{"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":"94c73060-3574-529f-befe-4bf69b6df2cd","task_key":"precalculus--test--94c73060-3574-529f-befe-4bf69b6df2cd","task_revision_id":"1","upstream_id":"","short_description":"The planes defined by","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"The planes defined by\\n\\\\begin{align*}\\n-x + cy + bz &= 0, \\\\\\\\\\ncx - y + az &= 0, \\\\\\\\\\nbx + ay - z &= 0\\n\\\\end{align*}all contain the same line.  Find all possible values of\\n\\\\[a^2 + b^2 + c^2 + 2abc.\\\\]Enter all the possible values, 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":[]}