{"group":{"group":{"id":59247,"name":"Sequences and Series VI","lockable":false,"created_at":"2023-01-02T15:30:09.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Sixteen more problems on sequences","is_default":false,"created_by":46909,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":29,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":6161,"published":true,"community_created":true,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"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\u003eSixteen more problems on sequences\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\"}]}","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: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 290px 10.5px; transform-origin: 290px 10.5px; 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: 267px 10.5px; text-align: left; transform-origin: 267px 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: 117.483px 8px; transform-origin: 117.483px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSixteen more problems on sequences\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2023-01-02T15:36:24.000Z"},"current_player":null},"problems":[{"id":54355,"title":"Compute a determinant","description":"Write a function to compute the determinant of an  x  matrix with diagonal entries equal to an integer  and other entries equal to 1. For example, a 4x4 matrix with 3s on the diagonal and 1s elsewhere has a determinant of 48, and a 6x6 matrix with 4s on the diagonal and 1s elsewhere has a determinant of 2187. Return the answer as a character string, and see the test suite for forbidden functions. ","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: 84px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 42px; transform-origin: 407px 42px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 155.058px 7.50833px; transform-origin: 155.058px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the determinant of an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.38333px 7.50833px; transform-origin: 7.38333px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 148.6px 7.50833px; transform-origin: 148.6px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix with diagonal entries equal to an integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.5417px 7.50833px; transform-origin: 55.5417px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and other entries equal to 1. For example, a 4x4 matrix with 3s on the diagonal and 1s elsewhere has a determinant of 48, and a 6x6 matrix with 4s on the diagonal and 1s elsewhere has a determinant of 2187. Return the answer as a character string, and see the test suite for forbidden functions. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function d = det1m1(m,n)\r\n%  m = value of the diagonal elements\r\n%  n = number of rows (and number of columns) in the matrix\r\n  d = det(m*ones(n)); \r\nend","test_suite":"%%\r\nm = 3;\r\nn = 4;\r\nd_correct = '48';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 4;\r\nn = 6;\r\nd_correct = '2187';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 8;\r\nd_correct = '196608';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 6;\r\nn = 10;\r\nd_correct = '29296875';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 7;\r\nn = 12;\r\nd_correct = '6530347008';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 8;\r\nn = 14;\r\nd_correct = '2034669218547';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 9;\r\nn = 16;\r\nd_correct = '844424930131968';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 10;\r\nn = 18;\r\nd_correct = '450283905890997363';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 3;\r\nn = 11;\r\nd_correct = '13312';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 4;\r\nn = 23;\r\nd_correct = '815907549834';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 35;\r\nd_correct = '11510768301994760208384';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 6;\r\nn = 47;\r\nd_correct = '7389644451905041933059692382812500';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 7;\r\nn = 59;\r\nd_correct = '88244140798466714911277191605426368090776535040';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 8;\r\nn = 61;\r\nd_correct = '34545486530294388841908797440350722120525547688848068';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 9;\r\nn = 73;\r\nd_correct = '8530295625153132122531360242377305017830502727444478011599189180416';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 10;\r\nn = 85;\r\nd_correct = '13474065260887738958592269707715179680415947079403261118461216165154684923152533534';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 3;\r\nn = 102;\r\nd_correct = '263671324847471715511314266718208';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 4;\r\nn = 204;\r\nd_correct = '1484516583827264085834448808857972334348585766879821838001899461159787931647377900755616082956921589';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 306;\r\nd_correct = '1317222222185582404750178752250122195777390931963039169534621462737000828454913561993123005617768628458845537125891322518059516757378713953735609547341136632820701551671775183198685757440';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 6;\r\nn = 408;\r\nd_correct = '124951598502560034896394269652129946331757853618449267769253601154315933731589398710022481465344299103361544144970312116700012143186237553149274793353112011968516101168494470432107221238134466674961271002967647750880848795089462041698055925535390010827629936329685733653604984283447265625';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 7;\r\nn = 131;\r\nd_correct = '19787144122548913527680843308148452884189065069542617898413668362936707627112683949809939148161587085312';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 8;\r\nn = 253;\r\nd_correct = '239706290717189721123302390680335669996774024601257391994275410885640688563963931353802954101567887964817392073386621397628285918677445066165167532386216609465769894926518235382109183970227816546732204593629492112260';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 9;\r\nn = 275;\r\nd_correct = '7914853329031654317236831887919901653197511900121381509601494400150421009291867067475308053933954912350106192489235274200248351166261489849830021845471460969340960380037223657169438239256397454763033517899984282261414401045612047034322789796027564032';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nm = 10;\r\nn = 299;\r\nd_correct = '71255522567471178828644915252719777959098869895626873084614916973200846625340632259847469229339030912305938532041146325885842950734329231286703535740125377847932872013226581480729929782019398917380980682083141726871697818941018246912605765632004456807782308943877135926039567345812106868';\r\nassert(strcmp(det1m1(m,n),d_correct))\r\n\r\n%%\r\nmn = [4 30; 5 23; 6 21; 7 18; 8 15];\r\ns_correct = [101 97 115 94 111];\r\nfor k = randi(5,[1 3])\r\n    s = sum(factor(str2num(det1m1(mn(k,1),mn(k,2)))));\r\n    assert(isequal(s,s_correct(k)));\r\nend\r\n\r\n%%\r\nfiletext = fileread('det1m1.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'java') || contains(filetext, 'py'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-04-24T23:49:15.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-04-23T21:41:11.000Z","updated_at":"2026-02-01T14:01:13.000Z","published_at":"2022-04-23T21:51:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the determinant of an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e x \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e matrix with diagonal entries equal to an integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and other entries equal to 1. For example, a 4x4 matrix with 3s on the diagonal and 1s elsewhere has a determinant of 48, and a 6x6 matrix with 4s on the diagonal and 1s elsewhere has a determinant of 2187. Return the answer as a character string, and see the test suite for forbidden functions. \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":54645,"title":"Determine whether the input is an anagram number","description":"In Cody Problem 44293, Mehmet OZC asks us to spell numbers as words. For example, 67 would be “sixty-seven” and 76 would be “seventy-six”. Notice that the spelled-out versions are anagrams of each other. \r\nWrite a function to determine whether a number is an anagram number. The input number will be 1000 or smaller, and the function should also return a vector of numbers corresponding to the anagrams or an empty vector if there are none. One change from CP 44293 is to omit “and” in writing numbers larger than 100 (e.g., “one hundred seven” instead of “one hundred and seven”). ","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: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 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: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44293-write-out-numbers-in-words\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 44293\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: 306.1px 8px; transform-origin: 306.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Mehmet OZC asks us to spell numbers as words. For example, 67 would be “sixty-seven” and 76 would be “seventy-six”. Notice that the spelled-out versions are anagrams of each other. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.35px 8px; transform-origin: 378.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a number is an anagram number. The input number will be 1000 or smaller, and the function should also return a vector of numbers corresponding to the anagrams or an empty vector if there are none. One change from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44293-write-out-numbers-in-words\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 44293\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: 290.567px 8px; transform-origin: 290.567px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is to omit “and” in writing numbers larger than 100 (e.g., “one hundred seven” instead of “one hundred and seven”). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [tf,m] = anagramNumber(n)\r\n%  tf = true if n is an anagram number and false otherwise\r\n%  m  = vector of numbers corresponding to the anagrams (empty if none)\r\nm = randperm(num2str(n));\r\nend","test_suite":"%%\r\nn = 15;\r\n[tf,m] = anagramNumber(n);\r\nassert(~tf \u0026\u0026 isempty(m))\r\n\r\n%%\r\nn = 67;\r\n[tf,m] = anagramNumber(n);\r\nassert(tf \u0026\u0026 isequal(m,76))\r\n\r\n%%\r\nn = randi(66);\r\nassert(~anagramNumber(n))\r\n\r\n%%\r\nn = 102;\r\n[tf,m] = anagramNumber(n);\r\nassert(tf \u0026\u0026 isequal(m,201))\r\n\r\n%%\r\nn = 222+randi(7);\r\nassert(anagramNumber(n))\r\n\r\n%%\r\nn = 10*randi(66,[1 5]);\r\nassert(all(~arrayfun(@(k) anagramNumber(k),n)))\r\n\r\n%%\r\nn = 364;\r\n[tf,m] = anagramNumber(n);\r\nassert(tf \u0026\u0026 isequal(m,463))\r\n\r\n%%\r\ntf = arrayfun(@(k) anagramNumber(10*k+1),10:99);\r\nindx_correct = [10:19 31:10:91];\r\nassert(isequal(find(~tf)+9,indx_correct))\r\n\r\n%%\r\nn = 679;\r\n[tf,m] = anagramNumber(n);\r\nassert(tf \u0026\u0026 isequal(m,[697 769 796 967 976]))\r\n\r\n%%\r\nn = 896;\r\n[tf,m] = anagramNumber(n);\r\nassert(tf \u0026\u0026 isequal(m,[698 869 968]))\r\n\r\n%%\r\nfiletext = fileread('anagramNumber.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'import') || contains(filetext, 'read'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2022-05-20T13:59:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2022-05-20T13:59:21.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-11T03:12:41.000Z","updated_at":"2026-02-01T15:48:57.000Z","published_at":"2022-05-11T03:13:00.000Z","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\u003eIn \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44293-write-out-numbers-in-words\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 44293\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, Mehmet OZC asks us to spell numbers as words. For example, 67 would be “sixty-seven” and 76 would be “seventy-six”. Notice that the spelled-out versions are anagrams of 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:t\u003eWrite a function to determine whether a number is an anagram number. The input number will be 1000 or smaller, and the function should also return a vector of numbers corresponding to the anagrams or an empty vector if there are none. One change from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44293-write-out-numbers-in-words\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 44293\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is to omit “and” in writing numbers larger than 100 (e.g., “one hundred seven” instead of “one hundred and seven”). \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":54660,"title":"Generate the Figure-Figure sequence","description":"After discussing Scott Kim’s FIGURE-FIGURE Figure (below) in Gödel, Escher, Bach, Douglas Hofstadter introduced an integer sequence  (say) generated by this rule: it starts with 1, and each later term equals the sum of the previous term in  and the latest term that is not already contained the sequence .\r\nFor example, the second term in the sequence is 3 because the first number not in the sequence is 2, and 1+2 = 3. The third term is 7 because the next term not in  is 4 and 3+4 = 7. \r\nNot only is the complement of the sequence  equal to the differences between the terms, but together the two sequences contain all positive integers. \r\nWrite a function that returns the th term of the sequence.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 430.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 215.35px; transform-origin: 407px 215.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.383px 8px; transform-origin: 199.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter discussing Scott Kim’s FIGURE-FIGURE Figure (below) 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: 63.7833px 8px; transform-origin: 63.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eGödel, Escher, Bach\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.083px 8px; transform-origin: 110.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, Douglas Hofstadter introduced an integer sequence \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 320.092px 8px; transform-origin: 320.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) generated by this rule: it starts with 1, and each later term equals the sum of the previous term in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.258px 8px; transform-origin: 195.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the latest term that is not already contained the sequence \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 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: 371.075px 8px; transform-origin: 371.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the second term in the sequence is 3 because the first number not in the sequence is 2, and 1+2 = 3. The third term is 7 because the next term not in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56.0167px 8px; transform-origin: 56.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 4 and 3+4 = 7. \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: 138.083px 8px; transform-origin: 138.083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNot only is the complement of the sequence \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.525px 8px; transform-origin: 237.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e equal to the differences between the terms, but together the two sequences contain all positive integers. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.4333px 8px; transform-origin: 99.4333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75.45px 8px; transform-origin: 75.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of the sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 226.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 113.35px; text-align: left; transform-origin: 384px 113.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 295px;height: 221px\" src=\"https://media.npr.org/assets/img/2012/04/25/figure-aaff187b96098dc83797e603a3c6bd02877591fc.jpg\" data-image-state=\"image-loaded\" width=\"295\" height=\"221\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = DiffEqComplement(n)\r\n  a = a+~a;\r\nend","test_suite":"%%\r\nn = 1;\r\na_correct = 1;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 2;\r\na_correct = 3;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 20;\r\na_correct = 260;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 50;\r\na_correct = 1509;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 191;\r\na_correct = 20320;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 463;\r\na_correct = 115291;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 1250;\r\na_correct = 818269;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 3121;\r\na_correct = 5019531;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 2063;\r\na_correct = 2207441;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 4530;\r\na_correct = 10523362;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 8144;\r\na_correct = 33803039;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 9876;\r\na_correct = 49626045;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 10144;\r\na_correct = 52344305;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 35649;\r\na_correct = 641423921;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\nn = 88888;\r\na_correct = 3974405754;\r\nassert(isequal(DiffEqComplement(n),a_correct))\r\n\r\n%%\r\na = arrayfun(@DiffEqComplement,1:300);\r\nc = diff(a);\r\nassert(isempty(setdiff([a(1:22) c],1:322)))\r\n\r\n%%\r\nfiletext = fileread('DiffEqComplement.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'import') || contains(filetext, 'read'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-05-21T05:41:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-21T05:39:03.000Z","updated_at":"2026-02-02T16:47:24.000Z","published_at":"2022-05-21T05:41:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAfter discussing Scott Kim’s FIGURE-FIGURE Figure (below) in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGödel, Escher, Bach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, Douglas Hofstadter introduced an integer sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) generated by this rule: it starts with 1, and each later term equals the sum of the previous term in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the latest term that is not already contained the sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the second term in the sequence is 3 because the first number not in the sequence is 2, and 1+2 = 3. The third term is 7 because the next term not in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 4 and 3+4 = 7. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNot only is the complement of the sequence \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equal to the differences between the terms, but together the two sequences contain all positive integers. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term of the sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\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=\\\"221\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"295\\\"/\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.jpg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpg\",\"contentType\":\"image/jpg\",\"content\":\"https://media.npr.org/assets/img/2012/04/25/figure-aaff187b96098dc83797e603a3c6bd02877591fc.jpg\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54680,"title":"Determine whether a number is practical","description":"A number  is practical if all smaller numbers can be written as a sum of the proper divisors of . The number 24 is practical because its proper divisors are 1, 2, 3, 4, 6, 8, and 12 and for example\r\n5 = 4+1, 7 = 4+3, 9 = 6+3, 10 = 8+2, 11 = 8+3, 13 = 12+1, 14 = 12+2, 15 = 12+3, 16 = 12+4, \r\n17 = 12+4+1, 18 = 12+6, 19 = 12+3+4, 20 = 12+8, 21 = 12+8+1, 22 = 12+8+2, 23 = 12+8+3\r\nHowever, 23 is not practical because its only proper divisor, 1, cannot be repeated in the sum.\r\nWrite a function to determine whether a number is practical.","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: 153.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 76.9333px; transform-origin: 407px 76.9333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.2833px 8px; transform-origin: 32.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 26.0667px 8px; transform-origin: 26.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003epractical\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 165.3px 8px; transform-origin: 165.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if all smaller numbers can be written as a sum of the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/ProperDivisor.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eproper divisors\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: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 60.2833px 8px; transform-origin: 60.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The number 24 is practical because its proper divisors are 1, 2, 3, 4, 6, 8, and 12 and for example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 350.35px 8px; tab-size: 4; transform-origin: 350.35px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e5 = 4+1, 7 = 4+3, 9 = 6+3, 10 = 8+2, 11 = 8+3, 13 = 12+1, 14 = 12+2, 15 = 12+3, 16 = 12+4, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.8px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.8px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.8px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.8px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 327.25px 8px; tab-size: 4; transform-origin: 327.25px 8px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e17 = 12+4+1, 18 = 12+6, 19 = 12+3+4, 20 = 12+8, 21 = 12+8+1, 22 = 12+8+2, 23 = 12+8+3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289.783px 8px; transform-origin: 289.783px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, 23 is not practical because its only proper divisor, 1, cannot be repeated in the sum.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 184.633px 8px; transform-origin: 184.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a number is practical.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = ispractical(n)\r\n  tf = sum(factor(n))\u003cn;\r\nend","test_suite":"%%\r\nassert(ispractical(24))\r\n\r\n%%\r\nassert(ispractical(1))\r\n\r\n%%\r\nassert(ispractical(2))\r\n\r\n%%\r\nassert(~ispractical(3))\r\n\r\n%%\r\nassert(~ispractical(14))\r\n\r\n%%\r\nassert(~ispractical(15))\r\n\r\n%%\r\nassert(ispractical(18))\r\n\r\n%%\r\nassert(ispractical(32))\r\n\r\n%%\r\nassert(~ispractical(174))\r\n\r\n%%\r\nassert(ispractical(544))\r\n\r\n%%\r\nassert(~ispractical(3140))\r\n\r\n%%\r\nassert(ispractical(9044))\r\n\r\n%%\r\nassert(~ispractical(17822))\r\n\r\n%%\r\nassert(ispractical(25650))\r\n\r\n%%\r\nassert(~ispractical(33022))\r\n\r\n%%\r\nassert(ispractical(46170))\r\n\r\n%%\r\nassert(~ispractical(49584))\r\n\r\n%%\r\nassert(~ispractical(56702))\r\n\r\n%%\r\nassert(ispractical(59000))\r\n\r\n%%\r\nassert(ispractical(70866))\r\n\r\n%%\r\nassert(ispractical(83840))\r\n\r\n%%\r\nassert(ispractical(262144))\r\n\r\n%%\r\nassert(~ispractical(1048598))\r\n\r\n%% \r\nassert(ispractical(60466176))\r\n\r\n%%\r\nassert(ispractical(279936000))\r\n\r\n%%\r\nassert(ispractical(21047953604832))\r\n\r\n%%\r\nassert(~ispractical(2*randi(1e6)+1))\r\n\r\n%%\r\nassert(ispractical(prod([2 3 5 7].^randi(6,[1 4]))))\r\n\r\n%%\r\nfiletext = fileread('ispractical.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'read'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-05-25T03:47:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-25T03:46:48.000Z","updated_at":"2026-02-02T17:02:08.000Z","published_at":"2022-05-25T03:47:34.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epractical\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if all smaller numbers can be written as a sum of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/ProperDivisor.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproper divisors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The number 24 is practical because its proper divisors are 1, 2, 3, 4, 6, 8, and 12 and for example\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[5 = 4+1, 7 = 4+3, 9 = 6+3, 10 = 8+2, 11 = 8+3, 13 = 12+1, 14 = 12+2, 15 = 12+3, 16 = 12+4, \\n17 = 12+4+1, 18 = 12+6, 19 = 12+3+4, 20 = 12+8, 21 = 12+8+1, 22 = 12+8+2, 23 = 12+8+3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, 23 is not practical because its only proper divisor, 1, cannot be repeated in the sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether a number is practical.\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":54770,"title":"Count the peaceful queens","description":"In a 5x5 chessboard with a queen of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \r\nWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an x chessboard.  \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 328.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 164.35px; transform-origin: 407px 164.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.1833px 8px; transform-origin: 85.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn a 5x5 chessboard with a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Queen_(chess)#Placement_and_movement\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003equeen\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: 272.283px 8px; transform-origin: 272.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \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: 372.883px 8px; transform-origin: 372.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 8px; transform-origin: 3.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.0083px 8px; transform-origin: 42.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e chessboard. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 226.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 113.35px; text-align: left; transform-origin: 384px 113.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 764px;height: 221px\" 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\" data-image-state=\"image-loaded\" width=\"764\" height=\"221\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = peacefulQueens(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 5;\r\nassert(isequal(peacefulQueens(n),12))\r\n\r\n%%\r\nn = 8;\r\nassert(isequal(peacefulQueens(n),42))\r\n\r\n%%\r\nn = 64;\r\nassert(isequal(peacefulQueens(n),3906))\r\n\r\n%%\r\nn = 4096;\r\nassert(isequal(peacefulQueens(n),16764930))\r\n\r\n%%\r\nn = 262144;\r\nassert(isequal(peacefulQueens(n),68718690306))\r\n\r\n%%\r\nn = 2097152;\r\nassert(isequal(peacefulQueens(n),4398040219650))\r\n\r\n%%\r\nn = 16777216;\r\nassert(isequal(peacefulQueens(n),281474926379010))\r\n\r\n%%\r\nm = randi(1000)+4;\r\ny = sum(arrayfun(@peacefulQueens,3:m));\r\nassert(isequal(y,polyval([1 3 2 0],m-2)/3))\r\n\r\n%%\r\nfiletext = fileread('peacefulQueens.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-07-02T17:52:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-02T02:16:14.000Z","updated_at":"2026-01-26T15:48:57.000Z","published_at":"2022-07-02T02:17:02.000Z","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\u003eIn a 5x5 chessboard with a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Queen_(chess)#Placement_and_movement\\\"\u003e\u003cw:r\u003e\u003cw:t\u003equeen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of one color (white, say) on the perimeter, one can place 12 black queens on the board such that none of the black queens can attack the white one (or vice versa). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the number of queens that cannot attack a queen of the other color placed anywhere on the perimeter of an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr 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the parity of digits in a decimal expansion","description":"The number 349 has the decimal expansion . If we change the even digits from positive to negative, then the number becomes 269 (i.e., 300-40+9). A similar operation could be applied to the odd digits. \r\nWrite a function that takes a number  and produces two arrays: a vector  with the even digits of 1 to  with flipped parity and a vector  with the odd digits of 1 to  with flipped parity. \r\nAt first these sequences did not seem interesting, but plotting them--using plot(a,1:n,b,1:n) with , say—convinced me that they are.","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: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72px; transform-origin: 407px 72px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.1px 8px; transform-origin: 138.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 349 has the decimal expansion \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"3*100+4*10+9*1\" style=\"width: 168px; height: 19px;\" width=\"168\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 141.958px 8px; transform-origin: 141.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If we change the even digits from positive to negative, then the number becomes 269 (i.e., 300-40+9). A similar operation could be applied to the odd digits. \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: 114.217px 8px; transform-origin: 114.217px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109.292px 8px; transform-origin: 109.292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and produces two arrays: a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.7833px 8px; transform-origin: 84.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the even digits of 1 to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.9583px 8px; transform-origin: 57.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with flipped parity and a vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.2833px 8px; transform-origin: 81.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the odd digits of 1 to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.3833px 8px; transform-origin: 59.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with flipped parity. \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: 229.875px 8px; transform-origin: 229.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAt first these sequences did not seem interesting, but plotting them--using \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.45px 8px; transform-origin: 65.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eplot(a,1:n,b,1: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: 16.3333px 8px; transform-origin: 16.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 10^4\" style=\"width: 49px; height: 19px;\" width=\"49\" height=\"19\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.775px 8px; transform-origin: 21.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, say—convinced me that they are.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [a,b] = flipDigParity(n)\r\n x = 1:n;\r\n a = x; a(2:2:end) = -a(2:2:end);\r\n b = x; b(1:2:end) = -b(1:2:end);\r\nend","test_suite":"%%\r\nn = 10;\r\na = flipDigParity(n);\r\na_correct = [1 -2 3 -4 5 -6 7 -8 9 10];\r\nassert(isequal(a,a_correct))\r\n\r\n%%\r\nn = 40;\r\n[~,b] = flipDigParity(n);\r\nb11_40 = [-11 -8 -13 -6 -15 -4 -17 -2 -19 20 19 22 17 24 15 26 13 28 11 -30 -31 -28 -33 -26 -35 -24 -37 -22 -39 40];\r\nassert(isequal(b(11:40),b11_40))\r\n\r\n%%\r\nn = 1000;\r\n[a,b] = flipDigParity(n);\r\ny1 = trapz(a);\r\ny1_correct = 55999.5;\r\ny2 = std(b);\r\ny2_correct = 535.282895;\r\nassert(isequal(y1,y1_correct) \u0026\u0026 abs(y2-y2_correct)\u003c1e-6)\r\n\r\n%%\r\nn = 3e5;\r\n[a,b] = flipDigParity(n);\r\na1 = a([123456 145623 234567 273456]);\r\na1_correct = [82644  64383 -173553 -127356];\r\nb1 = b([189432 194328 234891 289431]);\r\nb1_correct = [-28628 -186272 174709 271369];\r\n\r\n%%\r\nn = 4e7;\r\n[a,b] = flipDigParity(n);\r\nc = cumsum(a);\r\ny1 = c([(1:4)*1e7]);\r\ny1_correct = [0.05555565 1.1111109 -0.83333305 2.2222218]*1e14;\r\ny2 = std(b);\r\ny2_correct = 18802537.42144525;\r\nassert(all(abs(y1-y1_correct)\u003c0.1) \u0026\u0026 abs(y2-y2_correct)\u003c1e-6)\r\n\r\n%%\r\na1 = flipDigParity(3456);\r\n[~,b1] = flipDigParity(a1(3221));\r\na2 = flipDigParity(b1(2732));\r\n[~,b2] = flipDigParity(a2(1253));\r\nb2_781_correct = -621;\r\nassert(isequal(b2(781),b2_781_correct))\r\n\r\n%%\r\nfiletext = fileread('flipDigParity.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-07-06T14:29:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-06T05:15:25.000Z","updated_at":"2026-02-02T17:09:39.000Z","published_at":"2022-07-06T05:31:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 349 has the decimal expansion \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=\\\"3*100+4*10+9*1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e3\\\\times 10^2 + 4\\\\times 10^1 + 9\\\\times 10^0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If we change the even digits from positive to negative, then the number becomes 269 (i.e., 300-40+9). A similar operation could be applied to the odd digits. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and produces two arrays: a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the even digits of 1 to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with flipped parity and a vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the odd digits of 1 to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with flipped parity. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAt first these sequences did not seem interesting, but plotting them--using \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eplot(a,1:n,b,1:n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 10^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, say—convinced me that they are.\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":54780,"title":"Trap a knight","description":"Consider a knight on an infinite chessboard labeled with numbers spiraling outward. A knight starting on the square labeled 1 can reach 8 squares, marked in green below (i.e., squares 10, 12, 14, 16, 18, 20, 22, and 24). Take the smallest of these numbers, or 10. Repeating the step while avoiding squares already visited puts the knight at squares 3, 6, 9, 4, 7, 2, 5, etc. This tour continues until step 2016, when the knight reaches square 2084. At that point the knight is trapped: it has visited all eight possible squares. \r\nWrite a function that takes the starting square and returns the sequence of squares visited by the knight on the tour. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 415.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 207.85px; transform-origin: 407px 207.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; 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: 35.7917px 8px; transform-origin: 35.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Knight_(chess)#Movement\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eknight\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: 327.942px 8px; transform-origin: 327.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on an infinite chessboard labeled with numbers spiraling outward. A knight starting on the square labeled 1 can reach 8 squares, marked in green below (i.e., squares 10, 12, 14, 16, 18, 20, 22, and 24). Take the smallest of these numbers, or 10. Repeating the step while avoiding squares already visited puts the knight at squares 3, 6, 9, 4, 7, 2, 5, etc. This tour continues until step 2016, when the knight reaches square 2084. At that point the knight is trapped: it has visited all eight possible squares. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 358.867px 8px; transform-origin: 358.867px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes the starting square and returns the sequence of squares visited by the knight on the tour. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 271.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 135.85px; text-align: left; transform-origin: 384px 135.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 275px;height: 266px\" 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\" data-image-state=\"image-loaded\" width=\"275\" height=\"266\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = trappedKnight(n)\r\n  y = randi(n^2,1,2016);\r\nend","test_suite":"%%\r\nn = 1;\r\ny = trappedKnight(n);\r\ny_correct = [1 10 3 6 9 4 7 2 5 8 11 14 29 32 15 12 27 24 45 20 23 44 41 18 35 38 19 16 33 30 53 26 47 22 43 70 21 40 17 34 13 28 25 46 75 42 69 104 37 62 95 58 55 86 51 48 77 114 73 108 151 68 103 64 67 36 39 66 63 96 59 56 87 52 49 78 115 74 71 106 149 102 99 140 61 94 31 54 85 50 79 116 161 76 113 72 107 150 201 146 65 98 139 60 93 90 129 176 125 82 119 164 217 160 111 154 205 264 331 200 101 142 97 138 187 92 89 128 175 84 81 118 163 216 159 110 153 204 105 148 199 144 147 100 141 190 137 186 91 130 57 88 127 174 83 80 117 162 215 112 109 152 203 262 329 198 195 252 143 192 249 188 135 132 179 234 297 230 123 120 165 218 279 214 157 208 267 334 263 330 259 196 253 318 191 248 313 244 133 180 235 298 177 126 173 122 167 220 281 350 277 158 155 206 265 202 261 328 197 254 145 194 251 316 189 136 185 182 131 134 181 184 239 242 305 238 183 304 237 178 233 296 229 124 121 166 219 280 349 276 211 156 207 266 333 408 491 404 257 322 395 476 317 390 247 312 243 240 303 236 299 232 295 172 169 222 283 352 429 278 213 210 269 336 411 332 407 260 327 256 321 394 475 564 389 246 311 384 241 310 245 314 387 468 309 306 377 302 373 452 369 294 171 168 221 282 351 428 347 212 209 268 335 410 493 406 489 326 323 258 255 320 193 250 315 388 469 558 383 380 459 376 301 372 451 368 231 370 449 366 227 224 285 354 431 516 427 346 273 340 415 270 337 412 495 586 409 492 405 488 325 398 479 568 393 474 563 470 385 308 379 382 461 378 307 460 381 466 555 462 465 554 551 464 553 648 463 550 645 458 375 300 371 450 367 228 225 286 355 432 517 610 513 348 275 272 339 414 497 588 687 494 585 490 403 324 397 478 319 392 473 562 659 764 557 654 759 650 653 552 647 548 457 374 453 540 635 448 293 170 223 284 353 430 515 426 345 342 271 274 341 344 419 422 505 418 343 424 509 420 423 508 599 504 417 338 413 496 587 686 583 682 487 400 481 396 477 566 391 472 561 386 467 556 657 560 471 660 559 656 761 652 649 752 549 644 545 454 541 636 537 446 291 288 357 434 519 612 713 514 425 510 421 598 503 416 499 590 689 796 685 582 681 486 483 402 399 480 569 666 565 662 767 658 763 876 655 760 651 754 865 646 547 456 543 638 539 634 447 292 289 358 435 520 613 714 609 512 605 706 507 604 511 608 709 818 603 506 597 502 593 498 589 688 795 584 683 580 401 482 571 668 567 664 769 882 661 766 879 762 875 758 755 866 751 862 643 544 639 742 853 738 535 364 361 226 287 356 433 518 611 712 607 708 817 602 701 704 811 600 699 596 501 592 691 798 913 794 909 684 581 680 485 574 671 570 667 772 663 768 881 1002 765 878 999 874 757 868 753 864 749 546 455 542 637 538 633 534 363 360 437 522 615 716 825 942 711 606 707 816 601 700 807 696 803 594 693 500 591 690 797 912 793 908 789 578 575 672 777 572 669 774 665 770 883 1004 1133 880 1001 1130 877 998 873 756 867 986 863 748 641 744 855 740 851 632 445 290 359 436 521 614 715 824 941 710 819 936 705 702 809 698 595 694 801 916 1039 1170 911 792 907 788 577 484 573 670 775 888 771 884 1005 1134 1271 1000 1129 996 871 990 1117 1252 985 750 861 642 745 856 741 852 737 536 365 444 441 526 619 438 523 616 717 826 943 822 939 1064 935 814 929 810 703 928 813 934 1059 930 933 812 815 932 1055 1058 1189 1054 927 808 697 804 919 692 799 914 1037 910 791 906 679 576 579 678 675 780 893 776 889 1010 773 886 1007 1136 1003 1132 1269 1128 995 870 989 1116 1251 984 1111 860 979 746 857 640 743 854 739 850 631 532 529 362 439 524 617 718 827 944 823 940 1065 820 937 1062 1195 1336 1057 1188 931 1060 1193 1056 1187 1052 925 806 695 802 917 1040 1171 1036 1167 1032 905 786 783 674 779 892 1013 1142 887 1008 1137 1274 1419 1270 1415 1266 997 872 869 988 1115 1250 983 1110 859 978 1105 974 1101 970 735 628 443 440 525 618 719 828 945 1070 1203 1066 821 938 1063 1196 1337 1192 1331 1334 1481 1190 1329 1186 1051 924 805 920 1043 800 915 1038 1169 1034 1165 1030 787 676 781 894 673 778 891 1012 1141 1278 1009 1138 885 1006 1135 1272 1131 1268 1127 994 991 1118 987 1114 1249 982 747 858 977 1104 973 1100 849 630 531 528 621 722 831 948 1073 1206 1069 1202 1343 1198 1061 1194 1335 1332 1479 1328 1053 926 1049 922 1045 918 1041 1172 1311 1168 1033 790 1031 904 677 782 895 1016 1145 890 1011 1140 1277 1422 1273 1418 1571 1414 1265 1124 1121 1256 1399 1550 1253 1396 1113 1248 981 1108 1243 976 1103 972 1099 848 629 442 527 620 721 830 947 1072 1205 1068 1201 1342 1197 1338 1487 1644 1333 1480 1191 1330 1477 1326 1183 1048 921 1044 1175 1314 1461 1310 1035 1166 1305 1162 903 784 897 1018 1147 1014 1143 1280 1139 1276 1421 1574 1417 1570 1267 1126 993 1120 1255 1398 1549 1394 1247 980 1107 1242 975 1102 971 736 533 734 627 624 725 834 951 720 829 946 1071 1204 1067 1200 1341 1490 1647 1486 1643 1482 1485 1642 1639 1484 1641 1804 1483 1638 1801 1478 1327 1184 1323 1050 923 1046 1177 1042 1173 1312 1459 1308 1455 1164 1029 902 899 1020 1149 896 1017 1146 1283 1428 1279 1424 1275 1420 1573 1416 1569 1412 1125 992 1119 1254 1397 1548 1393 1112 1395 1546 1391 1244 1109 1390 1541 1386 1239 1382 1235 968 733 530 623 724 833 950 1075 1208 1349 1498 1345 1494 1199 1340 1489 1646 1811 1984 1807 1640 1803 1636 1799 1476 1185 1324 1181 1320 1047 1178 1317 1174 1313 1460 1309 1456 1611 1304 1161 1026 785 898 1019 1148 1015 1144 1281 1426 1579 1740 1423 1576 1737 1572 1733 1568 1411 1262 1259 1402 1553 1712 1879 1708 1545 1246 1389 1106 1241 1384 1237 1098 847 732 625 726 835 622 723 832 949 1074 1207 1348 1497 1344 1493 1650 1339 1488 1645 1810 1983 1806 1809 1982 1979 1808 1805 1976 1637 1800 1633 1474 1629 1322 1179 1318 1465 1176 1315 1462 1617 1458 1307 1454 1163 1028 901 1022 1151 1288 1433 1284 1429 1582 1425 1578 1739 1908 1575 1736 1905 1732 1413 1264 1123 1258 1401 1552 1711 1878 1547 1392 1245 1388 1539 1240 1383 1236 969 846 731 728 837 954 1079 1212 1353 1076 1209 1350 1499 1346 1495 1652 1491 1648 1813 1986 2167 2356 1981 2160 1977 1802 1635 1798 1475 1630 1325 1182 1321 1468 1623 1316 1463 1618 1781 1614 1777 1610 1303 1160 1025 900 1021 1150 1287 1432 1585 1282 1427 1580 1741 1910 1577 1738 1907 1734 1903 1730 1565 1408 1263 1122 1257 1400 1551 1710 1877 1706 1543 1702 1387 1538 1697 1534 1379 1096 845 626 727 836 953 1078 1211 1352 1501 1658 1347 1496 1653 1492 1649 1814 1987 2168 2357 2164 2161 1978 2157 1974 2153 1970 1631 1472 1627 1790 1467 1622 1785 1464 1619 1782 1615 1778 1457 1306 1453 1302 1027 1024 1153 1290 1435 1286 1431 1584 1745 1914 1581 1742 1911 2088 2273 1906 2083 1902 1567 1410 1261 1404 1555 1714 1881 2056 1709 1876 1705 1542 1701 1868 1537 1238 1381 1234 967 844 729 838 955 1080 1213 952 1077 1210 1351 1500 1657 1822 1995 1654 1819 1992 1651 1816 1989 1812 1985 2166 2355 2162 2165 1980 2159 2346 1975 2154 1971 1632 1473 1628 1469 1180 1319 1466 1621 1784 1955 1616 1779 1612 1775 1452 1301 1158 1155 1292 1023 1152 1289 1434 1285 1430 1583 1744 1913 2090 1909 2086 1735 1904 1731 1566 1409 1260 1403 1554 1713 1880 2055 2238 1875 1544 1703 1540 1385 1536 1695 1380 1097 966 843 840 957 1082 1215 1356 1505 1662 1827 1502 1659 1824 1655 1820 1993 2174 1815 1988 2169 2358 2555 2354 2351 2546 2347 2156 1973 1634 1797 1968 1793 1470 1625 1788 1959 1620 1783 1954 2133 1780 1613 1776 1609 1450 1159 1156 1293 1438 1591 1752 1587 1748 1917 2094 1743 1912 2089 2274 2085 2270 2081 1900 1727 1562 1559 1718 1405 1556 1715 1882 2057 2240 2053 1874 1707 2052 1873 2048 1869 1698 1535 1694 1531 1232 965 730 839 956 1081 1214 1355 1504 1661 1826 1999 1656 1821 1994 1817 1990 2171 2360 2557 2762 2553 2352 2547 2348 2543 2158 2345 2540 2155 1972 2151 1796 1967 1792 1471 1626 1789 1960 2139 1786 1957 2136 1953 2132 1949 1774 1451 1300 1157 1294 1439 1154 1291 1436 1589 1750 1919 1586 1747 1916 2093 2278 2471 2672 2275 2468 2087 2272 2465 2082 1901 1728 1563 1406 1557 1716 1883 2058 2241 2054 2237 2050 1871 1700 1867 1696 1533 1378 1095 964 841 958 1083 1216 1357 1506 1663 1354 1503 1660 1825 1998 2179 2368 2175 1818 1991 2172 2361 2558 2763 2554 2163 2350 2545 2748 2541 2342 2537 2150 1795 1966 1791 1624 1787 1958 2137 2324 2519 2134 1951 2130 1947 1608 1449 1298 1295 1440 1593 1754 1437 1590 1751 1920 2097 1746 1915 2092 2277 2470 2671 2466 2269 2080 1729 1564 1407 1558 1717 1884 2059 2242 2433 2632 2239 2430 2051 1704 2049 1870 1699 1866 2041 1862 1691 1376 1093 842 959 1084 1217 1358 1507 1664 1829 2002 2183 2372 1997 2178 2367 2564 2173 2362 2559 2170 2359 2556 2761 2552 2549 2752 2349 2544 2747 2344 2539 2152 1969 1794 1965 2144 1961 2140 2327 1956 2135 1952 2131 1948 1773 1606 1299 1296 1441 1594 1755 1924 2101 2286 1921 1588 1749 1918 2095 2280 2091 2276 2469 2670 2271 2464 2267 2078 1897 1724 1721 1888 2063 2246 1885 2060 2243 2434 2633 2840 2429 2234 2047 1872 2233 2046 2229 2042 1863 1532 1233 1094 963 960 1085 1218 1359 1508 1665 1830 2003 2184 2373 2000 1823 1996 2177 2366 2563 2768 2363 2560 2765 2978 3199 2760 2353 2548 2751 2962 3181 2746 2343 2538 2339 2148 2335 1964 2143 2330 2525 2138 2325 2520 2321 1950 2129 1946 1607 1448 1297 1442 1595 1756 1925 1592 1753 1922 2099 2284 2477 2096 2281 2474 2675 2884 3101 2880 2467 2084];\r\nlen_correct = 2016;\r\nyend_correct = 2084;\r\nassert(isequal(y,y_correct) \u0026\u0026 isequal(length(y),len_correct) \u0026\u0026 isequal(y(end),yend_correct))\r\n\r\n%%\r\nY = NaN(1,100); len = NaN(1,100);\r\nfor n = 1:100\r\n    y = trappedKnight(n);\r\n    Y(n) = y(end);\r\n    len(n) = length(y);\r\nend\r\nY_correct = [2084 711 3915 556 3915 556 3915 3380 2086 1339 1464 1572 4772 582 3959 682 2309 385 330 1142 706 2750 4256 4322 1413 1488 1685 6335 5214 906 2616 1038 582 1608 2675 6266 1120 3955 936 2773 1861 2213 2223 262 1147 4428 1126 3319 1040 1693 3614 1647 4122 2121 3496 2555 2508 5174 2961 1338 1607 4252 2826 1731 3915 2130 938 762 835 3437 708 1653 1133 4168 3918 150 1204 3087 1438 445 3104 969 906 822 3404 2922 125 329 3214 6185 3912 2181 1093 1379 4586 5335 790 3038 5262 3141];\r\nlen_correct = [2016 880 2741 857 2741 857 2741 3611 2590 1540 1846 2061 4892 1047 4139 753 3559 590 426 1205 1140 2759 3830 4687 1839 2101 2861 5892 5500 1295 2674 1213 890 1839 2749 6531 1118 3632 1496 2888 1995 2574 2713 495 1479 5509 1414 3926 1078 2344 4244 1932 4054 3382 4084 3410 4144 4079 2223 1151 1799 4863 3162 2292 2741 2271 840 1087 1397 2752 990 1664 1775 3915 5704 263 1658 2840 1510 486 3620 1146 1288 969 3688 3745 311 586 3146 5480 5116 2472 1473 1910 5128 5938 1128 4367 4412 5036];\r\nassert(isequal(len,len_correct) \u0026\u0026 isequal(Y,Y_correct))\r\n\r\n%%\r\nY = NaN(1,800); len = NaN(1,800);\r\nfor n = 200:1000\r\n    y = trappedKnight(n);\r\n    Y(n-199) = y(end);\r\n    len(n-199) = length(y);\r\nend\r\n[lensort,isortlen] = sort(len,'descend');\r\n[Ysort,isortY] = sort(Y,'descend');\r\nisortlen_correct = [396 662 246 49 125 462 267 336 683 797];\r\nlenmax10_correct = [12072 11058 10654 10553 10337 10031 9552 9469 9292 9259];\r\nisortY_correct = [662 683 267 246 396 497 49 443 541 462];\r\nYmax10_correct = [14176 12571 12303 11858 11802 11456 11168 10624 9594 8857];\r\nassert(isequal(lensort(1:10),lenmax10_correct) \u0026\u0026 isequal(Ysort(1:10),Ymax10_correct) \u0026\u0026 isequal(isortlen(1:10),isortlen_correct) \u0026\u0026 isequal(isortY(1:10),isortY_correct))\r\n\r\n%%\r\nn = 9999;\r\ny = trappedKnight(n);\r\nsum_correct = 77968774;\r\nassert(isequal(sum(y),sum_correct))\r\n\r\n%%\r\nn = 11509;\r\ny = trappedKnight(n);\r\nlen_correct = 21346;\r\nassert(isequal(length(y),len_correct))\r\n\r\n%%\r\nfiletext = fileread('trappedKnight.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2024-01-04T14:21:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-07T04:01:20.000Z","updated_at":"2026-02-03T16:00:59.000Z","published_at":"2022-07-07T04:03:44.000Z","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\u003eConsider a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Knight_(chess)#Movement\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eknight\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e on an infinite chessboard labeled with numbers spiraling outward. A knight starting on the square labeled 1 can reach 8 squares, marked in green below (i.e., squares 10, 12, 14, 16, 18, 20, 22, and 24). Take the smallest of these numbers, or 10. Repeating the step while avoiding squares already visited puts the knight at squares 3, 6, 9, 4, 7, 2, 5, etc. This tour continues until step 2016, when the knight reaches square 2084. At that point the knight is trapped: it has visited all eight possible squares. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 the starting square and returns the sequence of squares visited by the knight on the tour. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"266\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"275\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55280,"title":"Count estrangements","description":"Recently I made a puzzle for my wife that included a cryptogram, which involves an arrangement of the letters A through Z. I used MATLAB (of course) to permute the letters, but in the first arrangement, H was coded as H. I tried again until MATLAB gave me a derangement, a permutation such that none of the letters was in its original position. I later noticed that the letter I was coded as S and S was coded as I. Though I used that permutation, I really wanted one in which no two elements are simply swapped. I called such a permutation an estrangement, and although I later learned of a more technical and mathematical description, I will keep my name. \r\nWrite a function to count estrangements—i.e., the permutations of elements in a 1x vector such that (1) no element is in its original position and (2) no two elements are simply swapped. For example, if the vector is [1 2 3 4], then [3 2 4 1] and [4 1 3 2] would not be allowed under condition 1 and [4 3 2 1] and [2 1 4 3] would not be allowed under condition 2. Return the count as a string. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 219px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 109.5px; transform-origin: 407px 109.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRecently I made a puzzle for my wife that included a cryptogram, which involves an arrangement of the letters A through Z. I used MATLAB (of course) to permute the letters, but in the first arrangement, H was coded as H. I tried again until MATLAB gave me a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.2417px 7.79167px; transform-origin: 41.2417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ederangement\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 306.875px 7.79167px; transform-origin: 306.875px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, a permutation such that none of the letters was in its original position. I later noticed that the letter I was coded as S and S was coded as I. Though I used that permutation, I really wanted one in which no two elements are simply swapped. I called such a permutation an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7917px 7.79167px; transform-origin: 42.7917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eestrangement\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 165.708px 7.79167px; transform-origin: 165.708px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and although I later learned of a more technical and mathematical description, I will keep my name. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: 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: 256.575px 7.79167px; transform-origin: 256.575px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to count estrangements—i.e., the permutations of elements in a 1x\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.175px 7.79167px; transform-origin: 122.175px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector such that (1) no element is in its original position and (2) no two elements are simply swapped. For example, if the vector is [1 2 3 4], then [3 2 4 1] and [4 1 3 2] would not be allowed under condition 1 and [4 3 2 1] and [2 1 4 3] would not be allowed under condition 2. Return the count as a string. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = estrangements(n)\r\n  y = nchoosek(n,n-3);\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = '0';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct = '0';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 4;\r\ny_correct = '6';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 8;\r\ny_correct = '8988';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny_correct = '809856';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 12;\r\ny_correct = '106877320';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 15;\r\ny_correct = '291781655984';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 17;\r\ny_correct = '79364592318720';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 19;\r\ny_correct = '27142690734936864';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 22;\r\ny_correct = '250798462399300784640';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 24;\r\ny_correct = '138440751242507472273856';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 26;\r\ny_correct = '89986488307675206245836800';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 32;\r\ny_correct = '58712425785005411876628940337660160';\r\nassert(isequal(estrangements(n),y_correct))\r\n\r\n%%\r\nn = 23;\r\nassert(isequal(sum(factor(sum(estrangements(n)-'0'))),32))\r\n\r\n%%\r\nfiletext = fileread('estrangements.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp');\r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":46909,"edited_by":46909,"edited_at":"2023-04-24T19:49:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-04-24T19:23:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-09T02:45:28.000Z","updated_at":"2026-02-03T16:41:09.000Z","published_at":"2022-08-09T02:45:54.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRecently I made a puzzle for my wife that included a cryptogram, which involves an arrangement of the letters A through Z. I used MATLAB (of course) to permute the letters, but in the first arrangement, H was coded as H. I tried again until MATLAB gave me a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ederangement\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, a permutation such that none of the letters was in its original position. I later noticed that the letter I was coded as S and S was coded as I. Though I used that permutation, I really wanted one in which no two elements are simply swapped. I called such a permutation an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eestrangement\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and although I later learned of a more technical and mathematical description, I will keep my name. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 count estrangements—i.e., the permutations of elements in a 1x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e vector such that (1) no element is in its original position and (2) no two elements are simply swapped. For example, if the vector is [1 2 3 4], then [3 2 4 1] and [4 1 3 2] would not be allowed under condition 1 and [4 3 2 1] and [2 1 4 3] would not be allowed under condition 2. Return the count as a string. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56240,"title":"List numbers that are not squares","description":"The numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the th term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s Unsquare Dance.  ","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: 340.408px 8px; transform-origin: 340.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 8px; transform-origin: 31.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=lbdEzRfbeH4\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eUnsquare Dance\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = unsquare(n)\r\n  x = setdiff(1:n,(1:floor(sqrt(n))).^2);\r\n  y = x(n);\r\nend","test_suite":"%%\r\nn = 1:100;\r\ny_correct = [2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21 22 23 24 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46 47 48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 101 102 103 104 105 106 107 108 109 110];\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 5075;\r\ny_correct = 5146;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 61086;\r\ny_correct = 61333;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 721097;\r\ny_correct = 721946;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8321008;\r\ny_correct = 8323893;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 94321019;\r\ny_correct = 94330731;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 123456789101112;\r\ny_correct = 123456800212223;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 9e15;\r\ny_correct = 9000000094868330;\r\ny = unsquare(n);\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nfiletext = fileread('unsquare.m');\r\nillegal = contains(filetext, '*') || contains(filetext, '^') || contains(filetext, 'conv') || contains(filetext, 'setdiff') || contains(filetext, 'prod') || ...\r\n          contains(filetext, '==') || contains(filetext, '~=') || contains(filetext, 'isequal') || contains(filetext, 'pow') || contains(filetext, 'nthroot') || ...\r\n          contains(filetext, 'times') || contains(filetext, 'eq') || contains(filetext, '/') || contains(filetext, 'div') || contains(filetext, 'det');\r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-10-07T03:22:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-07T03:17:26.000Z","updated_at":"2026-03-16T12:45:20.000Z","published_at":"2022-10-07T03:22:08.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, etc. are not perfect squares. Write a function to list the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term in this sequence. Check the test suite to see which functions are banned for this problem. For background music while solving this problem, you can listen to Dave Brubeck’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=lbdEzRfbeH4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eUnsquare Dance\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:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56593,"title":"List the nth term of Rozhenko’s inventory sequence","description":"Consider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\r\n0\r\n1, 1, 0\r\n2, 2, 2, 0\r\n3, 2, 4, 1, 1, 0\r\n4, 4, 4, 1, 4, 0\r\nWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19th term is 4. \r\nThis sequence produces interesting plots and music. See the related Numberphile video for more. \r\nWrite a function to report the th term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 345px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 172.5px; transform-origin: 407px 172.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 374.6px 8px; transform-origin: 374.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.2167px 8px; transform-origin: 27.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2, 2, 2, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3, 2, 4, 1, 1, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7667px 8px; transform-origin: 42.7667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4, 4, 4, 1, 4, 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e term is 4. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.425px 8px; transform-origin: 112.425px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis sequence produces interesting \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A342585/graph\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eplots\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: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/play?seq=A342585\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003emusic\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 8px; transform-origin: 18.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. See \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=rBU9E-ZOZAI\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ethe related Numberphile video\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: 31.8833px 8px; transform-origin: 31.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for more. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.1px 8px; transform-origin: 90.1px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to report the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.5583px 8px; transform-origin: 78.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Rozhenko(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 19;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 53;\r\ny_correct = 5;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 347;\r\ny_correct = 25;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 823;\r\ny_correct = 27;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 1997;\r\ny_correct = 20;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 4721;\r\ny_correct = 68;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 13859;\r\ny_correct = 18;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 19793;\r\ny_correct = 7;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 24677;\r\ny_correct = 51;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 41903;\r\ny_correct = 357;\r\nassert(isequal(Rozhenko(n),y_correct))\r\n\r\n%%\r\nn = 25537;\r\ny_correct = 4;\r\nassert(isequal(Rozhenko(Rozhenko(Rozhenko(n))),y_correct))\r\n\r\n%%\r\nn = [1 4 8 14 20 28 37 46 57 69 82 95 110 125 142 159 177 196 216 238 260 285 310 335 362 390 418 448 478 511];\r\na = arrayfun(@Rozhenko,n);\r\ns_correct = 0;\r\nassert(isequal(sum(a),s_correct))\r\n\r\n%%\r\nfiletext = fileread('Rozhenko.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-13T14:07:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-13T04:07:55.000Z","updated_at":"2026-01-24T12:19:36.000Z","published_at":"2022-11-13T04:08:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a sequence constructed by repeated inventories. A new inventory begins each time a zero is encountered. The first few inventories are\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 2, 2, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3, 2, 4, 1, 1, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4, 4, 4, 1, 4, 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen the sequence is empty, there are zero 0s. We start a new inventory on the second line—looking at all numbers written so far: one 0, one 1, zero 2s. The zero triggers a new inventory, and the third line reports two 0s, two 1s, two 2s (from the beginning of the third line), and zero 3s. And so on. The sequence then is the rows strung together. For example, the 19\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 term is 4. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis sequence produces interesting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://oeis.org/A342585/graph\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eplots\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://oeis.org/play?seq=A342585\\\"\u003e\u003cw:r\u003e\u003cw:t\u003emusic\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=rBU9E-ZOZAI\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ethe related Numberphile video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 report the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56743,"title":"Count the unitary divisors of a number","description":"Cody Problem 56738 asks for a list of the unitary divisors of a number. For this problem, write a function to count the unitary divisors of a number. For example, the unitary divisors of 18 are 1, 2, 9, and 18; therefore, the number of unitary divisors is 4.","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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56738-list-unitary-divisors-of-a-number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 56738\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: 318.25px 8px; transform-origin: 318.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks for a list of the unitary divisors of a number. For this problem, write a function to count the unitary divisors of a number. For example, the unitary divisors of 18 are 1, 2, 9, and 18; therefore, the number of unitary divisors is 4.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = countUDivisors(n)\r\n  y = length(n(y/n==true));\r\nend","test_suite":"%%\r\nn = 18;\r\ny_correct = 4;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 128;\r\ny_correct = 2;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 996;\r\ny_correct = 8;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 1228;\r\ny_correct = 4;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 54321;\r\ny_correct = 8;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 648207;\r\ny_correct = 8;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 840519372;\r\ny_correct = 128;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 7420738134810;\r\ny_correct = 4096;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = flintmax/2-7;\r\ny_correct = 8;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%%\r\nn = flintmax-4;\r\ny_correct = 64;\r\nassert(isequal(countUDivisors(n),y_correct))\r\n\r\n%% \r\np = primes(randi(1000000));\r\nn = p(end);\r\nassert(isequal(countUDivisors(n),2))\r\n\r\n%%\r\nfiletext = fileread('countUDivisors.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-24T17:08:57.000Z","deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-24T17:07:22.000Z","updated_at":"2026-02-03T16:47:48.000Z","published_at":"2022-11-24T17:08:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56738-list-unitary-divisors-of-a-number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 56738\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks for a list of the unitary divisors of a number. For this problem, write a function to count the unitary divisors of a number. For example, the unitary divisors of 18 are 1, 2, 9, and 18; therefore, the number of unitary divisors is 4.\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":57288,"title":"Sum the unitary divisors of a number","description":"Cody Problems 1933 and 46898 deal with , the sum of divisors function. This problem deals with , the sum of unitary divisors functions. Unitary divisors are defined in Cody Problem 56738, which asks for a list of the unitary divisors of a number, and they appear in Cody Problem 56743, which asks for a count. \r\nWrite a function to sum the unitary divisors of a number. For example, the unitary divisors of 18 are 1, 2, 9, and 18; therefore, the sum is 30.","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: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; 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: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1933\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e1933\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: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46898\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e46898\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: 31.5083px 8px; transform-origin: 31.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deal with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD0AAAAlCAYAAADx5+EfAAADrElEQVRoQ+2YN6sVURSF3/sBgqkSK0MhCAqGSgsFAwp2onaCYiwFBS0sxIxamQrhFYqhsVIMhaB2WmhtwMrK8BN0fXA2bMaT5npnHo97Dyy4c0/aa+eZyYkRHJMjyHliTHpUrD4dlj4r5T4SPg5ByYt0xj7hqvCz9ry+Sd+QYK+FB7UCVqxbpzXXhK21xPskDeFvwqUKIm2X7NaGY8Kamo19kT4oYfbXClUjeGQNSv0tnCrt74M0cfdFWC+8LQn0H/PztPeTsKN0Tx+ksQDEibmuB0lyl7Akd1HXpM3K2yXE064ZB+XiVdn7uiaN5k8KXd/j9fkuhBPJLTq6FuazbgV9uLYRLCq6LWmSxbKMm37X3Ncwb659Qs9tyhR3LBR888JZCwR/fkoMLHxfSCbOGtIIQddzQFhciEvmjTRNwxvhkHA7s2+b5pYLG4W1why3B7Ikwi1hPyVpQ0MhzaOL95ZIozUuRZDSIIH4rHlczxdzGg8HmhWnnFJR3izhlXAhrOMsxjkhV4tXaP6DkPSwHGkailuOKZfdETYJ54VSPawlbVeQgFYLz4UjwnvBrGrWY+0eodTG/tGah0I0maVIW1yYQM34eKYJXDFHvA1pQuhHuIxwoHu74sh5A8zX/6WXC0ijvGgCjZHG3dCyuXRMs6aUXIy1IU1cPwmkEZa8gLVtEGKHc0TcWn62Jm0pn80pF/HuloqdNqSNFHc2cwP//QpGqKkExaoRs7RdwGUrhdh7ryedSixmvZpujFpulaG53hJTTh5vaJOtOpGZllIat8O9N6TqYTGLhsM8qZhnWTwTSnMbbhx7NGVX1+kaC3KRWYbYz73D4jUvhGRLqDmfpGJeQdKkTt8UfJyn+FtYJRNe07291lNu64X0zUhMCGJ1s5B76zFSMUv6rG4JlXJFyUx9bqL0MZLGiMW0WTHmam3jy1wtlRsQjkzLiFnSl04sd0bIfSgwJWVreYw0xOiEKFnmbtaK0hWhjKNCqVaa5VEiLh5zTV+qYq7tvYpQIrOXQgUvWJqTL9Wc2FfGVc5nH+v3S8F6azeV/QmxuwlBILA37I41Eij7ujBbmBJKnRgKvizkev3e3nMRlqRWk4hqldlcRwLbKRQ/DpZeOAYVoLkPi5GwTgtdfEGxkKR3L3piX6RRAiFDPqCvHsaHflOsKbT63D5JIyQC3hPoloZB3GI+V8L+8da+SXvr1Gb/XIhBmtHqrOkiPaxcMdA5Y9IDqW0GbhpbegYabSCR/wJjX9cmHBY+kQAAAABJRU5ErkJggg==\" alt=\"sigma(n)\" style=\"width: 30.5px; height: 18.5px;\" width=\"30.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.025px 8px; transform-origin: 168.025px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sum of divisors function. This problem deals with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sigma*(n)\" style=\"width: 35.5px; height: 19.5px;\" width=\"35.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38.4917px 8px; transform-origin: 38.4917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sum of unitary divisors functions. Unitary divisors are defined in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56738-list-unitary-divisors-of-a-number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 56738\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: 142.342px 8px; transform-origin: 142.342px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which asks for a list of the unitary divisors of a number, and they appear in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 56743\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: 77px 8px; transform-origin: 77px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which asks for a count. \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: 355.742px 8px; transform-origin: 355.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to sum the unitary divisors of a number. For example, the unitary divisors of 18 are 1, 2, 9, and 18; therefore, the sum is 30.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = sumUDivisors(n)\r\n  y = sum(n(n/d==true));\r\nend","test_suite":"%%\r\nn = 18;\r\ny_correct = 30;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 128;\r\ny_correct = 129;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 996;\r\ny_correct = 1680;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 1228;\r\ny_correct = 1540;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 5550;\r\ny_correct = 11856;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 54321;\r\ny_correct = 76320;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 648207;\r\ny_correct = 823200;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 840519372;\r\ny_correct = 1877160960;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = 7420738134810;\r\ny_correct = 30500034969600;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%%\r\nn = flintmax/2-7;\r\ny_correct = 4676986919109120;\r\nassert(isequal(sumUDivisors(n),y_correct))\r\n\r\n%% \r\np = primes(randi(1000000));\r\nn = p(end);\r\nassert(isequal(sumUDivisors(n),n+1))\r\n\r\n%%\r\ny = 2;\r\nfor k = 1:90\r\n    y(k+1) = sumUDivisors(y(k));\r\nend\r\nassert(isequal(y(end),18070243128000))\r\n\r\n%%\r\nfiletext = fileread('sumUDivisors.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-25T14:05:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-25T14:03:45.000Z","updated_at":"2026-02-03T16:53:02.000Z","published_at":"2022-11-25T14:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1933\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1933\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/46898\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e46898\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deal with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the sum of divisors function. This problem deals with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma*(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma^*(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the sum of unitary divisors functions. Unitary divisors are defined in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56738-list-unitary-divisors-of-a-number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 56738\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which asks for a list of the unitary divisors of a number, and they appear in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56743\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 56743\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which asks for a count. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 sum the unitary divisors of a number. For example, the unitary divisors of 18 are 1, 2, 9, and 18; therefore, the sum is 30.\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":57293,"title":"Compute the unitary totient of a number","description":"The totient function , the subject of Cody Problems 656 and 50182, gives the number of integers smaller than  that are relatively prime to --that is, that share no common factors with  other than 1. Therefore,  because 1, 2, 4, 5, 7, and 8 (i.e., six numbers less than 9) are relatively prime to 9. \r\nThe unitary totient function  is defined in terms of the function gcd*(,), which is the largest divisor of  that is also a unitary divisor of . Then the unitary totient function gives the number of  (with ) such that gcd*(,) = 1. For example,  because the unitary divisors of 9 are 1 and 9. Therefore, for , the largest divisors that are also unitary divisors of 9 are 1-8. \r\nWrite a function to compute the unitary totient function. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 61.45px 7.79167px; transform-origin: 61.45px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe totient function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi(n)\" style=\"width: 31.5px; height: 18.5px;\" width=\"31.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.2333px 7.79167px; transform-origin: 97.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/656\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e656\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: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; 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/50182\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e50182\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration-line: underline; \"\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: 132.25px 7.79167px; transform-origin: 132.25px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e gives the number of integers smaller than \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.55px 7.79167px; transform-origin: 15.55px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that are relatively prime to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136.117px 7.79167px; transform-origin: 136.117px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--that is, that share no common factors with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.3917px 7.79167px; transform-origin: 77.3917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e other than 1. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi(9) = 6\" style=\"width: 57.5px; height: 18.5px;\" width=\"57.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.4417px 7.79167px; transform-origin: 61.4417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because 1, 2, 4, 5, 7, and 8 (i.e., six numbers less than 9) are relatively prime to 9. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: 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: 84.4px 7.79167px; transform-origin: 84.4px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe unitary totient function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi*(n)\" style=\"width: 36.5px; height: 19.5px;\" width=\"36.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.908px 7.79167px; transform-origin: 122.908px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined in terms of the function gcd*(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.625px 7.79167px; transform-origin: 97.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), which is the largest divisor of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.1667px 7.79167px; transform-origin: 43.1667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that is also a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56738-list-unitary-divisors-of-a-number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eunitary divisor\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: 9.71667px 7.79167px; transform-origin: 9.71667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167.242px 7.79167px; transform-origin: 167.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Then the unitary totient function gives the number of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.6667px 7.79167px; transform-origin: 18.6667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"1 \u003c= k \u003c= n\" style=\"width: 62px; height: 18px;\" width=\"62\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.95px 7.79167px; transform-origin: 50.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) such that gcd*(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.525px 7.79167px; transform-origin: 30.525px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) = 1. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"phi*(9) = 8\" style=\"width: 63px; height: 19.5px;\" width=\"63\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 187.858px 7.79167px; transform-origin: 187.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the unitary divisors of 9 are 1 and 9. Therefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"1, 2, 3,...,8\" style=\"width: 101px; height: 18px;\" width=\"101\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.7833px 7.79167px; transform-origin: 77.7833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the largest divisors that are also unitary divisors of 9 are 1-8. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171px 7.79167px; transform-origin: 171px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the unitary totient function. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function uphi = unitaryTotient(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\nuphi_correct = 1;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 9;\r\nuphi_correct = 8;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 35;\r\nuphi_correct = 24;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 88;\r\nuphi_correct = 70;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 152;\r\nuphi_correct = 126;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 345;\r\nuphi_correct = 176;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 880;\r\nuphi_correct = 600;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 1190;\r\nuphi_correct = 384;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 2275;\r\nuphi_correct = 1728;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 3234;\r\nuphi_correct = 960;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 4701;\r\nuphi_correct = 3132;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 5237;\r\nuphi_correct = 5236;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 6456;\r\nuphi_correct = 3752;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 7092;\r\nuphi_correct = 4704;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 8808;\r\nuphi_correct = 5124;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 9498;\r\nuphi_correct = 3164;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 16034;\r\nuphi_correct = 8016;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 334257;\r\nuphi_correct = 173520;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 8423413;\r\nuphi_correct = 8151660;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = 2^42;\r\nuphi_correct = 2^42-1;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nn = flintmax-7;\r\nuphi_correct = 7197159936298816;\r\nassert(isequal(unitaryTotient(n),uphi_correct))\r\n\r\n%%\r\nassert(isequal(unitaryTotient(unitaryTotient(6503)),3528))\r\n\r\n%%\r\np = primes(2000);\r\nk = randi(length(p));\r\nassert(isequal(unitaryTotient(p(k)),p(k)-1))\r\n\r\n%%\r\ny = 1e5;\r\ncount = 1;\r\nwhile y \u003e 1\r\n    count = count+1;\r\n    y = unitaryTotient(y);\r\nend\r\nassert(isequal(count,20))\r\n\r\n%%\r\nfiletext = fileread('unitaryTotient.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-10T00:19:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-11-26T05:56:52.000Z","updated_at":"2026-02-03T17:01:38.000Z","published_at":"2022-11-26T06:20:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe totient function \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=\\\"phi(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varphi(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/656\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e656\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/50182\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e50182\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e gives the number of integers smaller than \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that are relatively prime to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e--that is, that share no common factors with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e other than 1. Therefore, \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=\\\"phi(9) = 6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varphi(9) = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e because 1, 2, 4, 5, 7, and 8 (i.e., six numbers less than 9) are relatively prime to 9. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 unitary totient function \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=\\\"phi*(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varphi^*(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined in terms of the function gcd*(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), which is the largest divisor of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e that is also a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56738-list-unitary-divisors-of-a-number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunitary divisor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Then the unitary totient function gives the number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"1 \u0026lt;= k \u0026lt;= n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\\\\le k \\\\le n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) such that gcd*(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"k\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) = 1. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"phi*(9) = 8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varphi^*(9) = 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e because the unitary divisors of 9 are 1 and 9. Therefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"1, 2, 3,...,8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek = 1, 2, 3,\\\\ldots,8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the largest divisors that are also unitary divisors of 9 are 1-8. \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\u003eWrite a function to compute the unitary totient function. \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":57472,"title":"Compute the Lagarias Riemann Hypothesis sequence","description":"Write a function that takes an input number  and produces a sequence (i.e., all values up to and including the th value) computed with \r\n\r\nwhere  is the th harmonic number and  is the sum of divisors of . \r\nLagarias proved that  for all  only if the Riemann Hypothesis is true. ","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: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 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: 135.225px 8px; transform-origin: 135.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an input number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 203.45px 8px; transform-origin: 203.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and produces a sequence (i.e., all values up to and including the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth value) computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n) = floor(H(n) + exp(H(n))ln(H(n)))-sigma(n)\" style=\"width: 280px; height: 18.5px;\" width=\"280\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"H(n)\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 8px; transform-origin: 7.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46000\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eharmonic number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sigma(n)\" style=\"width: 30.5px; height: 18.5px;\" width=\"30.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20.6083px 8px; transform-origin: 20.6083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46898\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003esum of divisors\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: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7917px 8px; transform-origin: 28.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLagarias \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://arxiv.org/abs/math/0008177\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproved\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: 15.55px 8px; transform-origin: 15.55px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAlCAYAAACao20PAAAFy0lEQVR4Xu2ay8t2UxjGv+8PkONMJD7FiHKaoJj4MCHlkCE5lgFyrm+CHEJJDkUZKIRIkUMxwEAOEWWCoZFj/gCu39e6637XXqdn773269HedfW877PXs9a97uu+r3WvtffePeu11R7Yu9XWr8bvWQnc8iBYCVwJbPbAKWp5uXBv8y/KDS/S7WOE52bqbyu7WSoDIe9h4Wrhtxk9dYf6Ok64acY+t6qrJQiEvDeEs2Ymzxz9tP74Y8bM3m0Czw4G/KLPn2vG9CbwSBnwuXCL8G7NmAn3f1xgjAnmVX96vFrcLlwpPBRaX6dP5nWn8G2uh94Ekh0Yt786hWkNiNq3hRMnZDl2ntQ50FKzRKE+Fn4XLnNkWfCfoO8uztnVk0Ac8pNwjvDpNH6afv2FWoGx6yFB8Emwubdi2IQ8STfoy7ggM5tof1QqOHsSSPadEdDEwMRGyM/LuYk29E3AYfMFoS3B15tIijCKO9bw04XUmoeMkoWvCsxxx9WLQCLrVwH9fqTBeXM0sTFTkbxJ/0T9fQsRiWweLnxZCHSC6sYwgUEW9iLQsmEp+TSCkFC2KXOsuSkiIfbDMMYmQZFqyz72nXDjGX3mpP963Xs2tLtKn6/4zjYlkAX3EOEHNwkmGpe8FjWb9o+McXkpSY2Zc97YcUtkxEQid3cLr08k0uSTsUuq4dfBAdEtDkaarhHuEj4QvhbOF74S7gkzP1WfvtR9T/+fKRxR8ozuEV3HCqcJtvZYXxj+ooD+cyEzZFbpIMCcEttTMaPp9txEkklXhJFbCRxIbY1A24TjRO8UW28Yn4iMifpH370fHF7yDv0fLZiUUDjsE5BgsglZucRNNFtOh0FMbnpK91xEEuQWtK0EDnxdItD2JyyyqYiGJK6UfrcSyO99MFD0fC88KdjJjZcaAql0OmFyM7WQaUlJxnpCoHrkwrkE3I41qtCRJ7CmGObrZgI9eYOFM3J66v4mBPrFnAx7KTjFiDKpKVVq5icjsHf1aycnVh0y/oPCC5UA83x6AkuKUVS7XAZSzRFZOad5p6c2mJsQ+IDGYS0lupDQx6Iotn1QCym9CYyJw2aOvihoqueWUTZ2k1DbAjBebs2xai9H8CYEGkGMF8sxSvBNmHjLutZr+5IibmolOqYKHWzmUxloDrWCIpZxOyIz2Ug93yODuTiJKV2+L9rF2WxFSapQSvVrTmkhu2Lawds9iLNxfaK0FjHI9A5/xwT6iB80DiP7k4Gco2zdqlW5fpOamoT1kzxGSjBgclwbt0ZeT+JsbB+8pfn5TB0oYjxR79CUfPpNZSpjzDjrp1Zd+b1Qbi2lz1ShlCKBdYVFv5b5OQJj4lgiWJPnOn2Jx7V1MKd2tDcf0WbwTDUmsMS2VaZs5tmA2vqHFBwq+JN0i66a4608TkWgL5TYPvwlMOEcOVat5ZSjlnVefYy41i1Bre/cfZ8QKTXzFWhSZmMCvdO8I+x523myhKfrOJT73wn3pyJD37EOEjWDE/QwG298imhfKHECA3kHhNyDYbO9tlcsOZN9XVwFjyWn9Xcm+6kgtoTKHoqUihgMIBK5cArkcVzmN5WcpudelbBFOudQM5z+U/Jp0kEBwziPCqUXmGh/mDD2IBvV2HQr0EpSrZ0FK0nxuMBxoS1DkJd9lyhFIGl7q8D55J/CW4KXEjq+VHhTqB3okoWvCalHShDIGJyppipZexEKG54SSg+FTbJra27Nkbt5H0W6MPgEO/DLZ0LxVZSp1VptwraujJW1Wv92H3nNBUJrHwTuya2NM+3+1vfZ91cm9p38eW8CGRQpvU0YWxnW5o0iXDtD/3GFXRs3db91uzOm710jkIF7vb9Jhj8v1B4ztTjMJLulba7NR7qx1BsIB21YIgNtsmTiucLYl45ip+FwjrNuFuZ8WXgKgYv/dkkCmRzrzFzO3s2qcXGicgMuTeB/ZuL/F0NWArecyZXAlcAt98CWm79m4JYT+C/hlHo1PW5AmgAAAABJRU5ErkJggg==\" alt=\"a(n) \u003e= 0\" style=\"width: 56px; height: 18.5px;\" width=\"56\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8333px 8px; transform-origin: 33.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e only if the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Riemann_hypothesis\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eRiemann Hypothesis\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: 24.8833px 8px; transform-origin: 24.8833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is true. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = LagariasRH(n)\r\n  a = floor(H(n)+exp(H(n))*ln(H(n))-sigma(n);\r\nend","test_suite":"%%\r\nn = 100;\r\ny = LagariasRH(n);\r\ny_correct = [0 0 1 0 4 0 7 2 7 5 13 0 17 9 12 8 23 5 27 8 21 20 34 1 33 25 30 17 46 7 50 22 40 37 46 6 62 43 50 19 70 19 74 37 46 55 82 9 79 46 70 47 95 32 83 38 81 74 107 2 112 81 76 56 102 45 125 70 103 58 133 14 138 101 94 81 129 60 151 48 116 115 160 23 142 122 137 80 173 33 158 105 148 136 163 34 192 122 140 82];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1000;\r\ny = LagariasRH(n);\r\nsum_correct = 914917;\r\nnprimes_correct = 155;\r\nassert(isequal(sum(y),sum_correct) \u0026\u0026 isequal(sum(isprime(y)),nprimes_correct))\r\n\r\n%%\r\nn = 10000;\r\ny = LagariasRH(n);\r\ny953_correct = [2461 4261 7113 8116 12978 11195 18980 16294 22215 21474];\r\nassert(isequal(y(953:953:n),y953_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = LagariasRH(n);\r\nsum_correct = 13587430007;\r\nnprimes_correct = 8811;\r\nassert(isequal(sum(y),sum_correct) \u0026\u0026 isequal(sum(isprime(y)),nprimes_correct))\r\n\r\n%%\r\nn = 1000000;\r\ny = LagariasRH(n);\r\ny95395_correct = [308341 521204 855014 963930 1629129 1304492 2221964 1881773 2573303 2750908];\r\nassert(isequal(y(95395:95395:n),y95395_correct))\r\n\r\n%%\r\ny1 = LagariasRH(20403);\r\ny2 = LagariasRH(y1(end));\r\nf  = factor(y2(end));\r\ns3 = sum(LagariasRH(prod(f(end-2:end))));\r\ns3_correct = 350693690;\r\nassert(isequal(s3,s3_correct))\r\n\r\n%%\r\nfiletext = fileread('LagariasRH.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-25T05:52:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-23T23:17:27.000Z","updated_at":"2026-02-03T17:06:47.000Z","published_at":"2022-12-23T23:19:21.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes an input number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and produces a sequence (i.e., all values up to and including the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth value) computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n) = floor(H(n) + exp(H(n))ln(H(n)))-sigma(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n) = \\\\lfloor H(n)+\\\\exp(H(n))\\\\ln(H(n))\\\\rfloor - \\\\sigma(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46000\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eharmonic number\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:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46898\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum of divisors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLagarias \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://arxiv.org/abs/math/0008177\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproved\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n) \u0026gt;= 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n) \\\\ge 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e only if the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Riemann_hypothesis\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRiemann Hypothesis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is true. \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":57487,"title":"Compute the largest number with a given integer complexity","description":"Cody Problems 42831 and 42834 ask us to compute integer complexity, the smallest number of 1s needed to construct a number with addition and multiplication. For example, the integer complexity of 11 is 8 because it can be written as . The other numbers with integer complexity 8 are 13, 14, 15, 16, and 18. Therefore  is the largest integer with complexity 8.\r\nWrite a function to determine the largest number with given integer complexities. Return the answers as a cell array of strings. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: 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: 49.7917px 8px; transform-origin: 49.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/42831\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e42831\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: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/42834\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e42834\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: 271.742px 8px; transform-origin: 271.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e ask us to compute integer complexity, the smallest number of 1s needed to construct a number with addition and multiplication. For example, the integer complexity of 11 is 8 because it can be written as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"(1+1)x(1+1+1+1+1)+1\" style=\"width: 204.5px; height: 18.5px;\" width=\"204.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 259.817px 8px; transform-origin: 259.817px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The other numbers with integer complexity 8 are 13, 14, 15, 16, and 18. Therefore \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"18 = (1+1+1)x(1+1+1)x(1+1)\" style=\"width: 249px; height: 18.5px;\" width=\"249\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.133px 8px; transform-origin: 122.133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the largest integer with complexity 8.\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: 366.283px 8px; transform-origin: 366.283px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the largest number with given integer complexities. Return the answers as a cell array of strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function E = maxWithCmplxty(n)\r\n  E = num2str(n);\r\nend","test_suite":"%%\r\nn = 0:4;\r\nE = maxWithCmplxty(n);\r\nE_correct = {'1' '1' '2' '3' '4'};\r\nassert(isequal(E,E_correct))\r\n\r\n%%\r\nn = 8;\r\nE = maxWithCmplxty(n);\r\nE_correct = '18';\r\nassert(strcmp(E{1},E_correct))\r\n\r\n%%\r\nn = 12;\r\nE = maxWithCmplxty(n);\r\nE_correct = '81';\r\nassert(strcmp(E{1},E_correct))\r\n\r\n%%\r\nn = [31 43 79];\r\nE = maxWithCmplxty(n);\r\nE_correct = {'78732','6377292','3389154437772'};\r\nassert(isequal(E,E_correct))\r\n\r\n%%\r\nn = [103 151 197];\r\nE = maxWithCmplxty(n);\r\nE_correct = {'22236242266222092','957197316922470118360332','20602102921755074907947094535686'};\r\nassert(isequal(E,E_correct))\r\n\r\n%%\r\nn = [241 307 349];\r\nE = maxWithCmplxty(n);\r\nE_correct = {'197078439219127897754777613608511063468','6184530248784135972437533557187455272425290264012','29580416459496810047953577440487325756896718148771211628'};\r\nassert(isequal(E,E_correct))\r\n\r\n%%\r\nn = 1000:1002;\r\nE = maxWithCmplxty(n);\r\nE_correct = {'1014650697509413079627234489686710374303861808496103820156013382714388841919074932817392194199171363410580468761266602680002445025736755375715839382921059431364','1521976046264119619440851734530065561455792712744155730234020074071583262878612399226088291298757045115870703141899904020003667538605133063573759074381589147046','2282964069396179429161277601795098342183689069116233595351030111107374894317918598839132436948135567673806054712849856030005501307907699595360638611572383720569'};\r\nassert(isequal(E,E_correct))\r\n\r\n%%\r\nE1 = maxWithCmplxty(20);\r\nE2 = maxWithCmplxty(str2num(E1{1}));\r\nE_correct = {'7602033756829688179535612101927342434798006222913345882096671718462026450847558385638399133044640009857513126790996106341658482736771462692522663416083613709397190583473914100243037919870652143046001421207236044960360057945209303129'};\r\nassert(isequal(E2,E_correct))\r\n\r\n%%\r\nfiletext = fileread('maxWithCmplxty.m');\r\nillegal = contains(filetext, 'assignin') ||  contains(filetext, 'oeis') || contains(filetext, 'java') || contains(filetext, 'py'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-03T15:30:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-02T00:54:13.000Z","updated_at":"2026-02-03T17:12:47.000Z","published_at":"2023-01-02T00:55:03.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/42831\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e42831\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/42834\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e42834\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ask us to compute integer complexity, the smallest number of 1s needed to construct a number with addition and multiplication. For example, the integer complexity of 11 is 8 because it can be written as \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=\\\"(1+1)x(1+1+1+1+1)+1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e(1+1)\\\\times(1+1+1+1+1)+1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The other numbers with integer complexity 8 are 13, 14, 15, 16, and 18. Therefore \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=\\\"18 = (1+1+1)x(1+1+1)x(1+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e18 = (1+1+1)\\\\times(1+1+1)\\\\times(1+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the largest integer with complexity 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\u003eWrite a function to determine the largest number with given integer complexities. Return the answers as a cell array of strings. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57492,"title":"Compute the Tetris sequence","description":"In the Tetris sequence, which starts with a 1, the next term is the smallest positive integer not already in the sequence that has no common 1-bits with the previous term. The first five terms are 1, 2, 4, 3, and 8 because the binary expansions 0001, 0010, 0100, 0011, and 1000 have no common ones among consecutive terms, and they are the smallest numbers with that property not already in the sequence. \r\nThe discussion of this sequence involves odd gaps in the plot of the terms  (say) as a function of their position  in the sequence. A plot of  vs.  (below) makes one think of the Sierpinski gasket. Neil J.A. Sloane uses this resemblance to propose using “facial recognition” to connect sequences.  \r\nWrite a function to compute the th term of the Tetris sequence.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 539.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 269.85px; transform-origin: 407px 269.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.833px 8px; transform-origin: 378.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the Tetris sequence, which starts with a 1, the next term is the smallest positive integer not already in the sequence that has no common 1-bits with the previous term. The first five terms are 1, 2, 4, 3, and 8 because the binary expansions 0001, 0010, 0100, 0011, and 1000 have no common ones among consecutive terms, and they are the smallest numbers with that property not already in the sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.658px 8px; transform-origin: 230.658px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe discussion of this sequence involves odd gaps in the plot of the terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n)\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.458px 8px; transform-origin: 110.458px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) as a function of their position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in the sequence. A plot of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n+1)\" style=\"width: 54px; height: 18.5px;\" width=\"54\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.825px 8px; transform-origin: 12.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vs. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a(n)\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.267px 8px; transform-origin: 237.267px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (below) makes one think of the Sierpinski gasket. Neil J.A. Sloane uses this resemblance to propose \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://sites.math.rutgers.edu/~zeilberg/EM22/C27.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eusing “facial recognition”\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.9px 8px; transform-origin: 73.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to connect sequences. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.6583px 8px; transform-origin: 98.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.1167px 8px; transform-origin: 94.1167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of the Tetris sequence.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 344.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 172.35px; text-align: left; transform-origin: 384px 172.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 346px;height: 339px\" 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\" data-image-state=\"image-loaded\" width=\"346\" height=\"339\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = tetris(n)\r\n  y = dec2bin(n);\r\nend","test_suite":"%%\r\nn = 5;\r\ny_correct = 8;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nn = 15;\r\ny_correct = 32;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nn = 51;\r\ny_correct = 29;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nn = 155;\r\ny_correct = 167;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nn = 515;\r\ny_correct = 480;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nn = 1155;\r\ny_correct = 872;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nn = 1511;\r\ny_correct = 3084;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nn = 5151;\r\ny_correct = 9480;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nn = 15151;\r\ny_correct = 7095;\r\nassert(isequal(tetris(n),y_correct))\r\n\r\n%%\r\nassert(isequal(tetris(tetris(10020)),18284))\r\n\r\n%%\r\nfiletext = fileread('tetris.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis') || contains(filetext, 'persistent') ||  contains(filetext, 'switch'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":46909,"edited_by":46909,"edited_at":"2023-01-05T14:35:12.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2023-01-05T14:35:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-01-02T15:12:40.000Z","updated_at":"2026-02-05T10:56:07.000Z","published_at":"2023-01-02T15:22:44.000Z","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\u003eIn the Tetris sequence, which starts with a 1, the next term is the smallest positive integer not already in the sequence that has no common 1-bits with the previous term. The first five terms are 1, 2, 4, 3, and 8 because the binary expansions 0001, 0010, 0100, 0011, and 1000 have no common ones among consecutive terms, and they are the smallest numbers with that property not already in the sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe discussion of this sequence involves odd gaps in the plot of the terms \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) as a function of their position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in the sequence. A plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n+1)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e vs. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a(n)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (below) makes one think of the Sierpinski gasket. Neil J.A. Sloane uses this resemblance to propose \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.math.rutgers.edu/~zeilberg/EM22/C27.pdf\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eusing “facial recognition”\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e to connect sequences. \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\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" 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