{"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":"a444368a-7983-576b-bbfe-6782b2beffcb","task_key":"precalculus--test--a444368a-7983-576b-bbfe-6782b2beffcb","task_revision_id":"1","upstream_id":"","short_description":"A sequence of complex numbers $z_0,z_1,z_2,\\ldots$ is defined by the rule \\[","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"A sequence of complex numbers $z_0,z_1,z_2,\\\\ldots$ is defined by the rule \\\\[\\nz_{n+1}=\\\\frac{\\\\ iz_n\\\\ }{\\\\overline{z}_n},\\n\\\\]where $\\\\overline{z}_n$ is the complex conjugate of $z_n$ and $i^2=-1$. Suppose that $|z_0|=1$ and $z_{2005}=1$. How many possible values are there for $z_0$?\",\"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":[]}