n* On your first trip, you start from the first door and toggle every door. Now all three doors are open.\r\n* On your second trip, you start from the second door and toggle every other door. Since there are only three doors, this means you shut the second door. Now doors 1 and 3 are open.\r\n* On your third trip, you start from the third door and toggle every third door. Now only door 1 is open.\r\n\r\nSo:\r\n\r\n Input  n = 3\r\n Output y is 1","description_html":"\u003cp\u003eThere are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut these doors in a particular manner:\u003c/p\u003e\u003cul\u003e\u003cli\u003eToggle the state of each door you visit. That is, if the door is shut, open it, and if the door is open, shut it.\u003c/li\u003e\u003cli\u003eOn the i-th trip down the alley, start with door i and visit every i-th door.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eGiven n doors, return the list of open doors.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003eLet's say n = 3.\u003c/p\u003e\u003cul\u003e\u003cli\u003eOn your first trip, you start from the first door and toggle every door. Now all three doors are open.\u003c/li\u003e\u003cli\u003eOn your second trip, you start from the second door and toggle every other door. Since there are only three doors, this means you shut the second door. Now doors 1 and 3 are open.\u003c/li\u003e\u003cli\u003eOn your third trip, you start from the third door and toggle every third door. Now only door 1 is open.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSo:\u003c/p\u003e\u003cpre\u003e Input  n = 3\r\n Output y is 1\u003c/pre\u003e","function_template":"function y = which_doors_open(n)\r\n  y = n;\r\nend","test_suite":"%%\r\n\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(which_doors_open(x),y_correct))\r\n\r\n%%\r\n\r\nx = 3;\r\ny_correct = 1;\r\nassert(isequal(which_doors_open(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = [1 4 9 16 25 36 49 64 81 100];\r\nassert(isequal(which_doors_open(x),y_correct))","published":true,"deleted":false,"likes_count":29,"comments_count":10,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3433,"test_suite_updated_at":"2012-03-01T23:30:24.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:23.000Z","updated_at":"2026-02-24T13:31:39.000Z","published_at":"2012-01-18T01:00:23.000Z","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\u003eThere are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut these doors in a particular manner:\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\u003eToggle the state of each door you visit. That is, if the door is shut, open it, and if the door is open, shut it.\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\u003eOn the i-th trip down the alley, start with door i and visit every i-th door.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n doors, return the list of open doors.\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\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet's say n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn your first trip, you start from the first door and toggle every door. Now all three doors are open.\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\u003eOn your second trip, you start from the second door and toggle every other door. Since there are only three doors, this means you shut the second door. Now doors 1 and 3 are open.\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\u003eOn your third trip, you start from the third door and toggle every third door. Now only door 1 is open.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 3\\n Output y is 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61082,"title":"Slicing the area of a circle","description":"Given the area, A, of a square, consider a circle having the area, πA, and the radius, r.\r\nFor a given slicing number n\u003e1, find the (n+1)×2 matrix, M = [A1/π a1; A2/π a2; ...; An/π an; A_r L], where\r\nin the first row (i=1), A1 stands for the area of one slice (like a pizza slice), and a1 stands for the logical 1 if A1 is smaller than or reaches the square's area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of two slices and a2 has the same previous false-true meaning relative to the areas A2 and A;\r\nand so on, until last slice of the circle;\r\nin the last row (i=n+1), A_r is the area of the rectangle, with dimensions L×r, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\r\nHint: Compare with Problem 61081.\r\ninput: (A,n)\r\noutput:  M = [A1/π a1; A2/π a2; ...; An/π an; A_r L]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 325.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 162.75px; transform-origin: 408px 162.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square, consider a circle having the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eπA,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given slicing number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(n+1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 163.5px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 81.75px; transform-origin: 391px 81.75px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of one slice (like a pizza slice), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is smaller than or reaches the square's area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e surpasses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of two slices and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand so on, until last slice of the circle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; 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 30.65px; text-align: left; transform-origin: 363px 30.6562px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=n+1),\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Compare with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61081\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_circle(A,n)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 8;\r\nn = 4;\r\ny_correct = [2 1; 4 0; 6 0; 8 0; 8*sqrt(2) 4];\r\nY = slicing_circle(A,n);\r\ntolerance = 1e-13;\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 ...\r\n    abs(Y(end)-y_correct(end)) \u003c tolerance \u0026 all(Y(1:end,2) == y_correct(1:end,2)))\r\n\r\n%%\r\nA = 36;\r\nn = 6;\r\ny_correct = [6 1; 12 0; 18 0; 24 0; 30 0; 36 0; 36 6];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n\r\n%%\r\nA = 36;\r\nn = 12;\r\ny_correct = [3 1; 6 1; 9 1; 12 0; 15 0; 18 0; 21 0; 24 0; 27 0; 30 0; 33 0; 36 0; ...\r\n    37.92731310242232  6.32121885040372];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing_circle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 70;\r\nn = 7;\r\ny_correct = [10 1; 20 1; 30 0; 40 0; 50 0; 60 0; 70 0; ...\r\n    94.4539467929851 11.28940594715244];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nA = 70;\r\nn = 10;\r\ny_correct = [7 1; 14 1; 21 1; 28 0; 35 0; 42 0; 49 0; 56 0; 63 0; 70 0; ...\r\n    88.7511366850995 10.6077897676978];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026  all(Y(1:n,2) == y_correct(1:n,2))  \u0026  ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))","published":true,"deleted":false,"likes_count":0,"comments_count":10,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-27T14:44:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2025-11-27T14:44:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-20T14:17:04.000Z","updated_at":"2025-12-17T10:09:27.000Z","published_at":"2025-11-21T15:27:17.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square, consider a circle having the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eπA,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given slicing number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one slice (like a pizza slice), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the square's area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on, until last slice of the circle;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=n+1),\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Compare with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61081\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\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":42976,"title":"iteration of N blank spot","description":"we have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8","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: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.5px 8px; transform-origin: 372.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewe have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 32;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 256;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 2048;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 16;\r\ny_correct = 65536;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":86389,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":59,"test_suite_updated_at":"2021-06-17T14:24:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-02T16:46:32.000Z","updated_at":"2026-02-26T11:42:20.000Z","published_at":"2016-09-02T16:46:32.000Z","restored_at":"2022-02-16T22:15:33.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewe have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8\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":42583,"title":"Find smallest number to leave a remainder of 1","description":"given a vector of numbers, find the smallest number to be divisible by all of them with a remainder of 1. Note: input numbers will always be greater than 1 ","description_html":"\u003cp\u003egiven a vector of numbers, find the smallest number to be divisible by all of them with a remainder of 1. Note: input numbers will always be greater than 1\u003c/p\u003e","function_template":"function num = OneDirection(vec)\r\n  num = vec;\r\nend","test_suite":"%%\r\nvec = [2,4];\r\ny_correct = 5;\r\nassert(isequal(OneDirection(vec),y_correct))\r\n%%\r\nvec = [16:18];\r\ny_correct = 2449;\r\nassert(isequal(OneDirection(vec),y_correct))\r\n%%\r\nvec = [2:6];\r\ny_correct = 61;\r\nassert(isequal(OneDirection(vec),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":15602,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2015-09-02T15:00:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-09-01T17:44:12.000Z","updated_at":"2026-03-31T12:48:56.000Z","published_at":"2015-09-01T17:53:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003egiven a vector of numbers, find the smallest number to be divisible by all of them with a remainder of 1. Note: input numbers will always be greater than 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":43216,"title":"Encode Me From The Past","description":"Given this input\r\n\r\n x = 2, 5, 1, 2, 4, 1, 1, 3\r\n\r\noutput should be (Five 2's, Two 1's, One 4, Three 1's)\r\n\r\n [2 2 2 2 2 1 1 4 1 1 1]","description_html":"\u003cp\u003eGiven this input\u003c/p\u003e\u003cpre\u003e x = 2, 5, 1, 2, 4, 1, 1, 3\u003c/pre\u003e\u003cp\u003eoutput should be (Five 2's, Two 1's, One 4, Three 1's)\u003c/p\u003e\u003cpre\u003e [2 2 2 2 2 1 1 4 1 1 1]\u003c/pre\u003e","function_template":"function y = encodeThePast(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [2, 5, 1, 2, 4, 1, 1, 3];\r\ny_correct = [2 2 2 2 2 1 1 4 1 1 1];\r\nassert(isequal(encodeThePast(x),y_correct))\r\n%%\r\nx = [2 3 4 3];\r\ny_correct = [2 2 2 4 4 4];\r\nassert(isequal(encodeThePast(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":0,"created_by":13865,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":"2016-10-29T16:40:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-08T10:22:58.000Z","updated_at":"2026-01-04T08:18:44.000Z","published_at":"2016-10-08T10:25:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven this input\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = 2, 5, 1, 2, 4, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput should be (Five 2's, Two 1's, One 4, Three 1's)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ [2 2 2 2 2 1 1 4 1 1 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44530,"title":"Are you more familiar with iteration methods or Linear Algebra? Let's see together.","description":"Given a sum result *_x_* value of a *_N_* number of addends, build an array of _*N*_ elements _*y*_ such that the following equality is satisfied: _sum(y) = x_ .\r\n\r\nFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\r\n\r\nMore formally if x = a and N = n it results: \r\n\r\ny = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\r\n\r\nImportant notice: All the elements in y must be *different from zero* and *different from each other* . On the other hand I will not take into account if they are _integers or decimal numbers_ .\r\n\r\nHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\r\n\r\nGood luck and enjoy with the solution ;)\r\n","description_html":"\u003cp\u003eGiven a sum result \u003cb\u003e\u003ci\u003ex\u003c/i\u003e\u003c/b\u003e value of a \u003cb\u003e\u003ci\u003eN\u003c/i\u003e\u003c/b\u003e number of addends, build an array of \u003ci\u003e\u003cb\u003eN\u003c/b\u003e\u003c/i\u003e elements \u003ci\u003e\u003cb\u003ey\u003c/b\u003e\u003c/i\u003e such that the following equality is satisfied: \u003ci\u003esum(y) = x\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or  [8 2].\u003c/p\u003e\u003cp\u003eMore formally if x = a and N = n it results:\u003c/p\u003e\u003cp\u003ey = [y_1 y_2 y_3 ... y_n]\r\nwhere:  y_1 + y_2 + y_3 +...+ y_n = a\u003c/p\u003e\u003cp\u003eImportant notice: All the elements in y must be \u003cb\u003edifferent from zero\u003c/b\u003e and \u003cb\u003edifferent from each other\u003c/b\u003e . On the other hand I will not take into account if they are \u003ci\u003eintegers or decimal numbers\u003c/i\u003e .\u003c/p\u003e\u003cp\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/p\u003e\u003cp\u003eGood luck and enjoy with the solution ;)\u003c/p\u003e","function_template":"function y = buildSumArray(x,N)\r\n  y = sum(1:N);\r\nend","test_suite":"%% Test Case 1\r\nx = 6;\r\nN = 3;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n%% Test Case 2\r\nx = 13;\r\nN = 5;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n\r\n%% Test Case 3\r\nx = 78;\r\nN = 11;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n\r\n\r\n%% Test Case 4\r\nx = 2689;\r\nN = 245;\r\ny = buildSumArray(x,N);\r\ny2 = unique(y);\r\n\r\nassert(isequal(round(sum(y)*100)/100,x))\r\nassert(isequal(length(y),N))\r\nassert(isequal(length(y2),N))\r\nassert(sum(y == 0) == 0)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":181340,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2018-02-24T12:07:13.000Z","rescore_all_solutions":false,"group_id":677,"created_at":"2018-02-24T11:21:15.000Z","updated_at":"2026-04-02T13:09:38.000Z","published_at":"2018-02-24T11:49:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a sum result\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e value of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e number of addends, build an array of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e elements\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that the following equality is satisfied:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum(y) = x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if: x = 10 and N = 2, possible solutions for y are: [7 3], or [8 2].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMore formally if x = a and N = n it results:\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\u003ey = [y_1 y_2 y_3 ... y_n] where: y_1 + y_2 + y_3 +...+ y_n = a\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\u003eImportant notice: All the elements in y must be\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\u003edifferent from zero\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edifferent from each other\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . On the other hand I will not take into account if they are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegers or decimal numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: You can use several approaches and the solution is not unique. For example you can think to approach with a iterative method or, if you are more accustomed with Algebra, by solving a linear system. This choice it's up to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck and enjoy with the solution ;)\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":61091,"title":"Slicing a 4-pointed star polygon","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the area, A_r, of the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \r\nGiven (A,h), find the 9×2 matrix, M = [A1 a1; A2 a2; ...; A8 a8; A_r/π n], where\r\nin the first row (i=1), A1 stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and a1 stands for the logical 1 if A1 does not exceed the circle's area, A_r, or a1 stands for the logical 0 otherwise;\r\nin the second row (i=2), A2 stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and a2 has the same previous false-true meaning relative to the areas A2 and A_r;\r\nand so on, until last slice of the 4-pointed star polygon;\r\nin the last row (i=9), A_r is the area of the circle, and n stands for the maximum number of slices that their cumulative area does not exceed the circle area.\r\nHint: The slices of the 4-pointed star polygon are not congruent among each other.\r\ninput: (A, h)\r\noutput: M = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 840.862px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 420.425px; transform-origin: 408px 420.431px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2L\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the vertices, consider the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,h)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 143.062px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 71.525px; transform-origin: 391px 71.5312px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e does not exceed the circle's area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e otherwise;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand so on, until last slice of the 4-pointed star polygon;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=9)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the circle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, h)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_star(A,h)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [3 1; 6.75 1; 10.5 1; 13.5 1; 16.5 1; 20.25 0; 24 0; 27 0; 6.25 5];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [3.75 1; 9 1; 14.25 1; 18 1; 21.75 1; 27 1; 32.25 1; 36 1; 12.25 8];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('slicing_star.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [7.75 1; 17 1; 26.25 1; 34 1; 41.75 1; 51 0; 60.25 0; 68 0; 13.69 5];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [9.5 1; 22.25 1; 35 1; 44.5 1; 54 1; 66.75 1; 79.5 1; 89 0; 26.01 7];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-08T13:42:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-03T13:58:16.000Z","updated_at":"2025-12-19T15:03:36.000Z","published_at":"2025-12-08T13:42:41.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not exceed the circle's area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e otherwise;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on, until last slice of the 4-pointed star polygon;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=9)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the circle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, h)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi 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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"479\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"601\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1024,"title":"Doubling elements in a vector","description":"Given the vector A, return B in which all numbers in A are doubling. So for:\r\n\r\nA = [  1   5   8 ]\r\n\r\nthen\r\n\r\nB = [  1   1   5   5   8  8 ]\r\n","description_html":"\u003cp\u003eGiven the vector A, return B in which all numbers in A are doubling. So for:\u003c/p\u003e\u003cp\u003eA = [  1   5   8 ]\u003c/p\u003e\u003cp\u003ethen\u003c/p\u003e\u003cp\u003eB = [  1   1   5   5   8  8 ]\u003c/p\u003e","function_template":"function B = your_fcn_name(A)\r\n  \r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = [1 1];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [0 -1 1 0 0 0 1 2];\r\ny_correct = [0 0 -1 -1 1 1 0 0 0 0 0 0 1 1 2 2];\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":69,"comments_count":13,"created_by":7968,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10270,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-11-03T15:44:34.000Z","updated_at":"2026-04-04T03:51:57.000Z","published_at":"2012-11-03T15:46:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the vector A, return B in which all numbers in A are doubling. So for:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 = [ 1 5 8 ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB = [ 1 1 5 5 8 8 ]\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":46,"title":"Which doors are open?","description":"There are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut these doors in a particular manner:\r\n\r\n* Toggle the state of each door you visit. That is, if the door is shut, open it, and if the door is open, shut it.\r\n* On the i-th trip down the alley, start with door i and visit every i-th door.\r\n\r\nGiven n doors, return the list of open doors.\r\n\r\nExample:\r\n\r\nLet's say n = 3.\r\n\r\n* On your first trip, you start from the first door and toggle every door. Now all three doors are open.\r\n* On your second trip, you start from the second door and toggle every other door. Since there are only three doors, this means you shut the second door. Now doors 1 and 3 are open.\r\n* On your third trip, you start from the third door and toggle every third door. Now only door 1 is open.\r\n\r\nSo:\r\n\r\n Input  n = 3\r\n Output y is 1","description_html":"\u003cp\u003eThere are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut these doors in a particular manner:\u003c/p\u003e\u003cul\u003e\u003cli\u003eToggle the state of each door you visit. That is, if the door is shut, open it, and if the door is open, shut it.\u003c/li\u003e\u003cli\u003eOn the i-th trip down the alley, start with door i and visit every i-th door.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eGiven n doors, return the list of open doors.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003eLet's say n = 3.\u003c/p\u003e\u003cul\u003e\u003cli\u003eOn your first trip, you start from the first door and toggle every door. Now all three doors are open.\u003c/li\u003e\u003cli\u003eOn your second trip, you start from the second door and toggle every other door. Since there are only three doors, this means you shut the second door. Now doors 1 and 3 are open.\u003c/li\u003e\u003cli\u003eOn your third trip, you start from the third door and toggle every third door. Now only door 1 is open.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSo:\u003c/p\u003e\u003cpre\u003e Input  n = 3\r\n Output y is 1\u003c/pre\u003e","function_template":"function y = which_doors_open(n)\r\n  y = n;\r\nend","test_suite":"%%\r\n\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(which_doors_open(x),y_correct))\r\n\r\n%%\r\n\r\nx = 3;\r\ny_correct = 1;\r\nassert(isequal(which_doors_open(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = [1 4 9 16 25 36 49 64 81 100];\r\nassert(isequal(which_doors_open(x),y_correct))","published":true,"deleted":false,"likes_count":29,"comments_count":10,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3433,"test_suite_updated_at":"2012-03-01T23:30:24.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:23.000Z","updated_at":"2026-02-24T13:31:39.000Z","published_at":"2012-01-18T01:00:23.000Z","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\u003eThere are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut these doors in a particular manner:\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\u003eToggle the state of each door you visit. That is, if the door is shut, open it, and if the door is open, shut it.\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\u003eOn the i-th trip down the alley, start with door i and visit every i-th door.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n doors, return the list of open doors.\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\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet's say n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn your first trip, you start from the first door and toggle every door. Now all three doors are open.\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\u003eOn your second trip, you start from the second door and toggle every other door. Since there are only three doors, this means you shut the second door. Now doors 1 and 3 are open.\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\u003eOn your third trip, you start from the third door and toggle every third door. Now only door 1 is open.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 3\\n Output y is 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61082,"title":"Slicing the area of a circle","description":"Given the area, A, of a square, consider a circle having the area, πA, and the radius, r.\r\nFor a given slicing number n\u003e1, find the (n+1)×2 matrix, M = [A1/π a1; A2/π a2; ...; An/π an; A_r L], where\r\nin the first row (i=1), A1 stands for the area of one slice (like a pizza slice), and a1 stands for the logical 1 if A1 is smaller than or reaches the square's area A or a1 stands for the logical 0 if A1 surpasses A;\r\nin the second row (i=2), A2 stands for the area of two slices and a2 has the same previous false-true meaning relative to the areas A2 and A;\r\nand so on, until last slice of the circle;\r\nin the last row (i=n+1), A_r is the area of the rectangle, with dimensions L×r, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\r\nHint: Compare with Problem 61081.\r\ninput: (A,n)\r\noutput:  M = [A1/π a1; A2/π a2; ...; An/π an; A_r L]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 325.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 162.75px; transform-origin: 408px 162.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a square, consider a circle having the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eπA,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the radius, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given slicing number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(n+1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 163.5px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 81.75px; transform-origin: 391px 81.75px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of one slice (like a pizza slice), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is smaller than or reaches the square's area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e surpasses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of two slices and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand so on, until last slice of the circle;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 61.3125px; 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 30.65px; text-align: left; transform-origin: 363px 30.6562px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=n+1),\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Compare with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 61081\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_circle(A,n)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 8;\r\nn = 4;\r\ny_correct = [2 1; 4 0; 6 0; 8 0; 8*sqrt(2) 4];\r\nY = slicing_circle(A,n);\r\ntolerance = 1e-13;\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 ...\r\n    abs(Y(end)-y_correct(end)) \u003c tolerance \u0026 all(Y(1:end,2) == y_correct(1:end,2)))\r\n\r\n%%\r\nA = 36;\r\nn = 6;\r\ny_correct = [6 1; 12 0; 18 0; 24 0; 30 0; 36 0; 36 6];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n\r\n%%\r\nA = 36;\r\nn = 12;\r\ny_correct = [3 1; 6 1; 9 1; 12 0; 15 0; 18 0; 21 0; 24 0; 27 0; 30 0; 33 0; 36 0; ...\r\n    37.92731310242232  6.32121885040372];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing_circle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 70;\r\nn = 7;\r\ny_correct = [10 1; 20 1; 30 0; 40 0; 50 0; 60 0; 70 0; ...\r\n    94.4539467929851 11.28940594715244];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026 all(Y(1:n,2) == y_correct(1:n,2)) \u0026 ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))\r\n\r\n%%\r\nA = 70;\r\nn = 10;\r\ny_correct = [7 1; 14 1; 21 1; 28 0; 35 0; 42 0; 49 0; 56 0; 63 0; 70 0; ...\r\n    88.7511366850995 10.6077897676978];\r\ntolerance = 1e-13;\r\nY = slicing_circle(A,n);\r\nassert(all(Y(1:n) == y_correct(1:n)) \u0026  all(Y(1:n,2) == y_correct(1:n,2))  \u0026  ...\r\n    all(abs(Y(end,:)-y_correct(end,:)) \u003c tolerance))","published":true,"deleted":false,"likes_count":0,"comments_count":10,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-27T14:44:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2025-11-27T14:44:37.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-20T14:17:04.000Z","updated_at":"2025-12-17T10:09:27.000Z","published_at":"2025-11-21T15:27:17.000Z","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\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a square, consider a circle having the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eπA,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and the radius, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given slicing number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one slice (like a pizza slice), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is smaller than or reaches the square's area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e surpasses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on, until last slice of the circle;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=n+1),\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains the maximum possible number of slices, such that have the true meaning of their sum has the area smaller or equal than the square's area, in their adjacent arrangement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Compare with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/61081-slicing-the-area-of-a-regular-polygon\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 61081\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:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1/π a1; A2/π a2; ...; An/π an; A_r L]\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\"}]}"}],"term":"tag:\"iteration\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"iteration\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"iteration\"","","\"","iteration","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fa2b56e6220\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fa2b56e6180\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fa2b56e58c0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fa2b56e64a0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fa2b56e6400\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fa2b56e6360\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fa2b56e62c0\u003e":"tag:\"iteration\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fa2b56e62c0\u003e":"tag:\"iteration\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"search","password":"J3bGPZzQ7asjJcCk","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"iteration\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"iteration\"","","\"","iteration","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007fa2b56e6220\u003e":null,"#\u003cMathWorks::Search::Field:0x00007fa2b56e6180\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007fa2b56e58c0\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007fa2b56e64a0\u003e":1,"#\u003cMathWorks::Search::Field:0x00007fa2b56e6400\u003e":50,"#\u003cMathWorks::Search::Field:0x00007fa2b56e6360\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007fa2b56e62c0\u003e":"tag:\"iteration\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007fa2b56e62c0\u003e":"tag:\"iteration\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":42976,"difficulty_rating":"easy"},{"id":42583,"difficulty_rating":"easy"},{"id":43216,"difficulty_rating":"easy-medium"},{"id":44530,"difficulty_rating":"easy-medium"},{"id":61091,"difficulty_rating":"easy-medium"},{"id":1024,"difficulty_rating":"easy-medium"},{"id":46,"difficulty_rating":"medium"},{"id":61082,"difficulty_rating":"medium-hard"}]}}