{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"928d6017-f955-5856-a907-2365471acc63","task_key":"precalculus--test--928d6017-f955-5856-a907-2365471acc63","task_revision_id":"1","upstream_id":"","short_description":"Find all positive integer values of $n$ that satisfy the equation","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Find all positive integer values of $n$ that satisfy the equation\\n\\\\[\\n  \\\\cos \\\\Bigl( \\\\frac{\\\\pi}{n} \\\\Bigr) \\\\cos \\\\Bigl( \\\\frac{2\\\\pi}{n} \\\\Bigr)   \\n     \\\\cos \\\\Bigl( \\\\frac{4\\\\pi}{n} \\\\Bigr) \\\\cos \\\\Bigl( \\\\frac{8\\\\pi}{n} \\\\Bigr)\\n     \\\\cos \\\\Bigl( \\\\frac{16\\\\pi}{n} \\\\Bigr)\\n    = \\\\frac{1}{32}.\\n\\\\]Enter all the solutions, separated by commas.\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}