{"group":{"group":{"id":47645,"name":"Sequences \u0026 Series V","lockable":false,"created_at":"2022-07-02T12:07:52.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"There's no general formula for the next term in this series.","is_default":false,"created_by":46909,"badge_id":62,"featured":false,"trending":false,"solution_count_in_trending_period":2,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":6556,"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\u003eThere's no general formula for the next term in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e series.\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: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 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-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere's no general formula for the next term 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: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e series.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2022-07-02T14:53:13.000Z"},"current_player":null},"problems":[{"id":51274,"title":"Solve a nonlinear difference equation","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 95.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 47.875px; transform-origin: 407px 47.875px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 44.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.25px; text-align: left; transform-origin: 384px 22.25px; 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: 102.967px 7.91667px; transform-origin: 102.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the difference equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-8px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_{n+1} = a_n^p\" style=\"width: 60.5px; height: 22px;\" width=\"60.5\" height=\"22\"\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: 48.2333px 7.91667px; transform-origin: 48.2333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with the initial (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" 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: 22.95px 7.91667px; transform-origin: 22.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.70833px 7.91667px; transform-origin: 9.70833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 7.91667px; transform-origin: 28.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 2 and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 2\" style=\"width: 38px; height: 18px;\" width=\"38\" 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: 19.4417px 7.91667px; transform-origin: 19.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a1 = 4\" style=\"width: 41.5px; height: 20px;\" width=\"41.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a2 = 16\" style=\"width: 49px; height: 20px;\" width=\"49\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a3 = 256\" style=\"width: 56.5px; height: 20px;\" width=\"56.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.1px 7.91667px; transform-origin: 17.1px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, etc. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.25px; 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 21.125px; text-align: left; transform-origin: 384px 21.125px; 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: 125.492px 7.91667px; transform-origin: 125.492px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes two values 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: 103.475px 7.91667px; transform-origin: 103.475px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the corresponding values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABNklEQVRYhe2VUbWDMAyGPw84wAAGqgAFOKgDHMwCGpBQD1hAAxbYA8lpxsrY4ZTdh9vvnD4sWfPTpEmhUCgUCoU/ogE80ANObE5+N3eKBmAWcQcMwASssuo7hDsJPgPVzrca30+Frfgjt3BrgruEvz7xX6YCFgk8HvxHs7KQzspleuKpjm5xEH/IKQzx1EeBnfm4PqfwN4ED55m5hE15m/B7YmZurfdevGNru5HXsgzELPXin9hasBL/KraPNEY8yOZKgmq/68kHWfuO0LK04nfEaXg6CfVkdo3EFC87+55FPjQQZ8As66sx3LKd1ic2fHpMbOa82HQgHc2MbOidmYiZ0oHkjzblQuvdGZteuNueXSX1EM3GlmrfLOiAsrXVOzCwtd5t4g/e50PNdvsXXktRKBT+CU+MO3Oqf1KjkgAAAABJRU5ErkJggg==\" alt=\"a_n\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 85.5833px 7.91667px; transform-origin: 85.5833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand returns the initial value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAABOUlEQVRYhe2VXbGDMBBGj4c4wEANREEV1AEO4qAW0ICEeLgWqgEL3Idkh21uEmiB2+lMzkweYMl+2T8CjUaj0Wh8iAvQAw6w8Z2Nz5czRT3wiOIWGIAfYI6rO0P4Fp0/AJPYZmX7V2Etfj9a+Kqc24y9W7G/jQGm6HgsfCNZmfibFUPoCVmeFxrSsURV2uSj3RcOPqpD9Su+npCoU8eCVYdziW0gX4qJMB1Vao4FTz4zRr1PSyF7qv2hU37N2HuWzKT1loPnIhS/1cmoid8IYzfyXJYh7pO9NfFSKYGQxll9aOJyLPMukUs3y0RsEV+tu0Sml+7eKXm/RWCzOISUO0KN0/926TKRkdot/g67G24vUo4UGbXcBB1G7SdTuqAOQ6ZBj5T0wqlRCx3LhXInTMShN1+j0fgefgFsKIIPBf1eagAAAABJRU5ErkJggg==\" alt=\"a0\" style=\"width: 15.5px; height: 20px;\" width=\"15.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.225px 7.91667px; transform-origin: 27.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the exponent \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);\"\u003ep\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 7.91667px; transform-origin: 3.88333px 7.91667px; 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 [p,a0] = recurrence1(n,a)\r\n  p = f1(n,a);\r\n  a0 = f2(n,a);\r\nend","test_suite":"%%\r\na = [16 65536];\r\nn = [2 4];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [512 134217728];\r\nn = [2 3];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [4.756828460010884 2684.848561202718];\r\nn = [2 6];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 3/2;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [0.840896415253715 0.999994711720674];\r\nn = [2 17];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/2;\r\na0_correct = 1/2;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-10)\r\n\r\n%%\r\na = [3.236570233533632 6.5197372744901154];\r\nn = [53 100];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1.01;\r\na0_correct = 2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [27.065907669081142 6576132142.795870];\r\nn = [4 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = (1+sqrt(5))/2;\r\na0_correct = (1+sqrt(5))/2;\r\nassert(abs(p-p_correct)\u003c1e-12 \u0026\u0026 abs(a0-a0_correct)\u003c1e-12)\r\n\r\n%%\r\na = [1.033024879021228 1.000000123944382];\r\nn = [2 8];\r\n[p,a0] = recurrence1(n,a);\r\np_correct = 1/8;\r\na0_correct = 8;\r\nassert(abs(p-p_correct)\u003c1e-10 \u0026\u0026 abs(a0-a0_correct)\u003c1e-9)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-02T16:23:14.000Z","updated_at":"2026-01-13T13:35:21.000Z","published_at":"2021-04-02T16:27:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the difference equation \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} = a_n^p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_{n+1} = a_n^p\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with the initial (\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 = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) value \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=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is 2 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=\\\"p = 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \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=\\\"a1 = 4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1 = 4\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=\\\"a2 = 16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_2 = 16\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=\\\"a3 = 256\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_3= 256\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, etc. \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 two values 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 and the corresponding values 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\\\"/\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:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand returns the initial value \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=\\\"a0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the exponent \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=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\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\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":51715,"title":"Iterate the sum of divisors and totient","description":"","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: 339px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 169.5px; transform-origin: 407px 169.5px; 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46898\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 46898\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: 160.25px 7.91667px; transform-origin: 160.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deals with the sum of divisors function, denoted by \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: 19px;\" width=\"30.5\" 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: 21.7833px 7.91667px; transform-origin: 21.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, while \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: underline; text-decoration-line: underline; \"\u003eCody Problem 656\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: 46.675px 7.91667px; transform-origin: 46.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e deals with the totient function, denoted by \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: 19px;\" width=\"31.5\" 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: 164.125px 7.91667px; transform-origin: 164.125px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The sum of divisors is straightforward: 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=\"sigma(12) = 1+2+3+4+6+12 = 28\" style=\"width: 227.5px; height: 19px;\" width=\"227.5\" 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: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. The totient 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: 95.2917px 7.91667px; transform-origin: 95.2917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e counts the numbers less 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: 84.4px 7.91667px; transform-origin: 84.4px 7.91667px; 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: 44.725px 7.91667px; transform-origin: 44.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. 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(12) = 4\" style=\"width: 65px; height: 19px;\" width=\"65\" 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: 68.5083px 7.91667px; transform-origin: 68.5083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e because the greatest common divisor of 12 and four numbers (1, 5, 7, 11) is 1. \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: 384px 7.91667px; transform-origin: 384px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat happens if you repeatedly apply the two functions, starting with the sum of divisors and alternating? For example, start with 7. Then \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,iVBORw0KGgoAAAANSUhEUgAAAvMAAAAmCAYAAABJaRRiAAAQC0lEQVR4nO2d63HrOAyFTw/uwA24AVfgCtxBOnAHacE1pIT0kBZSQ1q4+0M+K4ThA3xZpIVvRrOzvo4skQRwCFIQYBiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRiGYRg75x3AqdG5jo/zHRqdz2jDAcAd7frlAuCt0bmMelraMLCMlWPD8xn1tLbhPfrqkcf09XGUcsDvvrwBOFddkTEarf18DRYjBuMOvwO5YnEGmsP9+zOAL7xOkDhjEa683wvmurcDgE/EncABy33Kfk0FghuW8fOqXLDc4+iEbDjGAfE+PmKx4VECRwnueE4dIxOzYfPVfk5YxM/n4xh54nJFvi+9PP6G9+cmVw4APlA3QRiVM/ImKif8juEzTnJy/XzvNnqFGBHjhKUdppiw3OEPYgcAPwD+KQ/fOa5YOnpmLgC+sThKGgbv6+fx76NzwHK9McO8Ybmfd6z3+fb4LGWs98ffvRpnLGP7Z+sLSRCy4RSfWO4vtrpywjL+p3BmHniPmuNzo2vUELNh89V/od/+h0XMji42rsgbf/TX7M+YfXLszBCrNJyh813kiLAfmEmI5vj5Z7bR7DEihPSrw4+RN4Qd+BXLTVDIhg52eKgjZxZ6bANftoQO8h/Gn+F/IN4Hdyz34Zvxn7AM6JSxfuN1ggWw9C/FwMhiPmbDqb+j7aac/axC74i1/2I+jA575OxlzIbNV69wGxLvdQafRB+rEUPMhHJcawXUMfP7I+ITnCnfJQXZ1+Pv6dd5fGN8sab181u10awxIsYH1vsfenww0IWE6DfSjp3niHUiB8rogtcHB3jo2hlER87oXbHcR2hp+YQ1MIS+w+AYywqcE+eYDWnIo4r5lA2HYJ9rnT2wjPHRt6G4cPtBakwycI06dlM2bL56QSZYYpOW0fiGzrYo+tmPueP1hrFjVYwjFj/F/2p91weWNnPFGLeW8TwfLS+2MVo/v3UbzRgjQsj2G17MM9D5OEf+TcIbTnXgOxaHNRPcYhHryBm2YaQCxQ3pe+B3Usb8hdfYP8/tRe8Yu39jNhyCKw7sU62Yv2AugcT7TAkeTmxGFjkxGzZfvSIn4DNk5IH0RI24K4UldnjA+CtQGmRsjvkuiuBQ/Oa/p5JZW1Pi57doo9liRAjGBBkjhxXz7KCYw9N0CGdtqRvV/N5oaIyBg3fU5SWuHMQMUDNgKWpT2T/N740Os1988HVUMV9qUzJbnSPmAV0GeCQ0Poxje9SqTBqb2ruvBn5n0kbOsrpobUpOVGrG6h3jxistWqF6Q7ptR99KUWqPW7XRbDHChat7fHZw5LEBYA1gNXCQabM4X5jLyQLrkmZovxi3n4wqBLj/LYbcchHaksCMUGpAUyCO2h4aaMjA2GK+xIYv+J3VyxUH7xizLWrg2B41m6Sx4RSv7qvdB4CHDbwOTAaltk9IUaFZbdL85ixt5EMrVK9I2/Xo2ddSrbZVG80eI1j5ipX9njo2jliziKHDvRA+KFUDMyHaWViLCcSzkYP4G7+dLjNmH+iXiT4+fsc1RtnfIUNkANfsYZMPzHw659Tsl5e0EB9b8Y7fe1GfJeZ9JUHdw83M5NowH4CTS+y5Yl4rPmaBE9memcoDVnuVfoIlz1KlQXNsL8Sr+2r6YtmX0p6eUUa4xIbpW1PIB3pZWlPGgBx7ZMJl5r3NWqGqobePr7F/oFyrbdVGM8cId5vQ08S8LD2UOuQgahUgciu50OGWdHJurejQUZJ9k46U7cbZZ6+9h0esD6XIfmIJKE4s2AehUnPa9nYfHOO98an2nIGsDVA+cmplx44SaLhyjPR29Ef8HV+h4+L8Xa4Nf+Lv8wy5zr7GdxzRpm9bBgmK1h7C5oDVT9yx+mDWiqeNsf99AbvGZ0pe3Ve7yQi3Eof03a0ptWFAL9TkORgX3HPnlEmuSea16NvauNlSqHILSeutIS3sv8bfbtVGs8YIru7JsfkUMe86j+/HhfhKsLkBnBdY08G5y7a1v0tRVXuUdojb3j3ry3PPtltV4iA+p2PgTNJ3b7fA5yFcQc/+zZ0A5f6uJKcmeOgoEd5sW3ds9hTzMpvI36AI8ZUVlBPyXFu6wb88X+LsKShykY6x5mi5havXFhtpS+71coyfxXdD91ZjS2QPvtr1WdJvuhU5Woq2GhvmdadsybUbt2Y+H6Dlv2viEsVkCS36tnYLV0uhyrZr6QNa2X+NHW7ZRjPGiE/PNXcX827JPBqvtuPpbGuyPbnLtsDvJ4RzaZXtqVlqdYVua2EB/C495p777vlcDja3Xek0cuBWDDc45kxcODZKxleLzHxJn3zA73x6iXm37BX7jpOKlCPMsWHanc8ZlYxjJgxyaZV1aeVUe22xkYHc7cdr4HP2g9uuJTbs8uq+Wlbb+Bf4O1kJplVgrrVh+u5UG/u2ELnI5540e+qpIUpo0be1ibBWQpVtWzLOQ7S0/xqttmUbzRYj3uC3m65insvCIaP1CT6XFmK+9GVJLWblz0Yui13wV9S3yvTIgOM6bems5exYDjb3OnKFALfwfOJvtkeb8ZHXNMtDsCxD6QuAPcS8XE3x1fQOOXzfdaXsT5ah9FHi7GuyeiPRa4sNhZKvfGDo5VQhsdZCzL+6r5Y+MCYgpPiu9dktbFgr5uVKR+y7OWU5W6z4bEkLoUrfqHkPRQ4t7X9rMV/aRjPFCGorXxt3E/PyxKEXe0gnExoAtWK+ZNmWpBzuaMhZtm8vdcsMvTxn6EEpt+1kgKrJzHNFQD78ecDvAKEd0NogNQK875SttHJMbtUN37iRy66hNtTa8B1xeysV87UCcwR6bLGJTa4p8NyJo1tNSlLb1nvw1bLNY+JZtnPNakwrGy4R8zE7zZmstEjobUkLoXpHfWUgl9b2v7WYL22jWWIE9V3KRpuLeQq6mLHGBhOpNeSSZVsyS4AgbHPfvcrlz9oXTsgA4QZe+W/uoJNi2+3PHIOisPFldOS40/TdTGL+C6sx+w624Y/zeSmaJXMovqOxYU7s3xG+PymC+FnKL8ziqGP02mIjn/lwJwn8t14Tch978NVym01qJUH661Ja2XDJNpuYKNNOagAT81x5bv2sTGv731LM17TRLDGCDyiH4qOrufl59biRGdLQyWRmvjarF4LCL/fva5/MbrGXKqcTZHYllbkNCWEt0mG77RN7yJUi3xectAbF88cmJFLUptqwphLGs6vZ/Cs4aoSAdPahig5y3IXElMaG3dUj7ZFy/KWVMEaqZkMn3XLCKUWl2z6xh9xiL2SpDYp78dUacS2/N4INa8W8JkHnfi8l5jn+S2jRt1tWs+kl5HvY/1ZivraNZokRpQU3qrL0saUYiZxJhH6Q4q1EfPI6SpZtazK2pcKkphM0SyzSgGvfyheaFPDf3AAkJwA+J889wakVA7ZtLMDJ30q1YY0DenY1m5RTkNfDz2r6WU6+Qv2iycRpbFgjqqRP4Wep/k35oNj1tLDhFlvaelSwiNljyH6k//AJUa0N+9iTr5b7lGPw3DXPArSyYQo8zaoJf1OzB19jIzWTxBZ9u1U1m15Cnudubf81Wm3LNpolRqSSh1KX3cXnVVuzNLNzuR3jHjlXTaUCBpeSZdualwlsUc1GTqBigYXfqck2SNHoXmPIkTPrFgpg2qoy/F4sEMrxlzLymhfObFXNJoRmopNDzHETjoWYCKuxYd/1aNus5oUzo1SzoR9qvcVGilg3+IbEZir5UlMZak++Woql0DVLf17jI1rZMKCv+iETOqF2kds1UjZS82K/Fn27RTWbM9IilS9pLKGH/ddWldqijV4hRpAue+blDC7knDkwNA8saEpn+YjtrU7Bwd77TXwt4f2GBqbsF/e+bljr/KcGglxqCz0cIw1IOu5U8EoZsryH0LkYLDUC6FP5vRlIifkD1odM+WbGGKFqRUQ+JJUSUqU2LClx9qX2Pwr0kxqRe8Fafzh1z9Im3e/6kizStkP+RWvDPvbmq1PZ69ADiFvaMF8AlUIzEeG41oj00kneKOQKVRY6iNkCH4aU39na/vm3tTXbe7ZR6HdnjhFEI+ZzdN7/cLbvcyJv4t80DviO/OVXDr7Shz35sOFMMEP1DX9HhcrbSUPViOBQVkXO9jlbli+VSmURvhFfpSG8j1AJKm15u5yl4xlIiXm31rS2ioQv+8GsyDd0GdESG3bJFfM12z5GgYFV08ayakkqYxUSXDIg0F5llazUmNHasO9a9uirfUJClv11/21LG6bw12xpoO35YpHs79S5arZujILs65TvkvHyM3Kw3yQj2H+pn39WG7m8QowgKTGfq/P+xx0AZ6wzx2/kZW/Y0TlLB+yk3MACrCKv9sGXLbhgfcPuG5Z2P2PNqvja3X2RSaqtZd9KQc3PaEAMFl+J8xE+ra3hJs59xTq+vqAPThxXPfYkbkFKzMvl/dj3JMygMdtzfnz2A11mkJTYsEuumP9Cmf2Pgpyca6AA1LaTXB1lv8h3gxwfB21K4w9zbFj+zZ59NRMsGh+2pQ2zrXPe5ExBxVjEPc6f0E8KapMAW+K+6+UL8dVp930pscNNyo1g/yV+/plt5DJ7jJCkxHyuzvvDBW32B+VmfLifueT3Yi/mmQV3L+gZ8fvh92ngqXs/YGmnD6xLexwg/P935LU/B5s2MB/we3wxYGjhtb8K7MOYE6dd5GwvOqHNHtKSrK0kx4fEXq4xC+xPbXvLPZzabOYV67YNTvgZ4O+PI6e/c22Y12C+Wu/DtrTh3Myr66OvyOtnluKbkdznLHKfwXL/fgT7B/L8/LPbSPIKMUIi+z9037k6rwsXPM9p564cvBKcJeeieahLwzueI7ApOmZ9q2At73j+9qJn2vAdc7wRtAfMoOa2s8zc1AioZ9kwsG9fvYUNH6HbX9+CK9q/KGkPbG3/z/TzNew5RpTqvGZ8oP+SyA3z7b9sBbfPlDhqzvRavJBKu6RXAx8g2yMnbBckn2HDmioHr8wdZcG41YT8WTa8Z1+9pQ2/of/WF1a7m3mv/FZsbf/Ac/x8DXuOETU6r/lF9DJw7sfacweXtq2mtrAWBqpe/fAGEwFbjfHeNkwhuVcRcEf5JFVb/1xD73G2Z1+9tQ0DdeNMA7dpGnmMYv+9/XwNe44RQ/ULH8hovT2CN7nXbRcXlAeHVjWR3esJVaup4QR9FaVX5Irt772XDQNLQJrxYcgWnFCXbWk5IQf62fDeffUINgwsfdvD1t4wdlZ3VEaz/55+voY9x4gandeFAxZH0mqQHLB08GiDbhZkScqWbXhCWzFwwtLPIwTCvdPahoElI7VXJ11L6RsYU7S2YfPVY3FHW5u7wjLyW9DL/nv4+RosRgxKywBhAq8cPmHe40G0lv0y1IzUAGD9OwqyokqPTHrLc5mvHguz4fnpaf/odM4SbHwZhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYhmEYxkz8B+9eXgSCQ2hrAAAAAElFTkSuQmCC\" alt=\"sigma(7) = 8, phi(8) = 4, sigma(4) = 7, phi(7) = 6, sigma(6) = 12, phi(12) = 4, \" style=\"width: 377.5px; height: 19px;\" width=\"377.5\" 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: 13.2167px 7.91667px; transform-origin: 13.2167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e etc.\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: 117.458px 7.91667px; transform-origin: 117.458px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand the pattern 7, 6, 12, 4 will repeat. \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: 258.3px 7.91667px; transform-origin: 258.3px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOscillating behavior is plausible because the sum of divisors is always greater 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: 120.45px 7.91667px; transform-origin: 120.45px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the totient is always 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: 360.958px 7.91667px; transform-origin: 360.958px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Furthermore, because the totient has a minimum value and the sum of divisors has a maximum value, with enough iterations the sequence would have to hit a repeating pattern.\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: 383.4px 7.91667px; transform-origin: 383.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an initial seed and returns the repeating pattern and the index of the sequence where the pattern begins. With an initial seed of 7, the sequence would be 7, 8, 4, 7, 6, 12, 4, 7, 6, 12,… Therefore, the repeating pattern is [7 6 12 4] and the start index is 3.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [q,n0] = sigPhi(n)\r\n%  n  = initial seed\r\n%  q  = vector of repeating pattern\r\n%  n0 = index where the repeating pattern starts (counting the initial seed as index 1)\r\nend","test_suite":"%%\r\nn = 2;\r\nq_correct = [2 3];\r\nn0_correct = 1;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 3;\r\nq_correct = [2 3];\r\nn0_correct = 3;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 7;\r\nq_correct = [4 7 6 12];\r\nn0_correct = 3;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 12;\r\nq_correct = [12 28];\r\nn0_correct = 1;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 28;\r\nq_correct = [24 60 16 31 30 72];\r\nn0_correct = 3;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 101;\r\nq_correct = [72 195 96 252];\r\nn0_correct = 7;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 127;\r\nq_correct = [96 252 72 195];\r\nn0_correct = 7;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 256;\r\nq_correct = [432 1240 480 1512];\r\nn0_correct = 3;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 777;\r\nq_correct = [576 1651 1512 4800 1280 3066 864 2520];\r\nn0_correct = 3;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 1111;\r\nq_correct = [432 1240 480 1512];\r\nn0_correct = 7;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 5555;\r\nq_correct = [10368 30855 14080 36792];\r\nn0_correct = 23;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 7777;\r\nq_correct = [3024 9920 3840 12264 3456 10200 2560 6138 1800 6045 2880 9906];\r\nn0_correct = 11;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 11111;\r\nq_correct = [3024 9920 3840 12264 3456 10200 2560 6138 1800 6045 2880 9906];\r\nn0_correct = 11;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 77777;\r\nq_correct = [10368 30855 14080 36792];\r\nn0_correct = 27;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 123456;\r\nq_correct = [184320 638898 196560 833280];\r\nn0_correct = 21;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 666666;\r\nq_correct = [1658880 5946666 1801800 8124480];\r\nn0_correct = 39;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))\r\n\r\n%%\r\nn = 7777777;\r\nq_correct = [191102976000 715162215924 207622711296 859454668800 178362777600 757256331104 283740364800 1100946774480 233003796480 1053092362140 221908377600 1035248323200 204838502400 888208962000 214695936000 952677206208 237283098624 859638312960 185794560000 792731088600 178886400000 749337039360 150493593600 639777817224 152374763520 626874655824 202491394560 925865740800 167215104000 715161022368 219847799808 880002352320 161864220672 609720615224 247328774784 987821856000];\r\nn0_correct = 161;\r\n[q,n0] = sigPhi(n);\r\nassert(isequal(q,q_correct) \u0026\u0026 isequal(n0,n0_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2022-11-28T04:11:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2021-05-10T14:27:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-09T19:28:03.000Z","updated_at":"2026-01-14T13:15:59.000Z","published_at":"2021-05-09T19:36:55.000Z","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/46898\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 46898\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deals with the sum of divisors function, denoted by \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, while \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\u003eCody Problem 656\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e deals with the totient function, denoted by \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 sum of divisors is straightforward: 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=\\\"sigma(12) = 1+2+3+4+6+12 = 28\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(12) = 1+2+3+4+6+12 = 28\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The totient 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 counts the numbers less 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. 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(12) = 4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\varphi(12) = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e because the greatest common divisor of 12 and four numbers (1, 5, 7, 11) is 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat happens if you repeatedly apply the two functions, starting with the sum of divisors and alternating? For example, start with 7. Then \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=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sigma(7) = 8, phi(8) = 4, sigma(4) = 7, phi(7) = 6, sigma(6) = 12, phi(12) = 4, \\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sigma(7) = 8, \\\\varphi(8) = 4, \\\\sigma(4) = 7, \\\\varphi(7) = 6, \\\\sigma(6) = 12, \\\\varphi(12) = 4,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e etc.\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\u003eand the pattern 7, 6, 12, 4 will repeat. \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\u003eOscillating behavior is plausible because the sum of divisors is always greater 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, and the totient is always 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. Furthermore, because the totient has a minimum value and the sum of divisors has a maximum value, with enough iterations the sequence would have to hit a repeating pattern.\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 an initial seed and returns the repeating pattern and the index of the sequence where the pattern begins. With an initial seed of 7, the sequence would be 7, 8, 4, 7, 6, 12, 4, 7, 6, 12,… Therefore, the repeating pattern is [7 6 12 4] and the start index is 3.\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":51813,"title":"Sum the elements in rows of the Levine triangle","description":"The Levine triangle starts as follows:\r\nRow 0:      2\r\nRow 1:     1 1\r\nRow 2:     1 2\r\nRow 3:    1 1 2\r\nTo construct each row, read the previous from the right. Row 0 tells us to put two 1s in row 1. Row 1 tells us to put one 1 and one 2 in row 2. Row 2 tells us to put two 1s and one 2 in row 3. Et cetera.\r\nWrite a function that computes the sum of the elements in the th row of the Levine triangle and reports the sum as a string. Codes that can handle the optional tests will earn ten (10) Chris R. Appreciation Points.  ","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: 245px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 122.5px; transform-origin: 407px 122.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 115px 8px; transform-origin: 115px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe Levine triangle starts as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003eRow 0:\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: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003eRow 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\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: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003e1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003eRow 2:\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: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\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: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003e1 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; \"\u003eRow 3:\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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; \"\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: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 20px 8.5px; transform-origin: 20px 8.5px; \"\u003e1 1 2\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: 377.5px 8px; transform-origin: 377.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo construct each row, read the previous from the right. Row 0 tells us to put two 1s in row 1. Row 1 tells us to put one 1 and one 2 in row 2. Row 2 tells us to put two 1s and one 2 in row 3. Et cetera.\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: 195px 8px; transform-origin: 195px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the sum of the elements in 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: 170.5px 8px; transform-origin: 170.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth row of the Levine triangle and reports the sum as a string. Codes that can handle the optional tests will earn ten (10) Chris R. Appreciation Points.\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: 4px 8px; transform-origin: 4px 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 s = LevineTriSum(n)\r\n  s = 2^n;\r\nend","test_suite":"%%\r\nn = 1;\r\ns_correct = '2';\r\nassert(isequal(LevineTriSum(n),s_correct))\r\n\r\n%%\r\nn = 3;\r\ns_correct = '4';\r\nassert(isequal(LevineTriSum(n),s_correct))\r\n\r\n%%\r\nn = 5;\r\ns_correct = '14';\r\nassert(isequal(LevineTriSum(n),s_correct))\r\n\r\n%%\r\nn = 7;\r\ns_correct = '213';\r\nassert(isequal(LevineTriSum(n),s_correct))\r\n\r\n%%\r\nn = 9;\r\ns_correct = '175450';\r\nassert(isequal(LevineTriSum(n),s_correct))\r\n\r\n%%\r\nn = 11;\r\ns_correct = '6837625106787';\r\nassert(isequal(LevineTriSum(n),s_correct))\r\n\r\n%%\r\nn = 10;\r\ns = LevineTriSum(n);\r\ne = round(eig(reshape(num2str(s)-'0',3,3)),2);\r\ne_correct = [11.33; -6.75; 1.41];\r\nassert(isequal(e,e_correct))    \r\n\r\n%%\r\nfiletext = fileread('LevineTriSum.m');\r\nillegal = contains(filetext, 'switch') || contains(filetext, 'if ') || contains(filetext, 'oeis'); \r\nassert(~illegal)\r\n\r\n%%\r\n% n = 13;\r\n% s_correct = '508009471379488821444261986503540';\r\n% assert(isequal(LevineTriSum(n),s_correct))\r\n\r\n%%\r\n% n = 15;\r\n% s_correct = '5347426383812697233786139576220450142250373277499130252554080838158299886992660750432';\r\n% assert(isequal(LevineTriSum(n),s_correct))\r\n\r\n%%\r\n% n = 17;\r\n% s_correct = '83941772663735173160560543672534726683873453747462593691278544525723285290023673872585715830432071384827472565652426695269724710458808241779132656748501183672544006254377431217217762964060736471826937656819379445242826439';\r\n% assert(isequal(LevineTriSum(n),s_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":7,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-23T03:29:56.000Z","updated_at":"2026-01-14T14:01:30.000Z","published_at":"2021-05-23T03:33:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Levine triangle starts as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRow 0:\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\u003e      \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\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRow 1:\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\u003e     \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\u003e1 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRow 2:\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\u003e     \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\u003e1 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRow 3:\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\u003e    \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\u003e1 1 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo construct each row, read the previous from the right. Row 0 tells us to put two 1s in row 1. Row 1 tells us to put one 1 and one 2 in row 2. Row 2 tells us to put two 1s and one 2 in row 3. Et cetera.\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 computes the sum of the elements in 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 row of the Levine triangle and reports the sum as a string. Codes that can handle the optional tests will earn ten (10) Chris R. Appreciation Points.\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":51950,"title":"Find the smallest integer m such that n divides m!","description":"Write a function that takes an integer  and finds the smallest integer  whose factorial is divisible by . For example, if , then the smallest factorial that is a multiple of  is 5! = 120; therefore, . ","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: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; 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 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: 115.775px 7.79167px; transform-origin: 115.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes 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);\"\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: 94.9083px 7.79167px; transform-origin: 94.9083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and finds the smallest 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: 93.75px 7.79167px; transform-origin: 93.75px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e whose factorial is divisible by \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: 52.1083px 7.79167px; transform-origin: 52.1083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, if \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\" style=\"width: 44px; height: 18px;\" width=\"44\" 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: 145.458px 7.79167px; transform-origin: 145.458px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then the smallest factorial that is a multiple 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: 70.2px 7.79167px; transform-origin: 70.2px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is 5! = 120; therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"m = 5\" style=\"width: 40px; height: 18px;\" width=\"40\" 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: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; 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 m = Kempner(n)\r\n  m = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\nm_correct = 1;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 2;\r\nm_correct = 2;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 3;\r\nm_correct = 3;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 10;\r\nm_correct = 5;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 16;\r\nm_correct = 6;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 53;\r\nm_correct = 53;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 180;\r\nm_correct = 6;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 223;\r\nm_correct = 223;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 254;\r\nm_correct = 127;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 268;\r\nm_correct = 67;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 288;\r\nm_correct = 8;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 788;\r\nm_correct = 197;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 1024;\r\nm_correct = 12;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 3333;\r\nm_correct = 101;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 7856;\r\nm_correct = 491;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 8863;\r\nm_correct = 8863;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 10000;\r\nm_correct = 20;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 95256;\r\nm_correct = 14;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 1234342;\r\nm_correct = 811;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%%\r\nn = 169831728;\r\nm_correct = 38;\r\nassert(isequal(Kempner(n),m_correct))\r\n\r\n%% anti-lookup\r\nn = 1535238;\r\nmmm_correct = 67;\r\nassert(isequal(Kempner(Kempner(Kempner(n))),mmm_correct))\r\n\r\n%%\r\np = primes(30);\r\nr = sort(randi(10,1,2));\r\nn = prod(p(r(1):r(2)));\r\nm_correct = p(r(2));\r\nassert(isequal(Kempner(n),m_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":6,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2021-06-03T15:10:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-03T13:52:10.000Z","updated_at":"2026-01-14T14:14:40.000Z","published_at":"2021-06-03T13:56:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes 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=\\\"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 finds the smallest 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 whose factorial is divisible by \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. For example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n = 10\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then the smallest factorial that is a multiple 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 is 5! = 120; 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=\\\"m = 5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em = 5\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\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":52060,"title":"Identify Ruth-Aaron numbers","description":"After Hank Aaron hit his 715th home run and passed Babe Ruth’s total of 714, Carl Pomerance noticed that the union of the prime factors of the numbers ( and ) comprises all of the prime numbers up to 17. \r\nHe told a colleague that he found an interesting property of the two numbers, and when the colleague posed the problem to a class, a student observed that the sums of the prime factors of these two consecutive numbers were equal—in this case, 29. Prof. Pomerance and colleagues named numbers with this property “Ruth-Aaron numbers.”*\r\nWrite a function to classify numbers in this way. In computing sums, include only the unique factors. If a number is the lesser of a Ruth-Aaron pair, return ‘R’. If it is the greater number, return ‘A’. If multiple pairs overlap, return ‘RA’ for numbers that can serve as either the lesser or greater. If the number is not part of a Ruth-Aaron pair, return ‘X’.\r\n*The story continues in a Numberphile video on this topic, and I highly recommend that you watch it. Go for the number theory and stay for the life lessons!","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: 237px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 118.5px; transform-origin: 407px 118.5px; 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: 16.7167px 7.91667px; transform-origin: 16.7167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=QjqYThEVoSQ\"\u003e\u003cspan style=\"perspective-origin: 70.8px 7.91667px; transform-origin: 70.8px 7.91667px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eHank Aaron hit his 715\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 5.83333px 7.91667px; transform-origin: 5.83333px 7.91667px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 31.5083px 7.91667px; transform-origin: 31.5083px 7.91667px; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e home run\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: 259.142px 7.91667px; transform-origin: 259.142px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and passed Babe Ruth’s total of 714, Carl Pomerance noticed that the union of the prime factors of the numbers (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"714 = 2*3*7*17\" style=\"width: 114.5px; height: 18px;\" width=\"114.5\" 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: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; 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,iVBORw0KGgoAAAANSUhEUgAAAM8AAAAkCAYAAAAuAm4eAAADrUlEQVR4nO2b3bXqIBCFdw/pwAbSQCqwAjuwAzuwBWuwhNODLaSGtHDvA5klRkkYGAR1f2vxZCDzw8AwQYAQQgghhBBCCCHkS+jm9k3sagtAbDgAOEW2g2JMzQRZk+GGzwueAWF9rgD29UQDoPePVd9SaGXqARxxn9NJ+nQAJgD/IttpY7wDgHF+to+UYbfxzku0Nu0gNnjVxopypfjHom8ptDL1CPtma26/fLk49G+lyQtCETq8ECrWwBe4AA69u7VVbguxaUifGrtOjn9y+pYiRaYe93m2n8c4LsY5aoQYAZw3npGd4Rb4fT+3Di4l0RhYxq6dxlgSY9N3kuOfnL6lSJVpxOtjR4d7AIXm+BMDXBRucUT8tnaCzsBnOME/7UwTYo/6k2sNrX+s+pYiViY5U4c4z2NMmpfHpEQ3xBtMY2A5b41zP1lNPhlJcbMOogX51eDpsT63ZJyYzSQaSatiD7kaA/vPLgsEQ4qwlRnwWp8/xFcpS/OrwbOFpH+mxwdJ2WJzeI0yfr5qUv2ozAnrlcsr6u+sDJ5neujmeDSSssXuBCnKdHARf4FNAO0Q/91qreXsfgOcM5bBZJoWJMDgeWSA85H5wqZN2YB8ZXZ4LI2njBNKn7RNVbYM0OF+GLUcNxUGj2PA82I9wTBt06ZsgJ2BfcW026nVzmM5QeTbj6ocWgAGz+Ptj+VCrcmyVtGmbICdgZNq740jZ7wJ+qskI2xWxhaCpxV9hGW2kz3fUlI2wHZ1Sqq9N4x8A9Laxi+s5F7taSF4WtHHx1+stYvbEykpG2AbPHJ2+ZbgAdJs49v0mvn+FoKnFX2WyJzPHkuiUJv/lQge7TbaQrUthNhGW9k5zC23ItRC8ABt6LPELzQl7zxS907ZUq0NnLL7tVRt89m6I/gOWgkeK0oET1YqKWeNlI9GlsrIIU47TovVNuBuG5aq7SiRtmV9nJeULaUSEquMlAtD11ZkFbgkyFADCdgjXqcico+v9h/7fjV4Org5FUrHpGCQ5R9J2abEQfwPgmvK+OnR3+JZ+ep7SZShBn6pc8TjwrODc8oN9S+KxvrHum8pYmXyK3wnPM6rDs43IzL9I8JoV/wObhfxr6NcV4TxVww/iESJVi5SxrLH81WcG5xOE54d9m60/rHqW4rc+eb/+XJEOGNQIf970KwsW2eMUI6/w/1/5JLCfeJtakEc6us9oP7umeqf3L6lSJWpXzy3Rzs7KCGEEEIIIYQQQgghhBBCCCGEtMV/m09p4GPXQvwAAAAASUVORK5CYII=\" alt=\"715 = 5*11*13\" style=\"width: 103.5px; height: 18px;\" width=\"103.5\" 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: 144.3px 7.91667px; transform-origin: 144.3px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) comprises all of the prime numbers up to 17. \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: 383.158px 7.91667px; transform-origin: 383.158px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHe told a colleague that he found an interesting property of the two numbers, and when the colleague posed the problem to a class, a student observed that the sums of the prime factors of these two consecutive numbers were equal—in this case, 29. Prof. Pomerance and colleagues named numbers with this property “Ruth-Aaron numbers.”*\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: 365.35px 7.91667px; transform-origin: 365.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify numbers in this way. In computing sums, include only the unique factors. If a number is the lesser of a Ruth-Aaron pair, return ‘R’. If it is the greater number, return ‘A’. If multiple pairs overlap, return ‘RA’ for numbers that can serve as either the lesser or greater. If the number is not part of a Ruth-Aaron pair, return ‘X’.\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: 78.9583px 7.91667px; transform-origin: 78.9583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e*The story continues in a \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=aCq04N9it8U\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eNumberphile 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: 232.967px 7.91667px; transform-origin: 232.967px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e on this topic, and I highly recommend that you watch it. Go for the number theory and stay for the life lessons!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = RuthAaron(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 5;\r\nassert(isequal(RuthAaron(n),'R'))\r\n\r\n%%\r\nn = 25;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 51;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 78;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 101;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 153;\r\nassert(isequal(RuthAaron(n),'R'))\r\n\r\n%%\r\nn = 222;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 493;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 713;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 714;\r\nassert(isequal(RuthAaron(n),'R'))\r\n\r\n%%\r\nn = 715;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 716;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 24024;\r\nassert(isequal(RuthAaron(n),'R'))\r\n\r\n%%\r\nn = 154843;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 977779;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 6905998;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 29817473;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 89460293;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 89460294;\r\nassert(isequal(RuthAaron(n),'R'))\r\n\r\n%%\r\nn = 89460295;\r\nassert(isequal(RuthAaron(n),'RA'))\r\n\r\n%%\r\nn = 89460296;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%  \r\nn = 89460297;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 144426976;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 333333333;\r\nassert(isequal(RuthAaron(n),'X'))\r\n\r\n%%\r\nn = 715159952;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 888681984;\r\nassert(isequal(RuthAaron(n),'A'))\r\n\r\n%%\r\nn = 1925922590;\r\nassert(isequal(RuthAaron(n),'R'))\r\n\r\n%%\r\nn = 1925922591;\r\nassert(isequal(RuthAaron(n),'A'))","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-11T02:03:10.000Z","updated_at":"2025-12-07T20:22:27.000Z","published_at":"2021-06-11T02:14:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAfter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=QjqYThEVoSQ\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHank Aaron hit his 715\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e home run\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and passed Babe Ruth’s total of 714, Carl Pomerance noticed that the union of the prime factors of the numbers (\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=\\\"714 = 2*3*7*17\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e714 = 2\\\\cdot 3\\\\cdot 7 \\\\cdot 17\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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=\\\"715 = 5*11*13\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e715 = 5\\\\cdot 11 \\\\cdot 13\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) comprises all of the prime numbers up to 17. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHe told a colleague that he found an interesting property of the two numbers, and when the colleague posed the problem to a class, a student observed that the sums of the prime factors of these two consecutive numbers were equal—in this case, 29. Prof. Pomerance and colleagues named numbers with this property “Ruth-Aaron numbers.”*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify numbers in this way. In computing sums, include only the unique factors. If a number is the lesser of a Ruth-Aaron pair, return ‘R’. If it is the greater number, return ‘A’. If multiple pairs overlap, return ‘RA’ for numbers that can serve as either the lesser or greater. If the number is not part of a Ruth-Aaron pair, return ‘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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e*The story continues in a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=aCq04N9it8U\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNumberphile video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e on this topic, and I highly recommend that you watch it. Go for the number theory and stay for the life lessons!\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":52283,"title":"Find numbers in the Popular Computing Z-sequence","description":"Here’s a quick one. In 1977 the magazine Popular Computing sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\r\n and  for \r\nAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\r\nWrite a function to find the index of the first occurrence of  (including the five numbers above) in the Popular Computing Z-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: 195.817px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 97.9083px; transform-origin: 407px 97.9083px; 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: 130.958px 7.79167px; transform-origin: 130.958px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHere’s a quick one. In 1977 the magazine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.9167px 7.79167px; transform-origin: 59.9167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ePopular Computing\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: 192.533px 7.79167px; transform-origin: 192.533px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; 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 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a1 = a2 = 1\" style=\"width: 72.5px; height: 20px;\" width=\"72.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"a_n = |2 a_{n-2} + a_{n-1} – n|\" style=\"width: 134.5px; height: 20px;\" width=\"134.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.79167px; transform-origin: 12.05px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"n \u003e 2\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\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: 383.65px 7.79167px; transform-origin: 383.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\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: 178.775px 7.79167px; transform-origin: 178.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the index of the first occurrence 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: 129.925px 7.79167px; transform-origin: 129.925px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (including the five numbers above) in the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.8583px 7.79167px; transform-origin: 61.8583px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ePopular Computing \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: 40.8417px 7.79167px; transform-origin: 40.8417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eZ-sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = findInPopCompZ(k)\r\n  y = f(k);\r\nend","test_suite":"%%\r\nassert(isequal(findInPopCompZ(1),1))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(2),4))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(4),35))\r\n    \r\n%%\r\nassert(isequal(findInPopCompZ(19),282))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(29),30))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(49),1398))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(211),241))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(245),11309))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(348),372))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(449),13409))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(569),19434))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(575),22350))\r\n    \r\n%%\r\nassert(isequal(findInPopCompZ(903),18057))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3347),74105))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3491),128405))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(3690),4083))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(4250),199563))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(7431),8346))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(7488),299263))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9735),390685))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9792),391799))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(9851),1562345))\r\n\r\n%%\r\nassert(isequal(findInPopCompZ(findInPopCompZ(4474)),15458))\r\n\r\n%%\r\nfiletext = fileread('findInPopCompZ.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-11T03:26:33.000Z","updated_at":"2026-01-14T15:14:04.000Z","published_at":"2021-07-11T03:30:22.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere’s a quick one. In 1977 the magazine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePopular Computing\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sought “problem situations for which the computer is the best (if not the only) tool for solution” and proposed the Z-sequence as a candidate “problem situation:”\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=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a1 = a2 = 1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_1 = a_2 = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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=\\\"a_n = |2 a_{n-2} + a_{n-1} – n|\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea_n = |2 a_{n-2} + a_{n-1} – n|\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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=\\\"n \u0026gt; 2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en \u0026gt; 2\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\u003eAmong the Z-sequence’s properties, the magazine staff pointed out that “successive values seem unpredictable; that is, the values jump around, but not too wildly” and “almost every integer appears as a term in the sequence sooner or later, except for a few numbers, such as 245, 449, 569, 575, and 903.”\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 find the index of the first occurrence 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 (including the five numbers above) in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePopular Computing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eZ-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":52619,"title":"Find the nth nude number","description":"The number 672 is a nude number because it openly displays three of its divisors: 6, 7, and 2. In other words, a nude number is divisible by its individual digits. \r\nWrite a function to return the th nude number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363.683px 7.79167px; transform-origin: 363.683px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 672 is a nude number because it openly displays three of its divisors: 6, 7, and 2. In other words, a nude number is divisible by its individual digits. \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 7.79167px; transform-origin: 90.1px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to return 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: 5.83333px 7.79167px; transform-origin: 5.83333px 7.79167px; 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: 44.7333px 7.79167px; transform-origin: 44.7333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e nude number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nudeNum(n)\r\n  y = f(n)\r\nend","test_suite":"%%\r\nn = 7;\r\ny_correct = 7;\r\nassert(isequal(nudeNum(n),y_correct))\r\n\r\n%%\r\nn = 17;\r\ny_correct = 44;\r\nassert(isequal(nudeNum(n),y_correct))\r\n\r\n%%\r\nn = 98;\r\ny_correct = 1236;\r\nassert(isequal(nudeNum(n),y_correct))\r\n\r\n%%\r\nn = 446;\r\ny_correct = 13248;\r\nassert(isequal(nudeNum(n),y_correct))\r\n\r\n%%\r\nn = 1151;\r\ny_correct = 46872;\r\nassert(isequal(nudeNum(n),y_correct))\r\n\r\n%%\r\nn = 9867;\r\ny_correct = 1148448;\r\nassert(isequal(nudeNum(n),y_correct))\r\n\r\n%%\r\nn = 10001;\r\ny_correct = 1164264;\r\nassert(isequal(nudeNum(n),y_correct))\r\n\r\n%%\r\nfiletext = fileread('nudeNum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-26T04:39:55.000Z","updated_at":"2026-01-14T15:21:01.000Z","published_at":"2021-08-26T04:43:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 672 is a nude number because it openly displays three of its divisors: 6, 7, and 2. In other words, a nude number is divisible by its individual 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 to return 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:r\u003e\u003cw:t\u003e nude number.\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":52624,"title":"Determine whether a number is a fibodiv number","description":"The number 14 is a fibodiv number because you can divide it into 1 and 4, use those numbers as the seeds for a Fibonacci sequence, and find 14 later in the sequence: 1, 4, 5, 9, 14. The number 549 is also a fibodiv number because dividing it into 54 and 9 gives the sequence is 54, 9, 63, 72, 135, 207, 342, 549. \r\nWrite a function to determine whether the input is a fibodiv number. ","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: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; 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: 381.975px 8.05px; transform-origin: 381.975px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe number 14 is a fibodiv number because you can divide it into 1 and 4, use those numbers as the seeds for a Fibonacci sequence, and find 14 later in the sequence: 1, 4, 5, 9, 14. The number 549 is also a fibodiv number because dividing it into 54 and 9 gives the sequence is 54, 9, 63, 72, 135, 207, 342, 549. \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: 209.133px 8.05px; transform-origin: 209.133px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether the input is a fibodiv number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isFibodiv(x)\r\n  tf = false\r\nend","test_suite":"%%\r\nassert(~isFibodiv(11))\r\n\r\n%%\r\nassert(isFibodiv(14))\r\n\r\n%%\r\nassert(isFibodiv(28))\r\n\r\n%%\r\nassert(~isFibodiv(191))\r\n\r\n%%\r\nassert(isFibodiv(199))\r\n\r\n%%\r\nassert(~isFibodiv(541))\r\n\r\n%%\r\nassert(isFibodiv(549))\r\n\r\n%%\r\nassert(~isFibodiv(1803))\r\n\r\n%%\r\nassert(isFibodiv(1822))\r\n\r\n%%\r\nassert(~isFibodiv(8198))\r\n\r\n%%\r\nassert(isFibodiv(8199))\r\n\r\n%%\r\nassert(isFibodiv(23418))\r\n\r\n%%\r\nassert(~isFibodiv(23456))\r\n\r\n%%\r\nassert(~isFibodiv(50014))\r\n\r\n%%\r\nassert(isFibodiv(50739))\r\n\r\n%%\r\nassert(isFibodiv(299998))\r\n\r\n%%\r\nassert(isFibodiv(889945))\r\n\r\n%%\r\nassert(~isFibodiv(1399999))\r\n\r\n%%\r\nassert(isFibodiv(1499999))\r\n\r\n%%\r\nassert(isFibodiv(54999966))\r\n\r\n%%\r\nassert(~isFibodiv(68528559))\r\n\r\n%%\r\nassert(isFibodiv(78545406))\r\n\r\n%%\r\nassert(isFibodiv(97499994))\r\n\r\n%% \r\nn = randi(45,1,randi(8));\r\nphi = (1+sqrt(5))/2;\r\nf = round(phi.^n/sqrt(5));\r\nassert(abs(sum(arrayfun(@isFibodiv,f))-besselj(randi(8),cos((2*randi(8)+1)*imag(log(-1))/2)))\u003ceps)\r\n\r\n%% Fibodiv magic square\r\nm = [74157 65050 71555; \r\n     67652 70254 72856;\r\n     68953 75458 66351];\r\nassert(isFibodiv(m(randi(9))))\r\n\r\n%%\r\nfiletext = fileread('isFibodiv.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-26T04:40:10.000Z","updated_at":"2026-01-14T15:31:07.000Z","published_at":"2021-08-28T12:39:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number 14 is a fibodiv number because you can divide it into 1 and 4, use those numbers as the seeds for a Fibonacci sequence, and find 14 later in the sequence: 1, 4, 5, 9, 14. The number 549 is also a fibodiv number because dividing it into 54 and 9 gives the sequence is 54, 9, 63, 72, 135, 207, 342, 549. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to determine whether the input is a fibodiv number. \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":52644,"title":"List modest numbers up to n","description":"After determining the nude numbers, or the numbers that openly display some of their divisors as their digits, one would think that the modest numbers were those not divisible by any of their digits. Instead a modest number  is one that can be divided into two parts  and  such that when  is divided by , the remainder is . For example, 411 is modest because it can be divided into 4 and 11, and dividing 411 by 11 leaves a remainder of 4. \r\nWrite a function to list the modest numbers up to . ","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: 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: 66.9px 8.05px; transform-origin: 66.9px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAfter determining the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52619-find-the-nth-nude-number\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003enude numbers\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: 259.833px 8.05px; transform-origin: 259.833px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, or the numbers that openly display some of their divisors as their digits, one would think that the modest numbers were those \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: 9.725px 8.05px; transform-origin: 9.725px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003enot\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: 176.2px 8.05px; transform-origin: 176.2px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e divisible by any of their digits. Instead a modest 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);\"\u003ex\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: 59.1167px 8.05px; transform-origin: 59.1167px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is one that can be divided into two parts \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: 15.5583px 8.05px; transform-origin: 15.5583px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \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: 50.95px 8.05px; transform-origin: 50.95px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that when \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);\"\u003ex\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: 42.4px 8.05px; transform-origin: 42.4px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is divided by \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: 56.0083px 8.05px; transform-origin: 56.0083px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the remainder is \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: 125.175px 8.05px; transform-origin: 125.175px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, 411 is modest because it can be divided into 4 and 11, and dividing 411 by 11 leaves a remainder of 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: 151.942px 8.05px; transform-origin: 151.942px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the modest numbers up 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: 3.88333px 8.05px; transform-origin: 3.88333px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = modest(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 100;\r\ny = modest(n);\r\ny_correct = [13 19 23 26 29 39 46 49 59 69 79 89];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 1000;\r\ny = modest(n);\r\ny_correct = [103 109 111 133 199 203 206 209 211 218 222 233 266 299 309 311 327 333 399 406 409 411 412 418 422 433 436 444 466 499 509 511 515 533 545 555 599 609 611 618 622 627 633 654 666 699 709 711 721 733 763 777 799 809 811 812 818 822 824 833 836 844 866 872 888 899 911 927 933 981 999];\r\nassert(isequal(y(y\u003e100),y_correct))\r\n\r\n%%\r\nn = 10000;\r\ny = modest(n);\r\nsum_correct = 1643003;\r\nassert(isequal(sum(y),sum_correct))\r\n\r\n%%\r\nn = 100000;\r\ny = modest(n);\r\ncubrt_correct = 12;\r\nsum_correct = 68950549;\r\np7_correct  = [2027 3037 4027 6037 7027 10037 11027 12037 13037 17027 19037 22027 22037 23027 25037 33037 36037];\r\np = y(isprime(y));\r\nd = p-10*floor(p/10);\r\nassert(isequal(nthroot(length(y),3),cubrt_correct))\r\nassert(isequal(sum(y),sum_correct))\r\nassert(isequal(p(d==7),p7_correct))\r\n\r\n%%\r\nn = 1e6;\r\ny = modest(n);\r\nsq_correct = [49 82369 312481];\r\ny1302_correct = [66999 174333 301387 478999 695999 999999];\r\npsum_correct = 169193200;\r\nassert(isequal(y(mod(sqrt(y),1)==0),sq_correct))\r\nassert(isequal(y(1302:1302:end),y1302_correct))\r\nassert(isequal(sum(y(isprime(y))),psum_correct))\r\n\r\n%%\r\nn = 1e7;\r\ny = modest(n);\r\ny3070_correct = [13 216296 623801 1481111 2561212 3720837 4901818 6070909 7358085 8600946];\r\npsum_correct = 4054289284;\r\nassert(isequal(y(1:3070:end),y3070_correct))\r\nassert(isequal(sum(y(isprime(y))),psum_correct))\r\n\r\n%%\r\nfiletext = fileread('modest.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-30T04:10:04.000Z","updated_at":"2026-01-14T21:15:59.000Z","published_at":"2021-08-30T12:37:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAfter determining the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52619-find-the-nth-nude-number\\\"\u003e\u003cw:r\u003e\u003cw:t\u003enude numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, or the numbers that openly display some of their divisors as their digits, one would think that the modest numbers were those \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enot\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e divisible by any of their digits. Instead a modest 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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is one that can be divided into two parts \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 \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\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that when \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\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is divided by \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\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the remainder is \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. For example, 411 is modest because it can be divided into 4 and 11, and dividing 411 by 11 leaves a remainder of 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\u003eWrite a function to list the modest numbers up 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\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\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":53880,"title":"List the vile numbers","description":"Evil numbers, the subject of Cody Problem 2733 have an even number of ones in their binary representations, whereas odious numbers, the subject of Cody Problem 2734, have an odd number of ones in their binary representations. For example, the numbers 3, 6, 10, and 12 are evil, and the numbers 2, 4, 7, and 14 are odious.\r\nVile numbers have binary representations that end with an even number of zeros (including zero zeros). Therefore, the numbers 3 and 12 are evil and vile, and the numbers 4 and 7 are odious and vile. The numbers 6 and 10 are evil but not vile, and the numbers 2 and 14 are odious but not vile. Got it?\r\nWrite a function to determine the th vile number. ","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: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; 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: 87.9px 8px; transform-origin: 87.9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvil numbers, the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2733\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 2733\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: 220.95px 8px; transform-origin: 220.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e have an even number of ones in their binary representations, whereas odious numbers, the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2734\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 2734\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: 203.433px 8px; transform-origin: 203.433px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, have an odd number of ones in their binary representations. For example, the numbers 3, 6, 10, and 12 are evil, and the numbers 2, 4, 7, and 14 are odious.\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: 368.633px 8px; transform-origin: 368.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVile numbers have binary representations that end with an even number of zeros (including zero zeros). Therefore, the numbers 3 and 12 are evil and vile, and the numbers 4 and 7 are odious and vile. The numbers 6 and 10 are evil but not vile, and the numbers 2 and 14 are odious but not vile. Got it?\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: 102.942px 8px; transform-origin: 102.942px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine 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: 47.45px 8px; transform-origin: 47.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth vile number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = vile(n)\r\n  y = 2*n-1;\r\nend","test_suite":"%%\r\nn = [2 8];\r\ny_correct = [3 12];\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = [3 5];\r\ny_correct = [4 7];\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = 80;\r\ny_correct = 119;\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = 519;\r\ny_correct = 779;\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = [830 834 837];\r\ny_correct = [1244 1251 1255];\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = [3082 3089 3097];\r\ny_correct = [4623 4633 4645];\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = 7310;\r\ny_correct = 10965;\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = 9999;\r\ny_correct = 14999;\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = 8675309;\r\ny_correct = 13012964;\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nn = 20000000;\r\ny_correct = 29999999;\r\nassert(isequal(vile(n),y_correct))\r\n\r\n%%\r\nfiletext = fileread('vile.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2022-07-02T13:04:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-16T16:22:52.000Z","updated_at":"2026-01-15T13:39:50.000Z","published_at":"2022-01-16T16:27:01.000Z","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\u003eEvil numbers, the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2733\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 2733\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e have an even number of ones in their binary representations, whereas odious numbers, the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2734\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 2734\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, have an odd number of ones in their binary representations. For example, the numbers 3, 6, 10, and 12 are evil, and the numbers 2, 4, 7, and 14 are odious.\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\u003eVile numbers have binary representations that end with an even number of zeros (including zero zeros). Therefore, the numbers 3 and 12 are evil and vile, and the numbers 4 and 7 are odious and vile. The numbers 6 and 10 are evil but not vile, and the numbers 2 and 14 are odious but not vile. Got it?\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 \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 vile number. \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":53910,"title":"List the dopey numbers","description":"If vile numbers have binary representations that end with an even number of zeros (even  vile), then numbers with binary representations that end with an odd number of zeros are dopey (odd  dopey). \r\nWrite a function to determine the th dopey number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 36px; transform-origin: 407.5px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 7.66667px; transform-origin: 5.825px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53880\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003evile numbers\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: 213.55px 7.66667px; transform-origin: 213.55px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e have binary representations that end with an even number of zeros (\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: 7.78333px 7.66667px; transform-origin: 7.78333px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eev\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: 9.725px 7.66667px; transform-origin: 9.725px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003een \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\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 7.66667px; transform-origin: 1.94167px 7.66667px; 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: 3.89167px 7.66667px; transform-origin: 3.89167px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ev\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: 3.11667px 7.66667px; transform-origin: 3.11667px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eil\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: 3.89167px 7.66667px; transform-origin: 3.89167px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ee\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: 86.35px 7.66667px; transform-origin: 86.35px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), then numbers with binary representations that end with an odd number of zeros are dopey (\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: 8.55px 7.66667px; transform-origin: 8.55px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eod\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 7.66667px; transform-origin: 5.83333px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ed \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\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 7.66667px; transform-origin: 1.94167px 7.66667px; 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: 8.55px 7.66667px; transform-origin: 8.55px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edo\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: 17.5px 7.66667px; transform-origin: 17.5px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003epey). \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: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.942px 7.66667px; transform-origin: 102.942px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine 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: 56.0083px 7.66667px; transform-origin: 56.0083px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth dopey number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = dopey(n)\r\n  y = 3*n;\r\nend","test_suite":"%%\r\nn = [2 8];\r\ny_correct = [6 24];\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = [3 5];\r\ny_correct = [8 14];\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = 80;\r\ny_correct = 238;\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = 519;\r\ny_correct = 1558;\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = [830 834 837];\r\ny_correct = [2488 2502 2510];\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = [3082 3089 3097];\r\ny_correct = [9246 9266 9290];\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = 7310;\r\ny_correct = 21930;\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = 9999;\r\ny_correct = 29998;\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = 8675309;\r\ny_correct = 26025928;\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nn = 20000000;\r\ny_correct = 59999998;\r\nassert(isequal(dopey(n),y_correct))\r\n\r\n%%\r\nfiletext = fileread('dopey.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-01-18T00:10:33.000Z","updated_at":"2026-01-15T13:49:44.000Z","published_at":"2022-01-18T00:14:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53880\\\"\u003e\u003cw:r\u003e\u003cw:t\u003evile numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e have binary representations that end with an even number of zeros (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003een \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=\\\"--\u0026gt;\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rightarrow\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:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eil\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), then numbers with binary representations that end with an odd number of zeros are dopey (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eod\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ed \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=\\\"--\u0026gt;\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\rightarrow\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:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edo\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003epey). \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 \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 dopey number. \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":53120,"title":"Compute the Sequence of the Day","description":"A sequence starts with 1 and 2, and each subsequent term is the sum of the digits of the product of the previous two terms. As a result, the third term is 2, the fourth is 4, and the fifth is 8. \r\nWrite a function to compute the th term of the 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: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.5px 8px; transform-origin: 367.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA sequence starts with 1 and 2, and each subsequent term is the sum of the digits of the product of the previous two terms. As a result, the third term is 2, the fourth is 4, and the fifth is 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: 100.5px 8px; transform-origin: 100.5px 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: 79px 8px; transform-origin: 79px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth term of the sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = seqOfDay(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 5;\r\ny_correct = 8;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 67;\r\ny_correct = 16;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 234;\r\ny_correct = 11;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 5142;\r\ny_correct = 5;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 8493;\r\ny_correct = 8;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 14243;\r\ny_correct = 11;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 20232;\r\ny_correct = 2;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 67423;\r\ny_correct = 4;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 563924;\r\ny_correct = 14;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 888889;\r\ny_correct = 1;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 1233657;\r\ny_correct = 8;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 2336582;\r\ny_correct = 5;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 5813231;\r\ny_correct = 5;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 8675319;\r\ny_correct = 5;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 19785386;\r\ny_correct = 2;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 44411412;\r\ny_correct = 14;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 567891243;\r\ny_correct = 2;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 12345678910;\r\ny_correct = 4;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 137858491861;\r\ny_correct = 10;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 2015993900465;\r\ny_correct = 8;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 63403380965386;\r\ny_correct = 7;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 52525252525252;\r\ny_correct = 4;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = 1e15;\r\ny_correct = 7;\r\nassert(isequal(seqOfDay(n),y_correct))\r\n\r\n%%\r\nn = flintmax;\r\ny_correct = 2;\r\nassert(isequal(seqOfDay(n),y_correct))","published":true,"deleted":false,"likes_count":7,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-12-04T00:07:15.000Z","updated_at":"2026-01-15T14:30:49.000Z","published_at":"2021-12-04T00:08:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA sequence starts with 1 and 2, and each subsequent term is the sum of the digits of the product of the previous two terms. As a result, the third term is 2, the fourth is 4, and the fifth is 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 \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\u003eth term of the 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":53990,"title":"Classify product/digit-sum sequences","description":"Cody Problem 53120 involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\r\nWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved Cody Problem 53120, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \r\nWrite a function to classify the product/digit-sum sequences given the first two terms  and . To encourage solvers to find the pattern, loops are banned, and to allow for large inputs,  and  are specified as 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: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 93px; transform-origin: 407.5px 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: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 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/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\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: 309.642px 7.66667px; transform-origin: 309.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\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: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 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: 383.883px 7.66667px; transform-origin: 383.883px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\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: 103.075px 7.66667px; transform-origin: 103.075px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \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: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.017px 7.66667px; transform-origin: 262.017px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \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: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \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: 93.35px 7.66667px; transform-origin: 93.35px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \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: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \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: 77.4px 7.66667px; transform-origin: 77.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are specified as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = PDSseq(a,b)\r\n  c = [1 9 26 62 163];\r\n  y = c(a+b);\r\nend","test_suite":"%%\r\na = '1';\r\nb = '2';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7';\r\nb = '31';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '17';\r\nb = '28';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '51';\r\nb = '77';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '82';\r\nb = '262';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7021';\r\nb = '8878';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264';\r\nb = '412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8675308';\r\nb = '2941300';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '9142534264';\r\nb = '8424812653';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164';\r\nb = '8424812753';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '1352408463575';\r\nb = '9898989898985';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264534264534264534264';\r\nb = '412578412578412578412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '86753088675308867530886753088675308';\r\nb = '28413002941300294130029413002941300';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '914253426491425342649142534264914253463';\r\nb = '842481265384248126538424812653842481265324';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164842481275380314231648424812753';\r\nb = '84248127538031423164842481275380314231648424812756';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '43524084635758031423164842481275380314231648424812753';\r\nb = '98989898989858031423164842481275380614231648424812753';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = num2str(randi(835042)*57);\r\nb = char(randi(9,20,1)+48);\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = repelem('1',1,23);\r\na(randi(23)) = '4';\r\nb = num2str(10^randi(14));\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\nfiletext = fileread('PDSseq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'system') || contains(filetext,'regexp') || contains(filetext,'java') || contains(filetext,'for') || contains(filetext,'while') || contains(filetext,'numpy'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2022-02-05T01:46:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-02-04T04:01:11.000Z","updated_at":"2026-01-15T18:05:52.000Z","published_at":"2022-02-04T04:04:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \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 classify the product/digit-sum sequences given the first two 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\\\"/\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 \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. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \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 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=\\\"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 are specified as 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":51820,"title":"Count unique orderings of vertices of a polygon","description":"Cody Problem 2671 asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\r\nHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \r\nWrite a function to determine the unique orderings of vertices of a polygon with  sides. \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: 356.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 178.458px; transform-origin: 407px 178.458px; 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\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/2671\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 2671\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: 294.433px 7.91667px; transform-origin: 294.433px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\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: 383.133px 7.91667px; transform-origin: 383.133px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 245.317px 7.91667px; transform-origin: 245.317px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine the unique orderings of vertices of a polygon 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: 22.1667px 7.91667px; transform-origin: 22.1667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 182.917px; 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 91.4583px; text-align: left; transform-origin: 384px 91.4583px; 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: 262px;height: 177px\" 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data-image-state=\"image-loaded\" width=\"262\" height=\"177\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = polyVert(n)\r\n  y = nchoosek(2*n,n);\r\nend","test_suite":"%% Rectangle\r\nassert(isequal(polyVert(4),3))\r\n\r\n%% Triangle\r\nassert(isequal(polyVert(3),1))\r\n\r\n%% Heptagon\r\nassert(isequal(polyVert(7),360))\r\n\r\n%% Dodecagon\r\nassert(isequal(polyVert(12),19958400))\r\n\r\n%% Heptadecagon\r\nassert(isequal(polyVert(17),10461394944000))\r\n\r\n%% \r\nd = num2str(polyVert(19))-'0';\r\np = polyval(d(1:3:end),4);\r\np_correct = 3760;\r\nassert(isequal(p,p_correct))\r\n\r\n%% \r\nd = num2str(polyVert(15));\r\ns = polyVert(str2num(d(4)))+polyVert(str2num(d(6:7)));\r\ns_correct = 3113512920;\r\nassert(isequal(s,s_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-27T04:52:02.000Z","updated_at":"2026-01-15T18:13:53.000Z","published_at":"2021-05-27T04:56:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/2671\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 2671\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks us to determine whether four points can be the corners of a rectangle. The points are not necessarily input in order (either clockwise or counterclockwise). My initial attempt at the problem involved determining how the points might be presented. If the corners are numbered as shown below, then they can be input in 24 ways.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, for the rectangle problem, many of the 24 ways are essentially the same. For example, 2341, 3214, and 4123 are effectively the same as 1234 because the numbers of the corners could be shifted around the rectangle. In fact, only three of the 24 ways are different (1234, 1243, and 1324). \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 unique orderings of vertices of a polygon 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\\\"/\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 sides. \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=\\\"177\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"262\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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the ways to draw non-intersecting chords between points on a circle","description":"There are 9 ways to draw non-intersecting chords between four points on the perimeter of a circle (including no chords at all). In this case there is no way to draw three chords between the four points because two would have to intersect at one of the points or elsewhere. \r\nWrite a function to count the ways to draw non-intersecting chords between a given number of points.\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: 467.517px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 233.758px; transform-origin: 407px 233.758px; 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: 375.758px 8.05px; transform-origin: 375.758px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThere are 9 ways to draw non-intersecting chords between four points on the perimeter of a circle (including no chords at all). In this case there is no way to draw three chords between the four points because two would have to intersect at one of the points or elsewhere. \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: 313.383px 8.05px; transform-origin: 313.383px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to count the ways to draw non-intersecting chords between a given number of points.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 365.517px; 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 182.758px; text-align: left; transform-origin: 384px 182.758px; 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: 640px;height: 360px\" 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yiy81YY5n6HM0m0WXHhEsjAAnivdPAIAoDAYACvIke7xzV+2stAFQUw1dSd2NJwVF41mXJv5IbeollUIBDGtr2juG54WF43SwCOYMABOKX08AgCgNhgAq8bMnUc5hTEWtCAopdaUHxwcvSkuHZ1YvLwaHwhAWZW4NUmXyrPErLhu1AUewYQBcErp4xEAALXBAFg1lqyuuT0xwoIWBKUU9WbmLauaff5CXD16sOmLrq6OXlYVEJRSOiyFCo+YKwyA0wmLAwMAFAADYKWojH1b3xhn4QqCMki3qU3a+6bKKltYJUBQBlV93bmneUhcQMoBj0gpDIAzSG2PAADoAAbA6vDwSWLx8moWqCAoq5ZtqB+/fk9cRqozb1kVVsaG7IouG1Vf+4RHpBQGwJmlsEcAAHQAA2B1KN8Zb2vtYVEKgrLqQv/girJmcRkpTWPn6NZdbaz4EJRV9Y3xyti34jJSCHhEOmEAnFmqegQAQBMwAFaEuw+eLinYx0IUBFlUfmnDpSvfi4tJUWafv1i8vBoPuyBnootHsaWz4REZhAFwVqnnEQAAfcAAWBHw+BdyIx0eAu9pHqr6upMVHIIsihpYambFxaQE8IgMwgA4q9TzCACAPmAArALPErPzllWx4ARBtpRbVHtt5gdxSanI60t3Jm5NslJDkHUp9sgLHpFBGABbER4CAwAiCgbAKhA/e61kyxEWmSDIlrZXt8eOXRSXlHIMjt5cU36QFRmCbGnzl61HusfFJRVx4BGZhQGwFankEQAArcAAWAWKtrT1xM+wyARBtjQ1PJxbXC8uKeX4rLqn+fApVmQIsqX+noHCiqPikoo48IjMwgDYilTyCACAVmAArAJ4kw3yRAq/z0ZFu391jJUXguyKGtvZ5y/EVRVl4BGZhQGwRSnjEQAArcAAOPLgTTbIK6n6Ptu1mR9yi2pZYSHIgdZXNPcNT4sLK7LAI7IKA2CLUsMjAAC6gQFw5Hk5k2cNZvKEPJCqs3rCRyCvpIaPwCOyCgNgi8Jc0ACAKIIBcOSh2EMRiMUkCLKlxK3Jnfs6/kfh1/+Qt+dP+/qeJWbF5aUElbFv6xvjrMgQZEvkI3QVvf1Bzbz3q2PHLkbaR+ARWYUBcFap5BEAAN3AADhiUIx575Mj81c2LyyMk+atPPyP7+89cuQ0i0wQZFHUifmnwtjCtd3JHb43Pup9Mz8W3Q4N5fw3m1pMN/mH/Oafr6y5PTHCyg5BFvXO2v0L1pxI9pFF606/tTIWoa8fKau7D55fuvEQ6dcfHjjU3M3KCCUr2dbsJ4ikgEcAAHQGA+Ao0Tc8vWhlQ3LIMbRgxcH9DSdZfIIgK3p/Yz3rxxha9GHPL1btF1depKg5PvVW8VlWHNKiVYfgJpADrfv3Q/NXt7PLibRwbfc76xvFZScxNCb59YcNKW5y/Xbv4+kJVljIUHJdsZ+gqHsEAABgABwlfrW27uVN1jlRZ3FR/8/+dRcLURBkRe+s3b9w3Ss9Y0Nvrv92Xl61uPIixZKPWllZDMFNIGda9L/20HCRXU6kxcUDf/cvO8VlJzHv/64l3U2un6/YywoLGUquKPYTFHWPAAAADICjxKo/tC34oIuFHBKNit9eXcNCFARl1Y+3pz7ePpR8Lf3843P0L/Vj3lxZd23mB3HlRYp0bkI9NrgJ5ED7G04uWnWIXU6kBQWtm6t7xWUnMe+sb2SPfw29vMn1XhUrLGQouaLYT1DUPQIAADAAjhKzz18s/O0+dud1cVH/37/3FVZ0hGzpycxUwdZXhr6/+Ljvv+V+9dq723+1tu7Sle/FNRdBUrqJqfhpeApkW1PDw79cFTNvrCxYc+IXH9SfuTQjrjm5efgksWj51xQpTC8gvbzJlR+jcrGSQoaS64r9BJEi7REAAIABcPS4++Dpqj+00UCF9P7vWv7XJ4f6ewZYcIKgdLr73RU29KU/aTxMP90YvZizrlZcZxEn2U0WrGj85f/+qbwkDIMhZ7o9MbJkdY24yCLFtZkflm48ZHjEz/6tqv4gZoHOpOTmgv0EJSu6HgEA0BkMgCMPlkGCLIqGvu9VvDL0/WTX8I+3Xw59DV3oH1xR1iwuLIUwfGRocPztjS9f8DaFYTBkV2r4CKJGViU3FOwnKFmqRg0AgNpgABx59jQPVdV0spgEQcm6PjaZU/rK2I8NfQ1Rn5h6xuLCUohkH8EwGHIjNXwEUSOrkpsI9hOULFWjBgBAbTAAjjx9w9PrK5pZTIIgQ3OHvttil9k+prbuamvsHBUXlkIc6R7f/GVrckkxDIacqaa2a0fjoLiwIstcj4CYkhsH9hOULDU8AgCgGxgAR57Z5y9eX7qTxSQImjvG23d4hO3DlFMYm7nzSFxYCvHwSWLx8mpWWNLcKmo/iWEwlEnLNtSPX78nLqzIks4jIFPJzQL7CUqWGh4BANANDIBVoLDiKObBgkzFT48l995ItS1Zhr4klWbAmkteSdPoufOsyIbmDoOtVBekoe5fHaNxo7ikIk4Gj4BIyQ0C+wkypZJHAAC0AgNgFcD7bJChuUNf62/2qv0mW+zYxe3V7azIyaJhMHtXHMNgiKn58KnPqnvEJRVxsnqE5kpuCthPkCmVPAIAoBUYAKsA3meDaLSW3GN7e+M5ux+1qv0m28ydRzmFMVbkuZr7yTSGwZCpNeUHB0dviksq4lj0iP9/e2f/FNWd7/k/KbO1U7l1a40xMZkpnaoZktmLd1fJRnQwggnNrJAwgZnFcRwxN2NUGIikRXmQVgzIQ2y0AxHSCCgP4UklUlhi0FJLqbjtFqU/zH4MZ7jHbyNCP5zu8/2+XvWqqdI+A+lzvm/P930ejdX+j4DyES6oUyIAwCgowJrg2dMY8J9Xdk5ogiW1/fa5mlTfnuCwsswLHe/rS82psgaTpsgXlK+pfPFFpQZjuA8mR1ZtKrUGkxYsPxEGao+/8hHOq18iAMAcKMCacHXqbqqnUtk/od4We5+pvtLZpLkpyyzT7CJfR9+kNZg0ZaXPS6cGo139npHOGwSW0B585SOcV9e3BgCACVCA9YGTwIb4aHr8o0N99vlZNNVXNOH07zxbCny9nSubzobX4Bc+TBv1c3pkYN22CmsYaUQEiTBEe+SVj1DUNREAYAgUYH3gni7tnZ1Sq+/Gop6Zy2PKYivVnPu4Lo3dTM+vVr7+cgyvwUu8Thn1s2BffVPHuDWMNCLiRGivPezKRyjqmggAMAQKsFYUHvQ3NgSUHRVqoFTfjL099jmZ/PHO99FWX7G3M7ilwGcNIAOI5pQXNdhM9T7ZxUngRbXHXPkIOf0LAG6HAqwVc4+frN1c/mByRNldoXuduTy2sUitvtKHlcUiVgbMvdmQNYAMYObOj+syDisrYUWGbxFqsN6m51dfGrtpDSDtiD4RWmoPuPIR6p0IADABCrBucEmbNoYXrY8O9T2ajln1Fc28jE2+snxxZVWsVGqwIZZ+0VLm67GGjqbEJBGaaY+28pHhmpAIANAeCrCGHKj+tuLoV8pOC11k+KW2uw9fim31FVub2z/8tNUaNIYhX1y+vrJCIpAarLeD3RfS8mqtQaM1sUqENtpDrXxksuYkAgD0hgKsJ7KLkh2VsuvC5LcnOOzMXaa3rwyt3VxuDRcjka8vK0FZLZG5aA2O+QELdNjQjVEZJA9Dc9aI0Z0YJkID7XFWPjJW0xIBABpDAdaTe7OhdRmHZXel7MAwaZXquz73meob17fOpnoqr07dtYaLkcT81dkOXLKOTmrCy7Ht8DJ5u/YgKx8Zq2mJAACNoQBrCx3YLfrPDdknW2JtQ3zfNEv7nSceM35qsB6aOdenAy9oj7DykZnSfgFAJyjAOsPjPZPcpjNq9ZUyrCwTc3mApx2Z0snETllF0Xvn+zHltVXUYBe5t+R0TfOANUQMI06JcJ328CofGajJiQAALaEAaw5H9JPTyvoB+wRrfW53T3BYWSYechQ/nPjN+MPf3kwNTn6Z69OBRXtslY9Mk0QAgH5QgPWHDpxUFnv77VMrx6qvSPt9HnGd8VODXSRz/XnowPbAKh8ZJYkAAC2hABsB9wMng0r1Tcnvnhhybotw3+/SxPs40aI1WP5SWQwTKEeI7Bh+5NQeVeUjcyQRAKArFGBTmHv8JC2vdryvT9nDYbx9ND0uVcc+ndpY1HN91Lnqe/vKUErWEd5d8UJkFcmKiuubYMJrsPyRGpxwQzdGU7K8M3d+tIYC/IQDiUha7SFVPjJBEgEAekMBNovCA2caG75WdnUYJ6XY7Pik1z6Rkuo7c3lMWSyu9nYGtxT4rM0Py0BWl6w0ZTXGVmpwUnlt8GJqzrG5x0+sEQDP4kAiklB7PJWPtJdEAID2UICNo6Z5YG/JaWWHh7E1SRpOVW3bPm+HteFh2chKk1WnrMyYSw1OBgP+8549jdaGh+fgTCKSSnswlY/0lkQAgAlQgE3k3mwoNeeomRe2xdvw18Du+KTX+VYTujGa6qmc+uG+tclhhciqkxXowG3z4VfIU4Mdk1eCLR/HEpEk2iOpfKSxJAIADIECbC5ldd2l3q+U/R9G7MTQqFJ9E/Ww38aGrwsPnLE2M0SBY7cMUIMdllsDIsOcm2jsYVQ+0lISAQBGQQE2Gk4Fx0Spvin53fYJU7G3X1nGGTnxG3OGJ26l59c4c+Jr0Rp853tHbxo3wexdvo7ea9YGhhXiZCISqD2Gykf6SSIAwDQowPCPA9VdFUfPKHtEXI49weH1uUlRfUVO/MYPz57GQFunssLj5KKPDXf42Wm6Oth9Ib3Ax9N9osfJRCREewCVj3SSRACAmVCA4Smy//P8paHz6y5l74jPs7PzO6X6VtYPKMs45nhfX/rHdbzoKK7I6pWV7NiLxKjBsfX2laG03Gpe6xJDHE6Ew9qjp3ykhyQCAEyGAgz/iUxo0vJqrg1eVPaUaNd/bsg+NxKbziTsGvIHkyOpnqNMYhxj6of7MmuU1a5siDhJDY7e0I3R7F0nggNT1iaEmOJwIhzTHjrlI7dLIgAAKMCgouuEJnor6wfssyJRyrCyjGMyiUkgstpl5Tt5G2Sxt98+8KjBy7S45HRNc7+12SBuOJ+IeGuPm/KRqyURAAACBRgW5+mTTv5QOz2SsMt6k0ql+q7P7e4JDivLOOZ89W1qH7U2FSQI2QTb/1hHDU5OZaJfVtdtbSpwBOcTET/tQVM+cqkkAgBgAQowLMXMnR/T8mp0vctrOSqVIyW/e6AvYdV3emQgLbf66tRda/NAEiCbQzaKk4eKwmvw9VHNH8m7fB9MjmTvOuHvumJtHnAc5xMRD+0RUz5ylyQCACAcCjC8mPlHZDU2tit7Vo19ND3+x79ftM+BpPpODCWsZjx9VufHddzrm7Tcmw3JBurtdG6uHH5oJoHjMxmUxpXqOcrhoSTB+UTEVnu4lI/cIokAAHgeFGBYAfu8Hdm7fHrfHpxUjx0K3RgtLjnt2dPIaypcwdNDRXsaZZM5dhUoNVisOn42vcDHU9CTEOcTESvtsVI+Sn5JBADA0lCAYcX8dF10re/kOWWn63Znp8Yz9vbY5z3v7k5Y9Q20dabmHBueuGWtdHAVsuFk8zn2olQza/Bg94VUz9GO3mvWSockxuFERK89UMpHSSuJAABYJhRgiBx/15W03GoNXpt05/sxpfrKH6UPK4s54O0rQ5t2VnlP9VqrGFxOTXN/en6NM/dDltQaUYMfTI5sLzx+oLrLWsXgKpxMRDTao6R8lGySCACAlUIBhmiZe/xEdr0pmd7B7gvKjjn5nbk8trHomer70aG+R9NOV99rgxel9xYeOMNFa1oim1U2rmxiB54npzyxXJsaLJVJZvmZRafuzYas1QquxclERKY9RMpHSSKJAACIGAowxJKm9rGUrCO+E2eVXXUSKq1AuoF9luN89Q34z8vq4nyvUcjmlo3e2hzfR8qF1+DRflfeut8Z6Er1VB6o7uI2eF1xJhEr1R4f5aPESiIAAKKHAgxxYXjiVlpebcG++iS81C28+hZ7+5Vl4uftK0N7S06n5hwLDl63VhYYiQwAGQYyGGRIKIMkVibV+6uX74PJkdIvWqUU+b+9aq0sMAAHErF87cFRPnJeEgEAEFsowBB3ZJ+dmlOVXeRL+NVuMvuXDmCf2Rw+4UQ/nx4ZKNhXv25bxcm2YQ7bQzhNHeMyPPL2nIxHRlxRgyUj0nzWZVTUNA+QEYhrIpajPTLKR85IIgAA4gcFGBwlOHh9S4EvPb+6tbndyRdj+M8NKdVXWoGyTGztDHTJ7E3mcDKTs748wDLo6JtMy6uNeUaSsAaTEVgOcUrE0trDonwUP0kEAIAzUIAhYTwMzcluXvrwuozDpV+0xPxiaZkqHTzcnJLzpX0qI0oZVpaM3ttXhqpq/CmZ3pQdlTUtgzyVBGJCzDMSXoML9vtTPZXinz9riOsrvskIRI8Dew0ZpRIHe0yUZWIliQAASBQUYEgihidu7S4PrNtWIZObXZ81tDa3R3YzmExifp3pfTWrzT6JeSMnuHbbiein+PITAv7zew81ysRl7ebywoN+7uYFx4hJRvznhp6Jxj997YP219/9nIyAi4jVXkN8K+vI6u1fKaEQoz/tTCIAAJIKCjAkO1M/3K9pGfTsaVy1qXTTzqrthcdLK1oaGwK9nc+dl7yTW7XoPGbN+4E3t3yuLLyo8sNlIiW/KLvIJ7/05Q0HM4tOeb+8eHXqrvWfBZA0RJaR13YElICIZAQ0IIJE7PhT3SvbmpQ4zCvFWFl4UUkEAIBboACDu3kYmrs0dvNk23CZr2dLgW/ef91Ypp7+/cnXs7/52W8PvvT2fjEtr3ZhefFATVAmTPKjuA4NNIOMANhZNBE/33DotQ/alTjM+7O3PyMRAAA6QQEGDZHpyJrNX6z1dNonMWtzul7fepSD8QACGQGwc6xpYE3GCXscFtxV3m4tBAAAWkABBm2RefyG3Lr5I/e/yjp6aeym9QEA/AQZAVhA4vDL946tfq91vveu3v7VL96rOn9pyvoYAAB0gQIMAAAAAAAARkABBgAAAAAAACOgAAMAAAAAAIARUIABAAAAAADACCjAAAAAAAAAYAQUYAAAAAAAADACCjAAAAAAAAAYAQUYAAAAAAAAjIACDAAAAAAAAEZAAQYAAAAAAAAjoAADAAAAAACAEVCAAQAAAAAAwAgowAAAAAAAAGAEFGAAAHOZe/yk5PiFDbl14l8OdzwMzVkfABjG//1/T+R/JRE1LYPzifB+eZFEAADoBwUYAMBEZKL/m/erX81qe+P3wQVf+6D99XQvk34wiotXHqzPuyDj/82cb1/NOmtPxJod597Y6pWwWIsCAID7oQCDnsgMfuNHJ1/Z6ns10y+u2nrirZzamTs/Wh8DGM87f6h/PfubN3/fbZ/uP53xvx/4xe+OWAsBGMDZi3eUFNh9Navtrewaa1EAAHA/FGDQkI6+yTVbq5VJjLgm48SxpgFrIQCNmHv85NLYzaaO8TJfT2bRqdScqpfe3p+S6U3Pry6taLHb2xkMfhPcvldNx4LSil/eUDK/8PbC46meyqc/akfllgKf/PCTbcPyizhFDEnOihIx76tbfUoW5l2b0/VffntgfmESAQCgARRg0JBfZR19et1a+DzG0/kv/6PEWgjAhUz9cF8m3B9+2rp2c7lMxPceagz4z4dujD6ZubwcZ6fGf7+/T8mFXZnrv57uHe/rU/6P4cov7Qx07S9v2rSzatWmUs+expqWwatTd63/UABHiDIRdo9Un1nzuzolEeJrWWf+z9++VBYOl0QAALgFCjC4AJniXBq7Webr2V0e2FLgk7nFyxsOpudXF+yrXziKLzY2BOYP5G/wVK5+r1WZxIjSil95p2x+Yfn/yk+QnyM/TX6m/GT5+fJb5HdZvxUg0ciALDzol5l93p6TMrynRwaUOffyleqbsbfHHgf5o/yldN35M1ri+m0VEh/l/7hSb18Zam1ul3zJf7bUko6+SevLAERNDBOxqBKHX/7Ou+juw39uSFl4mZIIAIBkgwIMScTwxC1poVJHpZduLzxeUdm6nDNR4YZujK5+p+y1D9rt05e1ns5VaWUyF1EWXlT5vVU1/uyip2U7La/2QE0wOHjd+q8EiA8PQ3Mn24ZlvK3LOFz6RUusJvczl8c2Fi1SfZXF4qeEznfirNTslB2V3lN992ZD1hcGWJI4JWL59gSH1+c+c5N8xDXYLokAAEgsFGBIDHOPnzR1jGcWnVq7uXzvocbOQFdkF60tocyWtubXzJ/aeie3KrIurdjbGdxf3iSzMZmTycyM+74gSmTuu8/bISOq4uhXDyZHlPEWpddHR5Xq+9GhvkfTzlXf59nYEJCvXHjQzwWioBDXRERmnGqwXRIBAOAkFGBwiKkf7h+o/nbdtor0/GrZ2SfJzCZKpbS3NrdnF/mkxu8uD3D5NCwHmeN++GmrzHclCMqIipUTQ6Mp+c9M2Yu9/clQfcMN+M+neiozi05dGrtprSAwDAcSEb0O1OB5SQQAQLyhAEMckf23Z0+j7Mtlj67s43W1tzMoDX9LgY8bvUDhpP+7lKwjjQ1fK2MmtoZP06X6KsskrZ2BrpQsr/dUL69dNQFnEhFbw/PVdCYuNXheEgEAEA8owBBjpPil5dVKCYz+aTpud7yvL7vIl7Kjsqlj3Fo7YBgPQ3P7vB2bdlYNdl9QhkfMDZ+aV9Y7fc9krLw2eHF74fEPP23l9kjNcDIR8dP5rJEIAIAYQgGGGCBzmgPVXameSlfPaeKqTF/S86sLD5xh+mICkgjPnsaCT04t86FrUeo/N2Sfi4v1zYPKMi71weTI/s9b0vJqCY6rcTgRzig1WLnRwIFDTiQCACB6KMAQOVM/3M8sOpW356ROc5p4K9OXvSWnZfoyPHHLWo+gETXN/en5NY49rra2YcA+/xbjdF9iwpXgbC88fqC6i2tB3YXDiXDe8PvtnbnygkQAAEQMBRhWjPTe1JxjFUfPxPy5zabpO3E2JesITVgDZCNKKAJtncomjp8yybbPudfndvcEh5VltHSw+0Kq52hH7zVr1UNS4nwiEmuiarBIIgAAVgoFGJbL3OMnu8vO5f21nt4bc4tLTnv2ND7kpUoupKyuWzafk6Eo9vbb59ky7Tak+ipWHT8rqeH0V7LhfCKSxwTWYJFEAAAsEwowvJiO3mtpudUxeY8uLuH0yEB6fs1J/5C13iGJkVmmzDUbG9uVjRg/H02Ph1dfmXAri5nm0+euf1zH/ZAJx/lEJK3hNfjwCedqMIkAAHghFGB4LvMTmqrjZ5X9K8bb1paO9AIfJ4STE5lZyvzSyYecS/X96FCffT69sahn5vKYspjJTo8MpHqOXp26a20kcBDnE+EKw2uwky8kIxEAAEtAAYZFYEKTDI739aV/fHzqh/vWVoFEM3Pnx9Sco04+zmd2ajxjb499Dk31XcIHkyPZu04EB6asDQZxxvlEuM7E1mASAQCwKBRgeIarU3dTPUxokkiZwaTtrGIGk1gehubSP65z8i6A8Oorf5S/VBbDcCUy8o+YdDNr40EccD4Rrnbm8tjGomfi7HANJhEAAHYowGAhFSt71wnZUyr7TkwGQzdGCz75sql91Npa4CCZRac6v+5Stkj8DJ8rf3Soj+q7Un+6gKKO+wjigcOJ0MbE1mASAQCwAAUYfrqMzXOU6pv8Sg1Oz6/htUmOUVbX/XfvV8pWiJ8TQ6OphRfs82Opvo+mqb6R29rS8eF/tFibE6LG4URoaWJrMIkAABAowEbDZWxudHpkIP3j41zPFleGJ26l59c49iqXxN4oqL3Zu3y8JTVKHE6E9i5agx072kUiAMBwKMDm8uF/tLS2dCj7RXSLvZ3BzKJTvPIxHnj2NAbaOpUVHid7gsPrc5+pvn87dklZBqN3sPtCeoGPvESGk4kwykXvd3CmBpMIADAZCrCJdPRey97lU3aH6EaLS07XNPdb2xWixsnTXIH2IaX6Vtbz8Ln4yomvlcKJXwdMYA0mEQBgJhRgs5h7/CS9wDfYfUHZC6J7ffq+x5xjPNokehw7zeU/N2Sf7IryN8oyGCc58bV8OPHrpHe+H1Me/O5MDSYRAGAgFGCDCA5e3154XNn5oR7++bOGk/7vrC0NK+TebCg15+jtK3FvoZX1A/YJrkj1dd7QjdFUTyVv2F4CxxKBiuHvP3OgBpMIADANCrApbCnw9XYGld0e6uS1wYupOcc4kL9ShidubdpZpazMmHv4xDPVd31ud09wWFkGnTTvr/X+rivWIAAbziQClzAhNZhEAIA5UID1595saF3GYW7iMsRUT+XVqbvWtocXUdM8sLfktLIOY2uxt98+kU3J7x7t55VjSWFVbds+b4c1FOAnHEgELtNFa3BcXwlOIgDAECjAmsNlzwbK5dDLJK4PQn80PS6zVfvkVarvxBDHoZLLwe4LaXm11oAwHl4NkISG12D5Y/xqMIkAABOgAOtMWV13qfcrZfeGJtjY8HXhgTPWOIDFePqAH/95Zb3FxPDqu7GoZ+bymLIYJonjfX2pOVXWsDCY+CUCo9fJGkwiAEB7KMDawmzGcJnELEGc0rHoJJXqm/wSFvYXrtCxGkwiAEBvKMB6kpZXy7uOcHpkYN22CmtMwD/Z5+2oqm1T1lWUSst9d7dzlylizJX6JyXQGiKGEY9EYPwMv8YkHv/amJwIANAeCrCGcCwfF+RAvkLM5/pSfTcWPVN9HXheK8ZDM2f8tF+X6kANpgMDgK5QgHWD9ouKdOAFYvuE24mh0ZT8bvsE9I9/v0j1dbWmPQWXZz673UVr8J3vY3bbhWmJAABDoABrReFBf2NDQNmBIXYGujKLTlmjxFSuTt1N9VQqayYyR/tHlOpb7O1XlkGXml3k6+ibtAaN1sQwEZhYw2twDB+8Z04iAMAcKMD6UObrKf2iRdl1Ic7b2BAoPOi3xoqRrN1cfvvKkLJaVmpPcHh97jPVt7J+QFkGXW3oxqgMlYehOWvc6EtMEoHJY5xqsDmJAABzoABrwqWxm+n51cp+C9Fuwb76po5xa8QYxoeftrY2tysrZEX6zw3ZZ5Yi1VdXTXgVavSJwOQ0HjWYlwMDgGZQgHVg7vGTtZvLH0yOKDstREUZJ/dmQ9a4MQap/VL+lVWxfMOrr/yNsgxqZukXLWW+HmsAaUeUiUBXWOztt/+rFWUN1jsRAGAaFGAdyCw61RnoUnZXiOFeG7yYsqPSGjfGsGpTaWSHhyrrB+wzyPW53Z2d3ynLoK7KsNH1ss+IE4GuM4Y1WONEAIBpUIBdD4/xxBVp3HNuWwb3HmpUVsIL/duxS/ZZo1TfnuCwsgzqbVWNf5/3G2sYaURkiUBXG16Dr4+OKsu8UF0TAQAGQgF2N3OPn6zaVBq6seI9GZrsuozDM3d+tMaQ1kRwd4AyU0zJ754YIl+Gqt8tA9wvY7LR/+Nm5k00AKAfFGB3w5OfMQLNeSL08gMS/uSY1MILVF/D1S8p7DIwmhrM2wQAQA8owC6G078YsYacBH55w8EXBmR2avz3++P1Ck10u5qd8lpOItAEI67BnAQGAA2gALsYjuVjxJpwID84eH174XHli9uV6puxt8c+C5Q/yl8qi6HJ7vqs4WTbsDWkXM4LE4GmWVK74hqsUyIAwFgowC6GY/kYjdofyN9dHvCdOKt863lnLo9tLKL64ovtDHRlFp2yhpTLWSIRaLLK4+6XrsE6JQIAjIUC7FY4lo9Rqv2BfGn4t6+oL+y9PjqqVN+PDvU9mqb64nN9ecPBucdPrFHlZhZNBOK84TV4tH/xh6VpkwgAMBYKsFvhWD5Gqd4H8q9O3U31VNq/78TQqEzp7DO8Ym8/1RdfaHaRr6Nv0hpYriU8EYjhhr/8PPwNcHokAgBMhgLsVjiWj9Gr8YH8p3fIV1h3yMsETqZx9lmdVN+FlYC4tHrcMG9PBOLSLl2DeRY0ALgdCrAr4Vg+xkSND+Tv835TVeMPr74ysVNWAuLzDN0YlVG0/r2KVe+Ue7+8+DA0Zw0vFzKfCOULIi7h82pwwH/es6fRGlgAAC6EAuxKOJaPMVGzA/lzj5+UHL+wIbdO/FV2g33qJtY3DypfH3EJ38o6snr7V/YhtGbHuTe2el100YQ9Eb95/1idr035jogvVKnBb+R8K0F4NdP/37Z++cttlVen7lqjDQDAPVCAXYN9KvPff19TUfmVspdCXJGhG6P/+8++Ve+Uy4j6y+EOV5/dknT85v3qV7Panpmo/VP/OW4WwJW54091r2xrUgaSKGPsrewaa9glMYsm4rUP2l9/9/MHk4s/2QhxCQsPBOxjacHVGQ27ytutYQcA4BIowC6AqQzGVqm+v870LjKi0r0urcHv/KFeOVk3r3ypN7d8rnx9xBe65n+VyeBRhpO4Nqfrv/7bQWvYJTHPS8Sa9wMkAiNw1cbS17O/UYbTvC+9vd8adgAALoEC7AKeN5VBjMCZy2Pv5FY9b3L8i98dsYadq3gru2bR078yY5N5mzKTQ3yhFVVn1mZ/bR9Lb/7+6c3kbjnf9dxEeM6TCIzA4pLTr2ytV4aT+Mq2pvf3tFjDDgDAJVCAXcDzpjKIESgF+K2sI8+ti2nl1rBzFfdmQ2s2f7HW02n/Omtzul5P94739SkzOcQlnJ0az9j7zJui5129/atfvFd1/tKUNeaSm0UTMe+6ncHOzu+Ub434Qk+f/lr+RX010z8/kNbsOLdm69GTbaPWmAMAcA8UYBfA5B5j6+0rQ2ve/XyREbX1qKufaCL/8Rty6156e7/4L/+ztOo4z7zFFThzeUypvvJH6cPTIwPrtlVYg8xV2BOxakud/auJ3BuPkeneRAAAzEMBdg32qczP/73kdGNA2Schrsjxvr5/81TOj6hfZR29NHbTGmpaUHjQ39hARnBZSvXdWPRM9f3oUN+j6fH5T3s7g1sKfNbAci3ziQh/MRg1GFeqHokAAJOhALsS2ffIHkjZJyGuVI0P5POqMFyOE0OjKfnPFEJ79Z1Xj7eF2RNBDcZo1Oz9eQBgIBRgV8LZLYyJGh/IP9k2vOuzBuX7Ii4YXn2Lvf3KMvNWVLYeqAlaA8u1hCeCGoyRqUciAMBkKMCuhLNbGBM1PpB/bza0dnO58n0RxfDid/jEgLKM3U07q4YnblkDy7U8LxHUYFypeiQCAEyGAuxKOLuFMVHvA/lpebWD3ReUr4wmK9XO3vTEyvqlqq94+8qQ9EZrSLmcJRIRXoObzlCDcRF1SgQAGAsF2JVwdgtjot4H8r1fXtxf3qR8ZTTT8Oq7zPOcvhNnd5cHrCHlcl6YiPAa/MIDBGiaOiUCAIyFAuxWOLuFUar9gfypH+6nZHqVb42mKRXO3uik4K3oEt/thceDg9etIeVylpkIqcHK3dHUYFxQp0QAgLFQgN0KZ7cwSk04kJ+aU8W7so21pLbf3uKk+kq1U5ZZ2geTI6s2lVqDSQuWn4jwh4RRg1G/RACAmVCA3QpntzBKTTiQ39E3mV3kU744am+x95nqK0VO6pyyzHLce6ixpmXQGkxasNJEUIPRrn6JAAAzoQC7GM5uYcSacyCfl2ab46Pp8Y8O9dnbWsTVV9T1LdkRJIIajKLG740HANOgALsYzm5hxJpzIP/S2M30/Grl66Nmzk6p1XdjUc/M5TFlsRVZsK++qWPcGkYaEXEiwmvw0q+PQs3UNREAYCAUYHfDSWCMQNPu4+IksMZK9c3Y22NvZfLHO99HVX1FvU92RZOI8Bpc7O1XlkH95PQvAOgEBdjdcBIYI9C0+7hm7vy4LuOwshLQ7c5cHttYpFZf6cPKYpGZnl99aeymNYC0I/pEUINNU+9EAIBpUIBdDyeBcUWa+RjPpo7xgn31yqpAlxpefT861PdoOjbVVyz9oqXM12MNHU2JSSLCNwQ1WEtNSAQAGAUF2PXwOGhckca+xfHDT1tbm9uVtYHuMvzE4+7Dl2JYfcXB7gtpebXWoNGaWCWCGqy35iQCAMyBAqwDNc0De0tOKzstxHCratv2eTuscWMeazeX374ypKwTdIU9wWEHrrkN3RiVQfIwNGeNGN2JYSKowVpqWiIAwBAowJqQWXSqM9Cl7LoQ7V4bvJiyo9IaMUZydepuqqdSWS2Y5Er1XZ/7TPWN3zt4sot8HX2T1nAxgJgnYtEaHNtT9OikpiUCAAyBAqwJc4+frN1c/mByRNl7IS4oI+TebMgaMaZCB3aR/nND9iol1jbE8b07Zs7145GIeN+kjc5I+wUAXaEA6wPvO8Ul5BWOC/Ds9OS36YxafaUMK8vE1r0lp2uaB6whYhhxSgQ12NWanAgA0B4KsFYws8dFZSqjQFKS1sr6AXtlWp/b3RMcVpaJuQQkfom48/2Y8qJmanDySyIAQG8owLrBzB4VmcosCklJNou9/faa5Ez1FQnIPHFNxOzUODXYLZIIANAeCrCGMLPHBZnKLAH3AyeJSvVNye+eGBpVlomT8k+l/INpDQjjiXciqMHJL4kAABOgAOuJdB5pPsqODU3T8JceLYeHobmUrCO8GykhSvOR/mOvQxuLeq6POlR9QzdGU7K8M3d+tIYC/IQDiVi0BstfKouhw5IIADAHCrC28Ewswy345FRT+5g1GmBJthT4ejuDygrE+CltZ8cnvfYKJNV35vKYslj8vDZ4MTXn2NzjJ9YIgGdxIBHhNVj+SA1OlCQCAIyCAqwz92ZDKVlHeDeSaYZujKbtrLo6ddcaB7AM9nk7qmrblDWJMTcZak/Af96zp9Ha8PAcnEkENTgZJBEAYBoUYP1Jzaka7+tTdnioq7evDK3LqOBAfgRM/XA/1VMZuuHQJbimGf5SnB2f9DpfddLzqy+N3bQ2OSyJY4mgBidQEgEABkIBNoLd5QHfibPKbg/1szPQlVl0ytrqEBGFB840NnytrFiMxomh0WR4H2xvZ3BLgc/azLBsHEtE+D3h1OC4SiIAwFgowKYwPHFr084qZf+HOpn313p/1xVre0MUSFjS82s4FRy9Un1T8rvtlabY268s44zZu3wdvdesDQwrxMlEUIOdkUQAgMlQgM2Ch/1oKc8viQeePY2Btk5lVeMy7QkOr89Niuo72H0hvcBHOqLHyUQsWoPvfO/cY9I0lkQAAFCAjYOnQ2smT3uOHw9Dc+kf13EL/Yrs7PxOqb6V9QPKMs54+8pQWm41r3WJIQ4nYtEXZTn5tHDNJBEAAPNQgE1k7vGT9ALfYPcFZe+I7nJ6ZCA155hMSa3tCvFh6of7Mmvkaeov1H9uyN5VxKYziXnBcujGaPauE8GBKWsTQkxxOBHU4OglEQAAdijA5jJz50eZxNy+kpgZKkajzGZ40ZHDyNxRZpDcGLyolfUD9n4iShlWlnHM4pLTNc391maDuOFwIqjBEUsiAAAUKMCmw7TedRZ88mVT+6i1/cBZZM1v/2MdeVlQqb7rc7t7gsPKMo4pE/2yum5rU4EjOJ+IYm+/fchRg5eQRAAALAoFGJ5S09wve0pl34nJZtXxs/u8HdY2g8RxdepuWm719Ehibm1NEpUekpLfPdCXmOr7YHIke9cJHoGeQJxPBDV4CUkEAMDSUIDhPzlQ3UUNTk6l+hYeOGNtJ0gO7s2G0j+uM+2x6o+mx//494v27iHVd2IoMafEn94G7znKvQBJgvOJCK/B10eNvjqDRAAALAcKMKj4u65k7zrBI3+SwdCN0YJPvuT2rWRm7vETz57G4pLT2l8XnVQ3YVYdP5te4OMJcEmI84kIvxghUUdkEiiJAABYPhRgWJyrU3dTPUcNv8gzgT6YHEnbWcVDO13E8MSt1JxjWr46eHZqPGNvj71jvLs7MdV3sPuC/LvU0XvNWumQxDicCDNrMIkAAIgACjAsxdO3Phb4qo6fVXa6GD9bWzrS8mp4VaN7qWnuT8+v0ePg0Z3vx5TqK3+UPqwsFm8fTI5sLzx+oLrLWsXgKpxMhCE1mEQAAEQDBRiWhb/rSlpu9Xhfn7Ibxlgps0OZI3K1szY8DM0VHjizaWeVS1Mzc3lsY9Ez1fejQ32Pph2tvhIKmeVnFp26NxuyViu4FicTUVKrZw0mEQAAMYECDCtg7vGT3WXnCj45xWtgYuj+z1s8exq5d0tjvKd6U7KOtDa3K5s+OZWqIIXB3h8crr6dga5UT+WB6i75B8dag6AXziRCeUeXe2swiQAAiC0UYIiEqR/up+XVShO+fWVI2VXjcnwwOSK9N2VH5fDELWudggEEB6+n5hzbW3I6OYMTXn2Lvf3KMnFSElH6RauUIv+3V62VBQbgQCLCa/Bovwse8UgiAADiBwUYouJhaG53eWDTzqrB7gvK/hvDvTZ4cXvhcc+eRi5gg6aO8XXbKvL2nEyGa6R7gsPrc5+pvodPxP2OzemRAWk+6zIqapoHOLUFcU2EUoNltMuYV5ZJuCQCAMAZKMAQM2SfnZJ1pKq2jQukFRsbAilZ3rK6C8xpYFE6+ibT8mrT86tbm9sdjo//3JBSfaUqKMvE0M5AlzQc6TnSdqwvDxBGnBKRhDWYRAAAOA8FGGLPw9CclL11GYdLv2g18xrpB5MjVbVtsgb2eTs42QsrQuIjU+EtBb6fEtQyHYdn50qjqKrxp+R8aS8DopRhZckolfg//UWZ3pQdlTUtg2QBIiDmiQivwV2dgzJQUz2VYkVlq/wDrvxfYiWJAABIBijAEF/mHj+paR5Yl1Gx67MGvS+TvjZ4Ub6jTNGk/PNEK4ghwxO3dpcH1m2rkNElY6y1uT2a40pvZR1Zvf0rewF4Iyf4xnsnojzPJp0h4D+/91CjTO7Xbi4vPOgPDl63vgBATIlJIpQabHfNjnNvpH9OIgAAdIUCDI4yc+fHMl+PTFw27axqbAjE/EC7TFkOHm6eP5D/588a4ncgX36RzLq2Fx6Xmc0+7zdTP9y3viGAI8iQq2kZ9OxpXLWpVNIkQ7G0okUy1dsZXGLivuNPda9sa1Km++KrWW1SjJWFw5UfLsNeflF2kU9+6csbDmYWnfJ+efHq1F3rPwsgQUSWiLQ/NCtZmJdEAABoDAUYEsnc4yf+b6/KlEXmDTJ72F/eJPMJZYaxTGWK8+tMr8xa7JOY1z5of/3dz6OvwYPdFyoqW9Pzq196e7/Mb5o6xjnHC8mMjM9LYzdPtg2X+Xq2FPgW/PmGQxIKe0bmXZvT9bO3P5PhnZZXa1/+QE1QSoX8KK7VBFdDIgAAYAEKMCQjwcHrMs+QmceqTaVSO3d91lBa0SLd+NrgRaWaLvhObpV6YedPrnk/8OaWz5WFw5WfLD9ffov8LvmN8ntTc6r2eb/p6JvkyVWgDceaBtZknFAyIq7OaNhV3m4tBGAMJAIAwEAowOA+rk7dlYZc5uspPOhfODD/rxvLlNO/876e/c3Pfnvwpbf3r9tWsbCwKP9f+Qnyc7hWDYxCBvwv3zu2+r3W+YCs3v7VL96rOn9pyvoYwDBIBACAaVCAQRPuzYbWbP5iradzfhIz79qcrte3HqXiAgAAAACAQAEGrZCuuyG37qW394u/yjp6aeym9QEAAAAAABgPBRgAAAAAAACMgAIMAAAAAAAARkABBgAAAAAAACOgAAMAAAAAAIARUIABAAAAAADACCjAAAAAAAAAYAQUYAAAAAAAADACCjAAAAAAAAAYAQUYAAAAAAAAjIACDAAAAAAAAAbwj3/8f9GyU+Sj85HFAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\" width=\"640\" height=\"360\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = numChords(n)\r\n  y = f(n)\r\nend","test_suite":"%%\r\nn = 4;\r\ny_correct = 9;\r\nassert(isequal(numChords(n),y_correct))\r\n\r\n%%\r\nn = 7;\r\ny_correct = 127;\r\nassert(isequal(numChords(n),y_correct))\r\n\r\n%%\r\nn = 9;\r\ny_correct = 835;\r\nassert(isequal(numChords(n),y_correct))\r\n\r\n%%\r\nn = 15;\r\ny_correct = 310572;\r\nassert(isequal(numChords(n),y_correct))\r\n\r\n%%\r\nn = 20;\r\ny_correct = 50852019;\r\nassert(isequal(numChords(n),y_correct))\r\n\r\n%%\r\nn = 25;\r\ny_correct = 9043402501;\r\nassert(isequal(numChords(n),y_correct))\r\n\r\n%%\r\nn = 30;\r\ny_correct = 1697385471211;\r\nassert(isequal(numChords(n),y_correct))\r\n\r\n%%\r\nn = 33;\r\ny_correct = 40002464776083;\r\nassert(isequal(numChords(n),y_correct))\r\n\r\n%%\r\nn1 = 5;\r\nyy_correct = 142547559;\r\nassert(isequal(numChords(numChords(n1)),yy_correct))\r\n\r\n%%\r\nfiletext = fileread('numChords.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-26T04:40:18.000Z","updated_at":"2026-01-15T18:19:29.000Z","published_at":"2021-08-28T21:24:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are 9 ways to draw non-intersecting chords between four points on the perimeter of a circle (including no chords at all). In this case there is no way to draw three chords between the four points because two would have to intersect at one of the points or elsewhere. \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 the ways to draw non-intersecting chords between a given number of points.\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=\\\"360\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"640\\\"/\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":54345,"title":"Fill a rectangle with 1x1 and 2x2 tiles","description":"A 3x2 rectangle can be filled with 1x1 and 2x2 tiles in three ways:\r\n\r\nThe colors merely distinguish the sizes of the tiles. A 3x3 rectangle can be filled with 1x1 and 2x2 tiles in five ways:\r\n\r\nWrite a function to count the ways that a 3x rectangle can be filled. ","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: 468.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 234.15px; transform-origin: 407px 234.15px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201.883px 7.50833px; transform-origin: 201.883px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA 3x2 rectangle can be filled with 1x1 and 2x2 tiles in three ways:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 124.65px; 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 62.325px; text-align: left; transform-origin: 384px 62.325px; 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: 264px;height: 119px\" src=\"data:image/png;base64,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\" alt=\"Tilings of a 3x2 rectangle\" data-image-state=\"image-loaded\" width=\"264\" height=\"119\"\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: 354.742px 7.50833px; transform-origin: 354.742px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe colors merely distinguish the sizes of the tiles. A 3x3 rectangle can be filled with 1x1 and 2x2 tiles in five ways:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 244.65px; 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 122.325px; text-align: left; transform-origin: 384px 122.325px; 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: 395px;height: 239px\" src=\"data:image/png;base64,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\" alt=\"Tilings of a 3x3 rectangle\" data-image-state=\"image-loaded\" width=\"395\" height=\"239\"\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: 133.658px 7.50833px; transform-origin: 133.658px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to count the ways that a 3x\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: 73.9083px 7.50833px; transform-origin: 73.9083px 7.50833px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e rectangle can be filled. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = fillRectangle(n)\r\n  y = 2*n-1;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct = 1;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct = 3;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct = 5;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = 5;\r\ny_correct = 21;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = 8;\r\ny_correct = 171;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = 13;\r\ny_correct = 5461;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = 21;\r\ny_correct = 1398101;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = 34;\r\ny_correct = 11453246123;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = 50;\r\ny_correct = 750599937895083;\r\nassert(isequal(fillRectangle(n),y_correct))\r\n\r\n%%\r\nn = randi(30);\r\ny1 = fillRectangle(n);\r\ny2 = fillRectangle(n+1);\r\nassert(isequal(log2(y1+y2),n+1))\r\n\r\n%%\r\nfiletext = fileread('fillRectangle.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext, 'read'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-04-23T00:39:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2022-04-22T04:50:46.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-04-22T04:33:33.000Z","updated_at":"2026-01-15T18:25:04.000Z","published_at":"2022-04-22T04:47:56.000Z","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 3x2 rectangle can be filled with 1x1 and 2x2 tiles in three ways:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"119\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"264\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Tilings of a 3x2 rectangle\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe colors merely distinguish the sizes of the tiles. A 3x3 rectangle can be filled with 1x1 and 2x2 tiles in five ways:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"239\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"395\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Tilings of a 3x3 rectangle\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to count the ways that a 3x\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 rectangle can be filled. 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially 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