{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":42835,"title":"Return the sequence element II","description":"Given positive integers x and n, return a positive integer, y, which is the nth term in the \u003chttps://en.wikipedia.org/wiki/Juggler_sequence Juggler sequence\u003e beginning with x.\r\n\r\nThe Juggler sequence is defined by:\r\n\r\na(i+1) = floor(a(i)^0.5) , for even a(i).\r\n\r\na(i+1) = floor(a(i)^1.5) , for odd a(i).\r\n\r\nFor the purpose of this problem, the first element in the sequence is a(1) = x.\r\n\r\nExample:\r\n\r\nx = 3\r\n\r\nn = 5\r\n\r\ny = 6","description_html":"\u003cp\u003eGiven positive integers x and n, return a positive integer, y, which is the nth term in the \u003ca href = \"https://en.wikipedia.org/wiki/Juggler_sequence\"\u003eJuggler sequence\u003c/a\u003e beginning with x.\u003c/p\u003e\u003cp\u003eThe Juggler sequence is defined by:\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/p\u003e\u003cp\u003eFor the purpose of this problem, the first element in the sequence is a(1) = x.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ex = 3\u003c/p\u003e\u003cp\u003en = 5\u003c/p\u003e\u003cp\u003ey = 6\u003c/p\u003e","function_template":"function y = juggler(x,n)\r\n  y = x + n;\r\nend","test_suite":"%%\r\nx = 3;\r\nn = 5;\r\ny_correct = 6;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 33;\r\nn = 3;\r\ny_correct = 2598;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 45;\r\nn = 4;\r\ny_correct = 72;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 163;\r\nn = 23;\r\ny_correct = 333;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 13;\r\ny_correct = 34276462;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 18;\r\ny_correct = 1;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 99;\r\ny_correct = 1;\r\nassert(isequal(juggler(x,n),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-27T19:07:54.000Z","updated_at":"2026-03-05T12:02:09.000Z","published_at":"2016-04-27T19:07:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven positive integers x and n, return a positive integer, y, which is the nth term in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Juggler_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJuggler sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e beginning with x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Juggler sequence is defined by:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the purpose of this problem, the first element in the sequence is a(1) = x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42836,"title":"Juggler sequence revisited","description":"This problem is related to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii Problem 42835\u003e.\r\n\r\nFor any starting positive integer, a(1) = x, the \u003chttps://en.wikipedia.org/wiki/Juggler_sequence Juggler sequence\u003e is defined by:\r\n\r\na(i+1) = floor(a(i)^0.5) , for even a(i).\r\n\r\na(i+1) = floor(a(i)^1.5) , for odd a(i).\r\n\r\nWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\r\n\r\nLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\r\n\r\nLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\r\n\r\nGiven x, return l(x) and h(x).\r\n\r\nExample:\r\n\r\nx = 3\r\n\r\nl = 6\r\n\r\nh = 36","description_html":"\u003cp\u003eThis problem is related to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii\"\u003eProblem 42835\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eFor any starting positive integer, a(1) = x, the \u003ca href = \"https://en.wikipedia.org/wiki/Juggler_sequence\"\u003eJuggler sequence\u003c/a\u003e is defined by:\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/p\u003e\u003cp\u003eWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\u003c/p\u003e\u003cp\u003eLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\u003c/p\u003e\u003cp\u003eLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\u003c/p\u003e\u003cp\u003eGiven x, return l(x) and h(x).\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ex = 3\u003c/p\u003e\u003cp\u003el = 6\u003c/p\u003e\u003cp\u003eh = 36\u003c/p\u003e","function_template":"function [l h] = juggler(x)\r\n  l = x;\r\n  h = x;\r\nend","test_suite":"%%\r\nx = 3;\r\nl_correct = 6;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 5;\r\nl_correct = 5;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 10;\r\nl_correct = 7;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 77;\r\nl_correct = 19;\r\nh_correct = 2322378;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 99;\r\nl_correct = 11;\r\nh_correct = 37754276;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 117;\r\nl_correct = 11;\r\nh_correct = 44992;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 1;\r\nl_correct = 0;\r\nh_correct = 1;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 2;\r\nl_correct = 1;\r\nh_correct = 2;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-27T19:30:07.000Z","updated_at":"2025-12-31T12:07:49.000Z","published_at":"2016-04-27T19:30:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 42835\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any starting positive integer, a(1) = x, the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Juggler_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJuggler sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is defined by:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven x, return l(x) and h(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003el = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = 36\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":42835,"title":"Return the sequence element II","description":"Given positive integers x and n, return a positive integer, y, which is the nth term in the \u003chttps://en.wikipedia.org/wiki/Juggler_sequence Juggler sequence\u003e beginning with x.\r\n\r\nThe Juggler sequence is defined by:\r\n\r\na(i+1) = floor(a(i)^0.5) , for even a(i).\r\n\r\na(i+1) = floor(a(i)^1.5) , for odd a(i).\r\n\r\nFor the purpose of this problem, the first element in the sequence is a(1) = x.\r\n\r\nExample:\r\n\r\nx = 3\r\n\r\nn = 5\r\n\r\ny = 6","description_html":"\u003cp\u003eGiven positive integers x and n, return a positive integer, y, which is the nth term in the \u003ca href = \"https://en.wikipedia.org/wiki/Juggler_sequence\"\u003eJuggler sequence\u003c/a\u003e beginning with x.\u003c/p\u003e\u003cp\u003eThe Juggler sequence is defined by:\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/p\u003e\u003cp\u003eFor the purpose of this problem, the first element in the sequence is a(1) = x.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ex = 3\u003c/p\u003e\u003cp\u003en = 5\u003c/p\u003e\u003cp\u003ey = 6\u003c/p\u003e","function_template":"function y = juggler(x,n)\r\n  y = x + n;\r\nend","test_suite":"%%\r\nx = 3;\r\nn = 5;\r\ny_correct = 6;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 33;\r\nn = 3;\r\ny_correct = 2598;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 45;\r\nn = 4;\r\ny_correct = 72;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 163;\r\nn = 23;\r\ny_correct = 333;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 13;\r\ny_correct = 34276462;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 18;\r\ny_correct = 1;\r\nassert(isequal(juggler(x,n),y_correct))\r\n\r\n%%\r\nx = 37;\r\nn = 99;\r\ny_correct = 1;\r\nassert(isequal(juggler(x,n),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":45,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-27T19:07:54.000Z","updated_at":"2026-03-05T12:02:09.000Z","published_at":"2016-04-27T19:07:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven positive integers x and n, return a positive integer, y, which is the nth term in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Juggler_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJuggler sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e beginning with x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Juggler sequence is defined by:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the purpose of this problem, the first element in the sequence is a(1) = x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42836,"title":"Juggler sequence revisited","description":"This problem is related to \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii Problem 42835\u003e.\r\n\r\nFor any starting positive integer, a(1) = x, the \u003chttps://en.wikipedia.org/wiki/Juggler_sequence Juggler sequence\u003e is defined by:\r\n\r\na(i+1) = floor(a(i)^0.5) , for even a(i).\r\n\r\na(i+1) = floor(a(i)^1.5) , for odd a(i).\r\n\r\nWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\r\n\r\nLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\r\n\r\nLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\r\n\r\nGiven x, return l(x) and h(x).\r\n\r\nExample:\r\n\r\nx = 3\r\n\r\nl = 6\r\n\r\nh = 36","description_html":"\u003cp\u003eThis problem is related to \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii\"\u003eProblem 42835\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eFor any starting positive integer, a(1) = x, the \u003ca href = \"https://en.wikipedia.org/wiki/Juggler_sequence\"\u003eJuggler sequence\u003c/a\u003e is defined by:\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/p\u003e\u003cp\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/p\u003e\u003cp\u003eWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\u003c/p\u003e\u003cp\u003eLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\u003c/p\u003e\u003cp\u003eLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\u003c/p\u003e\u003cp\u003eGiven x, return l(x) and h(x).\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003ex = 3\u003c/p\u003e\u003cp\u003el = 6\u003c/p\u003e\u003cp\u003eh = 36\u003c/p\u003e","function_template":"function [l h] = juggler(x)\r\n  l = x;\r\n  h = x;\r\nend","test_suite":"%%\r\nx = 3;\r\nl_correct = 6;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 5;\r\nl_correct = 5;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 10;\r\nl_correct = 7;\r\nh_correct = 36;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 77;\r\nl_correct = 19;\r\nh_correct = 2322378;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 99;\r\nl_correct = 11;\r\nh_correct = 37754276;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 117;\r\nl_correct = 11;\r\nh_correct = 44992;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 1;\r\nl_correct = 0;\r\nh_correct = 1;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))\r\n\r\n%%\r\nx = 2;\r\nl_correct = 1;\r\nh_correct = 2;\r\n[l h] = juggler(x);\r\nassert(isequal([l h],[l_correct h_correct]))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-27T19:30:07.000Z","updated_at":"2025-12-31T12:07:49.000Z","published_at":"2016-04-27T19:30:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42835-return-the-sequence-element-ii\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 42835\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any starting positive integer, a(1) = x, the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Juggler_sequence\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eJuggler sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is defined by:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^0.5) , for even a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea(i+1) = floor(a(i)^1.5) , for odd a(i).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a Juggler sequence reaches 1, all subsequent elements will also be 1s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet l(x) be the number of Juggler sequence iterations required to reach 1 with a starting value of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet h(x) be the maximum value of a Juggler sequence with a starting value of x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven x, return l(x) and h(x).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003el = 6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = 36\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"term":"tag:\"juggler\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"juggler\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"juggler\"","","\"","juggler","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007faf509c8cc0\u003e":null,"#\u003cMathWorks::Search::Field:0x00007faf509c8c20\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007faf509c8360\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007faf509c8f40\u003e":1,"#\u003cMathWorks::Search::Field:0x00007faf509c8ea0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007faf509c8e00\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007faf509c8d60\u003e":"tag:\"juggler\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007faf509c8d60\u003e":"tag:\"juggler\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"juggler\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"juggler\"","","\"","juggler","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007faf509c8cc0\u003e":null,"#\u003cMathWorks::Search::Field:0x00007faf509c8c20\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007faf509c8360\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007faf509c8f40\u003e":1,"#\u003cMathWorks::Search::Field:0x00007faf509c8ea0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007faf509c8e00\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007faf509c8d60\u003e":"tag:\"juggler\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007faf509c8d60\u003e":"tag:\"juggler\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":42835,"difficulty_rating":"easy"},{"id":42836,"difficulty_rating":"easy-medium"}]}}