{"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":54089,"title":"Ramanujan's Number","description":"About 1729\r\n\r\n1729 is the first positive integer which can be expressed as the sum of two positive cubes in two different ways.\r\nCalculate the second, third, fourth ... positive integers which can be expressed as the sum of two positive cubes in two different ways.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 66px; transform-origin: 406.5px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/1729_(number)\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAbout 1729\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"169\" height=\"19\" style=\"width: 169px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1729 is the first positive integer which can be expressed as the sum of two positive cubes in two different ways.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate the second, third, fourth ... positive integers which can be expressed as the sum of two positive cubes in two different ways.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [n a b c d] = Ramanujans(x)\r\nn = 1729;\r\na = 1; b = 12; c = 9; d = 10;\r\nend","test_suite":"%%\r\n[n, a, b, c, d] = Ramanujans(1);\r\nn_correct = 1729;\r\nassert(isequal(Ramanujans(1),n_correct))\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)\r\n\r\n%%\r\n[n, a, b, c, d] = Ramanujans(2);\r\nassert(n\u003e1729)\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)\r\n\r\n%%\r\n[n, a, b, c, d] = Ramanujans(3);\r\nassert(n\u003eRamanujans(2))\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)\r\n\r\n%%\r\n[n, a, b, c, d] = Ramanujans(4);\r\nassert(n\u003eRamanujans(3))\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)\r\n\r\n\r\n%%\r\n[n, a, b, c, d] = Ramanujans(5);\r\nassert(n\u003eRamanujans(4))\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2022-03-04T07:47:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-03-04T06:21:56.000Z","updated_at":"2022-03-04T07:47:05.000Z","published_at":"2022-03-04T06:21:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/1729_(number)\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAbout 1729\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1729 = 1^3 + 12^3=9^3+10^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1729 is the first positive integer which can be expressed as the sum of two positive cubes in two different ways.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the second, third, fourth ... positive integers which can be expressed as the sum of two positive cubes in two different ways.\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":51251,"title":"Locate a family on a long street ","description":null,"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: 186.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93.25px; transform-origin: 407px 93.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.983px 7.91667px; transform-origin: 374.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTwo children, Matilda and Labrun, live on a street in which—unlike many streets in the U.S.—the houses on one side are numbered consecutively, starting at 1. They notice that the sum of the numbers on the houses to the left of theirs equals the sum of the numbers to the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.7083px 7.91667px; transform-origin: 82.7083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nmax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 281.6px 7.91667px; transform-origin: 281.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the maximum number of houses on the street, and returns the largest possible number of houses and the number of the house where the family of Matilda and Labrun lives. For example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nmax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.8667px 7.91667px; transform-origin: 46.8667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 10, then the function should find that the street has 8 houses and Matilda and Labrun live in house 6 because 1+2+3+4+5 = 7+8 = 15.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.158px 7.91667px; transform-origin: 157.158px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHenry Dudeney posed a version of this problem in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.9083px 7.91667px; transform-origin: 52.9083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eStrand Magazine\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 7.91667px; transform-origin: 79.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in the early part of the 20\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 7.91667px; transform-origin: 5.83333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.4917px 7.91667px; transform-origin: 69.4917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e century. Although the connections might not be immediately clear, you might try Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e1215\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/8057\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e8057\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45253\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e45253\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: 25.2833px 7.91667px; transform-origin: 25.2833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as well.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x,y] = houseNumber(nmax)\r\n  % x = number of the house of Matilda and Labrun\r\n  % y = number of houses on the street\r\n  x = f1(nmax)\r\n  y = f2(nmax)\r\nend","test_suite":"%%\r\nnmax = 10;\r\nx_correct = 6;\r\ny_correct = 8;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 100;\r\nx_correct = 35;\r\ny_correct = 49;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%% Dudeney's problem\r\nnmax = 500;\r\nx_correct = 204;\r\ny_correct = 288;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 2000;\r\nx_correct = 1189;\r\ny_correct = 1681;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 10000;\r\nx_correct = 6930;\r\ny_correct = 9800;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 100000;\r\nx_correct = 40391;\r\ny_correct = 57121;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 500000;\r\nx_correct = 235416;\r\ny_correct = 332928;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 2e6;\r\nx_correct = 1372105;\r\ny_correct = 1940449;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\n\r\n%%\r\nnmax = 2e7;\r\nx_correct = 7997214;\r\ny_correct = 11309768;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\n\r\n%%\r\nnmax = 1834432;\r\np_correct = 78376578048;\r\nds_correct = 48;\r\ndp_correct = 1866240;\r\n[x,y] = houseNumber(nmax);\r\nd = [num2str(x)-'0' num2str(y)-'0'];\r\nassert(isequal(x*y,p_correct) \u0026\u0026 isequal(sum(d),ds_correct) \u0026\u0026 isequal(prod(d),dp_correct))","published":true,"deleted":false,"likes_count":8,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2021-05-16T01:51:40.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-03-29T00:43:22.000Z","updated_at":"2026-03-22T23:36:57.000Z","published_at":"2021-03-29T00:53:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwo children, Matilda and Labrun, live on a street in which—unlike many streets in the U.S.—the houses on one side are numbered consecutively, starting at 1. They notice that the sum of the numbers on the houses to the left of theirs equals the sum of the numbers to the right. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nmax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the maximum number of houses on the street, and returns the largest possible number of houses and the number of the house where the family of Matilda and Labrun lives. For example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nmax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 10, then the function should find that the street has 8 houses and Matilda and Labrun live in house 6 because 1+2+3+4+5 = 7+8 = 15.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHenry Dudeney posed a version of this problem in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStrand Magazine\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the early part of the 20\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e century. Although the connections might not be immediately clear, you might try Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1215\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/8057\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e8057\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45253\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e45253\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e as well.\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":60171,"title":"Compute the Ramanujan tau function for large numbers","description":"The Ramanujan tau function  is defined by the relation\r\n\r\nwhere . The first few values of  are 1, -24, 252, -1472, and 4830.\r\nWrite a function to compute the Ramanujan tau function for large values of n (similar to problem 59981). Output a character array representing the number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 159.566px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 79.7743px; transform-origin: 406.493px 79.783px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 24.5312px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 12.2569px; text-align: left; transform-origin: 383.498px 12.2656px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Ramanujan tau function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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\u003cimg class=\"imageNode\" width=\"28\" height=\"18\" style=\"vertical-align: baseline;width: 28px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis defined by the relation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.5451px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.5312px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 12.2569px; text-align: left; transform-origin: 383.498px 12.2656px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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\u003cimg class=\"imageNode\" width=\"88\" height=\"18\" style=\"vertical-align: baseline;width: 88px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The first few values of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"28\" height=\"18\" style=\"vertical-align: baseline;width: 28px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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=\"\"\u003eare 1, -24, 252, -1472, and 4830.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 20.9896px; text-align: left; transform-origin: 383.498px 20.9896px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute 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=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/TauFunction.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRamanujan tau function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for large values of n (similar to problem 59981). Output a character array representing the number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = RamTAU(n)\r\n  t='1234';\r\nend","test_suite":"%%\r\nassert(isequal(sum(arrayfun(@(x)str2double(RamTAU(x)),1:300)),-33462718906943))\r\n%%\r\nassert(isequal('35026197988533741481392462014030777106032022900305174080200946515536689469217724416',RamTAU(1083591480746809)))\r\n%%\r\nassert(isequal('-56035830452204334365253043086653137034978298115410752581410092847542624691526041600',RamTAU(6396126482137392)))\r\n%%\r\nassert(isequal('60369351784615103602642893241540205064068509732817984073984584133811409912871577056147',RamTAU(3937376385699289)))\r\n%%\r\nassert(isequal('78999490468390654291533227192728431731231180919238405888372680396606799872000',RamTAU(304250263527210)))\r\n%%\r\nassert(isequal('59265915279995252022669251849330665821948761921021583428287020528137123479352033280',RamTAU(3074855972298005)))\r\n%%\r\nassert(isequal('-304100402266162242917469052031829545958531212926846642233958510388617161427169145383643',RamTAU(5620501349820009)))\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":145982,"edited_at":"2024-04-30T22:16:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2024-04-30T22:16:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-30T22:13:52.000Z","updated_at":"2025-12-14T20:29:34.000Z","published_at":"2024-04-30T22:16:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Ramanujan tau function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"28\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis defined by the relation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"172\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"88\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The first few values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"28\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eare 1, -24, 252, -1472, and 4830.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/TauFunction.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRamanujan tau function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for large values of n (similar to problem 59981). Output a character array representing the 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Number","description":"About 1729\r\n\r\n1729 is the first positive integer which can be expressed as the sum of two positive cubes in two different ways.\r\nCalculate the second, third, fourth ... positive integers which can be expressed as the sum of two positive cubes in two different ways.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 66px; transform-origin: 406.5px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/1729_(number)\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eAbout 1729\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"169\" height=\"19\" style=\"width: 169px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e1729 is the first positive integer which can be expressed as the sum of two positive cubes in two different ways.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21px; text-align: left; transform-origin: 383.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate the second, third, fourth ... positive integers which can be expressed as the sum of two positive cubes in two different ways.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [n a b c d] = Ramanujans(x)\r\nn = 1729;\r\na = 1; b = 12; c = 9; d = 10;\r\nend","test_suite":"%%\r\n[n, a, b, c, d] = Ramanujans(1);\r\nn_correct = 1729;\r\nassert(isequal(Ramanujans(1),n_correct))\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)\r\n\r\n%%\r\n[n, a, b, c, d] = Ramanujans(2);\r\nassert(n\u003e1729)\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)\r\n\r\n%%\r\n[n, a, b, c, d] = Ramanujans(3);\r\nassert(n\u003eRamanujans(2))\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)\r\n\r\n%%\r\n[n, a, b, c, d] = Ramanujans(4);\r\nassert(n\u003eRamanujans(3))\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)\r\n\r\n\r\n%%\r\n[n, a, b, c, d] = Ramanujans(5);\r\nassert(n\u003eRamanujans(4))\r\nassert(isequal(a^3+b^3, c^3+d^3))\r\nassert(isequal(n,a^3+b^3))\r\nassert(length(unique([a b c d]))==4)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2022-03-04T07:47:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-03-04T06:21:56.000Z","updated_at":"2022-03-04T07:47:05.000Z","published_at":"2022-03-04T06:21:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/1729_(number)\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAbout 1729\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1729 = 1^3 + 12^3=9^3+10^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1729 is the first positive integer which can be expressed as the sum of two positive cubes in two different ways.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the second, third, fourth ... positive integers which can be expressed as the sum of two positive cubes in two different ways.\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":51251,"title":"Locate a family on a long street ","description":null,"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: 186.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93.25px; transform-origin: 407px 93.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.983px 7.91667px; transform-origin: 374.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTwo children, Matilda and Labrun, live on a street in which—unlike many streets in the U.S.—the houses on one side are numbered consecutively, starting at 1. They notice that the sum of the numbers on the houses to the left of theirs equals the sum of the numbers to the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.7083px 7.91667px; transform-origin: 82.7083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nmax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 281.6px 7.91667px; transform-origin: 281.6px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the maximum number of houses on the street, and returns the largest possible number of houses and the number of the house where the family of Matilda and Labrun lives. For example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"nmax\" style=\"width: 27px; height: 20px;\" width=\"27\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46.8667px 7.91667px; transform-origin: 46.8667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 10, then the function should find that the street has 8 houses and Matilda and Labrun live in house 6 because 1+2+3+4+5 = 7+8 = 15.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.158px 7.91667px; transform-origin: 157.158px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHenry Dudeney posed a version of this problem in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.9083px 7.91667px; transform-origin: 52.9083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eStrand Magazine\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 79.3417px 7.91667px; transform-origin: 79.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in the early part of the 20\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 7.91667px; transform-origin: 5.83333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.4917px 7.91667px; transform-origin: 69.4917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e century. Although the connections might not be immediately clear, you might try Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e1215\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/8057\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e8057\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45253\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e45253\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: 25.2833px 7.91667px; transform-origin: 25.2833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as well.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [x,y] = houseNumber(nmax)\r\n  % x = number of the house of Matilda and Labrun\r\n  % y = number of houses on the street\r\n  x = f1(nmax)\r\n  y = f2(nmax)\r\nend","test_suite":"%%\r\nnmax = 10;\r\nx_correct = 6;\r\ny_correct = 8;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 100;\r\nx_correct = 35;\r\ny_correct = 49;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%% Dudeney's problem\r\nnmax = 500;\r\nx_correct = 204;\r\ny_correct = 288;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 2000;\r\nx_correct = 1189;\r\ny_correct = 1681;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 10000;\r\nx_correct = 6930;\r\ny_correct = 9800;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 100000;\r\nx_correct = 40391;\r\ny_correct = 57121;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 500000;\r\nx_correct = 235416;\r\ny_correct = 332928;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\nassert(isequal(sum(1:x-1),sum(x+1:y)))\r\n\r\n%%\r\nnmax = 2e6;\r\nx_correct = 1372105;\r\ny_correct = 1940449;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\n\r\n%%\r\nnmax = 2e7;\r\nx_correct = 7997214;\r\ny_correct = 11309768;\r\n[x,y] = houseNumber(nmax);\r\nassert(isequal(x,x_correct) \u0026\u0026 isequal(y,y_correct))\r\n\r\n%%\r\nnmax = 1834432;\r\np_correct = 78376578048;\r\nds_correct = 48;\r\ndp_correct = 1866240;\r\n[x,y] = houseNumber(nmax);\r\nd = [num2str(x)-'0' num2str(y)-'0'];\r\nassert(isequal(x*y,p_correct) \u0026\u0026 isequal(sum(d),ds_correct) \u0026\u0026 isequal(prod(d),dp_correct))","published":true,"deleted":false,"likes_count":8,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2021-05-16T01:51:40.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2021-03-29T00:43:22.000Z","updated_at":"2026-03-22T23:36:57.000Z","published_at":"2021-03-29T00:53:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwo children, Matilda and Labrun, live on a street in which—unlike many streets in the U.S.—the houses on one side are numbered consecutively, starting at 1. They notice that the sum of the numbers on the houses to the left of theirs equals the sum of the numbers to the right. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nmax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the maximum number of houses on the street, and returns the largest possible number of houses and the number of the house where the family of Matilda and Labrun lives. For example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"nmax\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en_{max}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e = 10, then the function should find that the street has 8 houses and Matilda and Labrun live in house 6 because 1+2+3+4+5 = 7+8 = 15.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHenry Dudeney posed a version of this problem in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStrand Magazine\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the early part of the 20\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e century. Although the connections might not be immediately clear, you might try Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1215\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/8057\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e8057\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45253\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e45253\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e as well.\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":60171,"title":"Compute the Ramanujan tau function for large numbers","description":"The Ramanujan tau function  is defined by the relation\r\n\r\nwhere . The first few values of  are 1, -24, 252, -1472, and 4830.\r\nWrite a function to compute the Ramanujan tau function for large values of n (similar to problem 59981). Output a character array representing the number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 159.566px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 79.7743px; transform-origin: 406.493px 79.783px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 24.5312px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 12.2569px; text-align: left; transform-origin: 383.498px 12.2656px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Ramanujan tau function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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\u003cimg class=\"imageNode\" width=\"28\" height=\"18\" style=\"vertical-align: baseline;width: 28px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis defined by the relation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.5451px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 20.7639px; text-align: left; transform-origin: 383.498px 20.7726px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"172\" height=\"35\" style=\"vertical-align: baseline;width: 172px;height: 35px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVgAAABGCAYAAACJx4wfAAASKUlEQVR4Xu2dWaguRxHHk3fF7UkJKtEHxS1gXEiIqLiARISIG0q4qMQYkCCixCASgkRxQSQPLqgEcYkGFVEEFRQURWMERSE+JAFF9ClG0XetX/j+l8rcnume6Z75er5TA8W955yZXqqr/11dXVV98UXxBAeCA8GB4MAqHLh4lVKj0OBAcCA4EBy4KAA2hCA4EBwIDqzEgQDYlRgbxQYHggPBgRTAvsrY8qPOWPNCa89vO2tTNGdfHPhfR80NxaajwVizKamBfppV+HujRw0q/oL9/O/GjXnJobxnJerzVX3LfnhT47qjuLPFgV8fuvtk+/eJI13/h/3+rxVsmZJjX/aLK+qIT3fEgbGV9Hrrw2cH/fiN/bymYADslxtdY/SaBOA+wX73zx3xNpraLwfYpX07IWOfsN99oKLZgPiLBt//2X6+0ejHFeXGpzvlwNRW5ZvWpzcO+lUrgHPYBMh/2EjaxpZ1z2lnvLtPDqSUiFoZSwHsqwNc9ykgLVo9BbCPtwr+5ABO9W0tMB+3it9vxBbrSS06HWUEB4wDqbOGNQA27K1nWNxyg/8C483dA/4AdM822nK7ri0dQPu5Mzxe0fV2HAiAbcfLKGmEAzmA5bMPGt02+B57Eprslg+HXO81WtMOvGV/oq7jciAA9rj8PxO1lwAsjMBtC4H0z832w0c35hJ24U8ahcvWxow/weoCYE9wUCu7hFmUw/2rjDj7+e/h59zBp5TQCw7iSwGWiv9iNHTd2to/FU8DaMsTWcwklxoB7i0eBmPrhalFu0+tjD0BLDLzeaMtzXKnMN6M8UOFChkY90ujnxvhYfJ8I5RIMG/Kg8q7tS4GWJidEkhcUK484YEHXG83wm2slXDL1NGyzFOYDFv3YS8Ay8L+M6M4e5gvIYDmN4y+W8A/FrGnGr3LVePPoMaUSXb3VxyAuApgqVcn+r6rpxoEAHO/stICgosQvpGnvDjNnw7bfrEHgAVcCfqJHc9y2ZBm+pkMyAKUNxjdP6jqXvv5GUZvNhruYlGW3m5E8ArvVAMsdatC345U5ctZcvwvZRJ5vTVlLXMEi9VTjCJC7Tjj3TvAIh9EOpYe6iKzNxm9zSjcGR8pU3I5fZ39eu75jXybhxqsL5NdLgEmTQA2FUqLMfiyBPofZ+rU1wpTsTmvCX4aIDwjWtl3fc+ZoM87rK7YldgCYcAneATTzjPr2bTrEnoGWLXt6QVzSsD6bnsXeyFz8dG7HpnpxoM/bONZfNAcmT8PGAnkCOn323yVhvxfu0Du/34oYOiaik2c1AEcgAmEmwAs9QE8dw74cCqTdo5w18oxpgKc29FkW9l4fZs08OwwCEH+khFbJbYzJZO3tn89f98zwJYu8MxDxvVfRtcdmH3qACuZInkPPvkALDzAuwif/amAJMDyqwdQLJFNwPw+IxYvbwNHdm410jlKc4ClcalQ2rHVo6QzvbxTKtwt2itTBH7Ga9jZ/mPlQiQwIewYc4dWZFxRhvamFn3aSxm9AuycBR4A0Bhqkp8FgNXhE6f7PG89/AsYTp34s6sDLEs1fDDusUZvMZICpJ3nucN8oupVAFbGY7Qh/2wdSttyQmvgtrQpM4iAXWu7mT8Blc+yVuRjBIq0HKcWZfUKsBy2sPWda8I5SwArv1MWE52TKLfElH/+mEaakifkg93e1W4R4z1A+jFG3gyxCsBSGZP4p0beP5ZOr7XlbTGxpsrArsJWa8vMXRKM1j7F8vjwrnQlQrg2j3spv0eARWl50GjJTvAsAaz66j2YtKPOzSN2cH80mopEBYh/cVB8/C5P50/vtL/hX6tHZjcUM35//mC8NNBgalKkQmnXTm241iTFQ4JnrvZQ0x5pmq0j4ySE3n5UKoQ1/dnLtz0CrM42luygzhLAYn9FkXu5kbwCxg6jhvIov9UxMwGL3A+NZFLz36dkJiXv5xW0FgBLBalQ2trMRLUT1butjCVYpg5/2MPA5RYHyiVvLZEeeE6grfPInYZJcosRppOhEIz1iXpL/YlZRbHZYlbAtsp2EveTVxg9zuh3RgCpDgH86acXwlce3qvl81bfazxfe6iQbRoHDWgMjAX/zrFj9wiw2nUsMbOdAsAyJu8zes5Bthljtujajt91kHHwxpu5tPVnDnHYxTPmjiUepw55Zfa8JTE3+I76U+WuZiLQ5BpLbZhT19eanCnTRaouv32WJplbGHjvDUZMdNmfpX3Knvp9+5tOdXOATbtKgJ33ZMJAuOQUPeQ9bQFkh0Ko/iGEnDpj2ilxDytdtXNjWaOhy9vib1aJT16NYOsWgbl25R4BVorKEsVnzwArrRFfUubfx4w4VGKMfGJ08IS5R1Y9L0/aRfM7lJ6pfCVTixg7WEAdTwP/oERBY9GXqwMsjUkJ7DFSG8pOgpr/HSM0GwzhAB62LQZMj49TVvtzAKtvfVQbqyFaJQ9bcoRDd0CVTHwGCE107KBLSSjwYQUgVYfaogHmZ9qCbx799VtN8YV35qR9PDbAavKwGKYOHOiL+D4nnLRHgNU4niWARS5/YISyklqENY+kDJEv4BIj73cv00rJ7REa96HrVcorSvOLf6cUhE0AlkYMQ2mPkauAzn7PyG8X2RpjJpjy/ZwLsGIqGuodRueMtMJpy1I68XMTS5oNdaVWUUXXHYPfXghb/9+fFqcCWaTRU+9cv94A2NajNb88v/tKHezp0I+SS01ouVbMnee58ib/vmSlzFXotypbR3fBPGyRPr2YVrecJjmX8V5DxWbk/Up9IEbJxJ8C2BzIeCEs1b5zY9jD372b2dihjxaWEjPMsE8BsBeOcirXyFxZmGMKyikOfh4tsUun2j53ns/t/yPebw2wWpE4ofMnfFWNrPxYgzjcEoxNuBKQGkayDQFA243S6LYx7wWfJnLMdUeuV/SnlRBWsrzJ536HkNLa/S6hZMwCYPPDsiXA+gVubAHVPGrp+lnjqZHn4OCN1gArjSIHZrMbuvADTcKSAdK7JZPVb01TmrFMEiVl0bWxQ66SLbDqOoa9e+GwZD/zC9iYLHmb2ZLD1B41WPVpybzc2yFXzqzlF9Dc7jMrUO6FGk+NOfU8/O6SgRyrRMJRCiqzG7vgA+9sX+LbWnqaL1BLJbnxglGqUVJvSkNVPWOasNdeW9moSjS9BUMxeUgwLM+DZyrow/N4qd25R4Ctmfx7Alg/fmM7My8DLRU28XiTYKJWAKtGrzXJl0xovtEq6QeRwcV7IJVcJXeaT5m5lVU201KNcuxUMyeEw1smWgqh5/cxvAhyC4v3mlgqcz0C7JgslMj/ngDWKwYp88BwbErOMUp4xDslc7y0rOx7LQBWzCq1N2Yb1egFf/gjgJUj8dDdR1UKHKdWNx+5ltJQZfPVtgZhIQBgzOdU5Q2FyAvZcJVXP2i3fHE3WZEbjU2uGO+aM9x5wMfnun4viXqi/h4BlnaRnOfrRqmUe1N82xPAelvvcPw43MQLiAfPn9a4An9x4VwzFen5caoFWJ30Lt2m5SZazd/9BGIrT/zwLUbkRh0T3pJkEALQlIbqQR2NEod/bkUYA3T6x8TgGSZW9qfo/pRc4Eo/yIkJwC45Ra/h7drfMgmU38LLKOCKwze5evEJLrGtj7W1V4BVsMrc5D97AlivpHiTogKE8G0mdzFPS5OjxrzUdFct5zUAK2bQiF48BjxDPEDp92N+pP67McDTO5r8qa2pn7RosLhvnTM6n/xhMGI5QPe3R9B2gIUTdTScLxrdfShvjmtMtdBsUIA/3GMhIzKOyDlCg0lNRyIOtJuaw49eAXYJCAzNRb3vZoZJ+5lLpAW8wug2I0x4AtglB5hjIrp08Vos8ksB1qcqbMmAxR0Z+VATVdfvKgRvqh4JeMru4yflmM3T+2amEkb4utkqARxjB3AsEh8xol768CujLxshKF4L6HkMloypItdYTHSr5x32fyYik7PFwtIrwMIvFvmSGzXowzuMxCfxGllhES4Nh14yRrXf+JwdLKIsmgpxndolLq1XixA72TFz3dKyR79bCrC9uWO1ZgzAzHUrpfchLalfq/jSe79ybi5L2rSHb0pc10r60TPA1spGSf97fWeN6C36usWcvoCnSwD2mO5YCB40tuVuJTTS0HM3UdbUh5aCHdVHnZWWl/MwKC1nj+/lPAxK+9QzwNIHDo/P4s3DOQ+D0vH17zHW5CDZPE/1XIDVtnSpa8wS5vhv2Dp8yGjuzZBL6lVU2pKbKHP1YRqouVH2VKO3cnyrjd4aTjrkyT+1ByrefUzlzp1jvj21cpLjZ49/bx29teY8zvJvzuB7d6wrreQ1LumbarBW9JKAgWzHC19QGrX3NAR1+vEyoxo3Edmoak7RC1nQ1Ws5F7k5je1dg1VfWsjLHL4c+10dIrfwjFlj/s7iTynAymOAzg+vr51V4cKXASNOzTlhnJNUeWF1j/hMCbZbmSXoS42R3XtHtPYRbMGvtcoY5r2tPSnfC8DCT9p6zxGUmrXGcqxcv4CORXjNadPR+VYCsD6P6DHcsbxTcu2kmjM4vb0LMHNFMUmJ/QPIrmkrPjYfkL+vGSmxttoj9625Dvn6fk8Ae+wxWLt+edMoaEb1odR8yqiVcrN2Py4oPwew3h1rM+dcayX14kiOmxP+jjw1Po+bMzYq7J4DAbDdD9H+G5gDWBnt14pz9xxE4Llb6aVGOBz7m2p5b2lI5P5HKXqwBgf8QaHKr7X7ycPBt3dLxWQNPkWZFRyYAlid5rEVG95RU1Hlw/6l3HujZ7j1S5XNYc7YLZA1bYlvzyYH5LYzXMThhr8TqpQ7/kqf4Tcl15iU1hPv7YwDYwDrjc09dKmFwbuHfkQbjscBhUBz95nMTlOtQZvlGfMgQQM+d3hnaBdPlYuiQqgvz5oBLMfjcNR8AQdSAJuK4T82604tFPTY/DyL9StD19y+j23xa7L/50xzc9sY73fKgRjoTgcmmhUcCA7snwMBsPsfw+hBcCA40CkHAmA7HZhoVnAgOLB/DvQGsDqNJWP9liGx+x/J6EFvHOAs43ajPxgtDYborU/RnpkcaA2wRN3cP7MNvA6wIoTXGhHNcZZCQBewKz5ZmQPII8+SfBvMAWQZ33HcwMIDZuXB6rn41gCr21E5YZ0DtAg091YhnCQyCYDtWWpOv23ykyX3BXlE5wCtLtW8yb7j6pMA2NOXl9EetgZYfAMV3kpo6w0zgVbhiwGwZ1goO+g6Cz4AKS10SfCB3LgCYDsY0GM1oTXAqh9LgTYA9liSEPWmOFADtAGwIVMXlQCsbErcYEoUDBmdHjDCgE8Ey9QKPRdoA2BDKNfkAPLFFT2EayPLVxldbvRpI6K7xvJdLAHaANg1R3InZZcArLqCfZVwPwD2GiMuKOPyOX6Xu2K4FGgDYHciODtupmSMUNg7jC49KAzcYpq7qWMO0AbA7lhIWjW9FGAVPqv4bK5O5rnPqDQDkU99yLepDF0BsK1GNsoZ44DybCjHKKGwyqxVemWMEtDjJUAiolSe5ADYkMEiEwFsklAiTLoFVUJ5s/1u6pYBv+pTFprCXUape7UCYEMo1+aArtvhIPVqI7xdlDkul/MCcxmeBeQqZud2q9FPDmUM2x0Au/ZI7qD8Ug1WeWH9FionlClgxeVlyn0rAHYHQrPzJirpi99BkceVZ+w6pBSwMhem3LcCYHcuKC2aXwqwCOVwKzQmlEuAVX0JgG0xqlHGGAe8fOniTt1Um7oxYwmwqu4A2JDDIhOBhNILoISSVZzDLh62/AgVmgGXI5KkO6exDocgADaEck0OCPS8WUumLuT2ISO2/DyYsjAF6M6znMY6bHcA7JojuZOySzTYlFDKJougXnYAWQAWrRa71FxhFLu42O/Og1BHLoKdCNGOmilTl7e1yiaLixbeMQAtrlvIMe5bS28ARrm4zigCDXYkIK2bWgKw91qllxyAVPZTD4Q32t9qb33UJYeUpZslOdEdOwxrzYco7/Q5gIw9mFi8BYRLIg9TXGN3h+aL8iEvA0Jmxw7DTp/zZ7iHJQA7hz1s8UsfwHpOvoLScuO94EAtBwBjtNjS5x57cU6+gtJy472dc6A1wM65liO2TjsXnhNufupK76nuxo3HJywMNV1rDbA1bYlvgwPBgeDASXEgAPakhjM6ExwIDvTEgQDYnkYj2hIcCA6cFAcCYE9qOKMzwYHgQE8cCIDtaTSiLcGB4MBJceD/ZpTAgx/IMZMAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.5312px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 12.2569px; text-align: left; transform-origin: 383.498px 12.2656px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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\u003cimg class=\"imageNode\" width=\"88\" height=\"18\" style=\"vertical-align: baseline;width: 88px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALAAAAAlCAYAAADiHGOuAAAIRUlEQVR4Xu2cS6h/UxTH739OXiMGFAaUojwjijxKJCmPGEj6e5QkEQb6JyEGkoFH0s3AqwyklEcUkWdRigHCgJFXzFmfnG+tdvuxzu+c8/vdc51Tq3vv7+zH2mt/93ru392ztTyLBGYsgT0z5n1hfZHA1gLgBQSzlsAC4Flv38L8AuD5YeAKY/l7o0/nx3qT4xutxctGvzVbdg0WAEcltTPascFnGwHi3ficbIt63OiW6AFdADwfGADeS40umA/LK3EKiF81uiQC4gXAK8l47Z3OtxlfMTqiYV5pd7vR6Ub7dVx+bD8fNXppYq6PsvHfN9rf6JwI+Cr8sI7HjM5orHfJQky8qWMMf7AN8qPRHUZPVgZ8yt7trbx/2t7dMAZDhTEe7njkNYfmtIFzvWH9f2jxvGjggVJeQ3eAcY3RYZW58IlfNHrT6Fmj342ONLrW6FTX7x77/cGJeMb0v2OE5r/JqHbYIiyg0b81wmViXdlnAXBElJtrE9W+fxmLzxe01d32+QPdEn5pHIShK4Xfg4y+GzpQ1/8j+/lnB+IFwCMJdZ3DCHyH2KSl1BLB3a1GNX/xZ3t/aMf40SMCbGpZsLYnjIo8Lxp46i0YNv7XXfdjK8MQnL1rFPWPT7G2c8khy40ouj7/NwDjK15nRJTL87fR60Y+r4rQ7jTyARHtMNH4o+cZPWKEr6f+CNibTfzB640uNsJ3TbMDkcwA5vhXozGCLwVY8HtCwuuwI/Zfb2R2ktGJRhRZhvq/nifcow+NsunDKIBhED/qTKOfjA43Ik93rhE+z+dGU6dphgoa/uCfRDn8wvczRgIi6R//KDDiMzbev9dYaa4Sk08SXuaafmQPMIOA9gCjY9wkNXACeiJxDgsHasijDMU3NkhJm3Ng7jLi0HkeS/PC19tGadouDeCQ420N5mtpPvxg8JYNYiMA1uKJBG82QtOw2K/cRkWjW23KkM2gb3Q+zYMGQrBoRX/QPD+sLz3ltL28G+TKrq/6lCLtVDYA9+pObgzFhurg8Hcpypb/W43Cg4LEFQGUJZ59BiE45JZ3RQCZsh2pv+plmBsbuV9lVPLxNXYWqzUAsxFoDjaQ+jSL95PUmC4JYRMAlh9Vyk1iopT0T4WvLIDX0oABK1SriEk2aOBc8cFnBnIHB/nJ7A8FsNZf0r6qfMkybdvcWBAOLOk4LBUpOvoTLOr5zOFBQSJt0mAS+WK9UYQePwo+L7LPa1kLySEbyNUAjPkCcGz8hcnkLEKnOsd0CcCb+FxgKZlifxBzmj11JdgQXJGa0D2AU9dEMtDBSd0TvR8LwGhA9u8yo1w+FWBR5eOdB7uAqEwASix3B0N94Dt1iRRPpAUUafxIxa4qhxKAteklp18BBkyP4aNNCWwP0NY8EZBHkvQRAEtBwFMuMzAGgFWCblXxJBeZey8HKaqSJRDAGUNuVk3OgPqLyoFK+/YGsDebpSDDMz3UxLVANfT9P90Aff1mP6/XMpFiQATAvvQ6BYC1j6UCRypXv+/iR+tmzccZ5fxUHcSSu+TnYY4PjJ4zilYEFYNlc+E5Dexr6qUEsnye2sKGAm+s/gLwEEuRBl6tw9AHwGx8zpRKSayiIASU92zs6P0HzeddQh2ykp/OHskVitx/UADd5zpo7yDOO+S5lIvXviW/qAS+TQRxAnBEwDm+pZkIaHEfSgGf79sXwDk/edU02irghXe5Cn5PhYVa9uKTbuEtBcFhON6olnHIyR9Zkn7Mpv9SDVxzyBncmxn+jviDnqlNAFgbAx+1kizvEVYasGIiyUMiQB/Q1Q5EBMBqU1MCHL4+SiIKXtp5d8DvizS+/0yWOL3r4LMptQofcttn1Mo45ABclUEKYM906v9KOEyiRHcLEDmG1v2Z9zVriXzM2x9G3uTKdfARvA8KSwe4BWApAmRRyg7wzh+eiNxYw4FGtRQfoCM1puKI9pU99RknLzftM+u610jZDPm/ciUZl7Sr92+VpmtlbnLroy8avqgoUwCrA4N5DeNP9lkdgFc1yZGNGLNNajWUz9QmcGjvM0LL+kClFAQpilZuOJfnbeXIBY6WdpW7FrmAo3QZxRryt7mHyilgUDlZBR65RR4ofg3wyTp5vIWS/6s6AQEauWLJVrjxn/XZW/FXvMifC+K8yQWkXKaGaaJZKkjyeVqBTB9Gp27bqjShQdKyMNqFbzbkhOcD3ZxW9xqYtakCyIai4UnstypQ9PP+d62c3Kp2efkqIPPKivcpP+mYuWBT8QUy4EmzC5ID8kVJ9L0jgQ/OtzyKQV8OwCzsfiM0E0xzkYJL0iwo6vNMDchVxvf3OXRXgQNKpP6QkXxCaWSVRtPgRBUkuVHwkh4AD2DAu89I7Zlzu8dmooVqF9r9YYrIxedq5QL4awIaQ6YfWcGzdx3URnOzfip53nXIHSqfzeBwvmD0pVHucCqHXb18FLkL4YUyl+pbZCOnbNPygfvOjdxfK2x037HW0R5w4gu/ZcQtNS7zSCHIcvt4KxdLhdbcB8CtDMU6BDOXOcYGcK9v6u5QIeEGcOsMjU6QyV0Krovm4gCsDrFW83t1fQA8p+rbpvdwbACzHjRW6Ju6m158Y35wxL8HILe73QE4TemF19kHwH1KhjtchpOzNwWAYVr/+CN3uWryRa1hgt7riwLYR6y1XOoa1jiLKXwmJyrj6MJw5fAx5/K1oOi6aIeboXJzqF9LuLpNLwdcgwJi1HzftEiIqRk3wsxTmNjr1qCsAwHNWN/WnbGIxmW9BeBxZ9v9o2GpqEblHooLu1FrbnRXFwBvVPzL5EMlsAB4qASX/huVwALgjYp/mXyoBP4Fy0c6RPG3PHIAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The first few values of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"28\" height=\"18\" style=\"vertical-align: baseline;width: 28px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 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=\"\"\u003eare 1, -24, 252, -1472, and 4830.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 20.9896px; text-align: left; transform-origin: 383.498px 20.9896px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute 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=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/TauFunction.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRamanujan tau function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for large values of n (similar to problem 59981). Output a character array representing the number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = RamTAU(n)\r\n  t='1234';\r\nend","test_suite":"%%\r\nassert(isequal(sum(arrayfun(@(x)str2double(RamTAU(x)),1:300)),-33462718906943))\r\n%%\r\nassert(isequal('35026197988533741481392462014030777106032022900305174080200946515536689469217724416',RamTAU(1083591480746809)))\r\n%%\r\nassert(isequal('-56035830452204334365253043086653137034978298115410752581410092847542624691526041600',RamTAU(6396126482137392)))\r\n%%\r\nassert(isequal('60369351784615103602642893241540205064068509732817984073984584133811409912871577056147',RamTAU(3937376385699289)))\r\n%%\r\nassert(isequal('78999490468390654291533227192728431731231180919238405888372680396606799872000',RamTAU(304250263527210)))\r\n%%\r\nassert(isequal('59265915279995252022669251849330665821948761921021583428287020528137123479352033280',RamTAU(3074855972298005)))\r\n%%\r\nassert(isequal('-304100402266162242917469052031829545958531212926846642233958510388617161427169145383643',RamTAU(5620501349820009)))\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":145982,"edited_at":"2024-04-30T22:16:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2024-04-30T22:16:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-04-30T22:13:52.000Z","updated_at":"2025-12-14T20:29:34.000Z","published_at":"2024-04-30T22:16:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Ramanujan tau function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"28\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis defined by the relation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"172\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"88\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The first few values of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"28\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eare 1, -24, 252, -1472, and 4830.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/TauFunction.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRamanujan tau function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for large values of n (similar to problem 59981). Output a character array representing the 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