{"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":"5f45c36e-b8cb-52f0-aacd-d0e1e075275a","task_key":"intermediate~5falgebra--test--5f45c36e-b8cb-52f0-aacd-d0e1e075275a","task_revision_id":"1","upstream_id":"","short_description":"Let $\\tau = \\frac{1 + \\sqrt{5}}{2}.$ Find","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $\\\\tau = \\\\frac{1 + \\\\sqrt{5}}{2}.$  Find\\n\\\\[\\\\sum_{n = 0}^\\\\infty \\\\frac{\\\\lfloor \\\\tau^n \\\\rceil}{2^n}.\\\\]Note: For a real number $x,$ $\\\\lfloor x \\\\rceil$ denotes the integer closest to $x.$\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}