{"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":"6149c3ee-f2a0-5039-9148-8cc372d0debf","task_key":"precalculus--test--6149c3ee-f2a0-5039-9148-8cc372d0debf","task_revision_id":"1","upstream_id":"","short_description":"For a point $P,$ let $d_1,$ $d_2$ and $d_3$ represents the distances from $P$ to…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"For a point $P,$ let $d_1,$ $d_2$ and $d_3$ represents the distances from $P$ to the planes $x - z = 0,$ $x - 2y + z = 0,$ and $x + y + z = 0.$  Let $S$ be the set of points $P$ such that\\n\\\\[d_1^2 + d_2^2 + d_3^2 = 36.\\\\]Find the region of the volume enclosed by $S.$\",\"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":[]}