{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-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":"27653039-612d-5787-965b-6ea213f91950","task_key":"test--27653039-612d-5787-965b-6ea213f91950","task_revision_id":"1","upstream_id":"","short_description":"Let $n$ be a positive integer, $n \\ge 2$, and put $\\theta = 2 \\pi / n$. Define…","config":"","split":"test","body":"{\"problem\":\"Let $n$ be a positive integer, $n \\\\ge 2$, and put $\\\\theta = 2 \\\\pi / n$. Define points $P_k = (k,0)$ in the $xy$-plane, for $k = 1, 2 , \\\\dots, n$. Let $R_k$ be the map that rotates the plane counterclockwise by the angle $\\\\theta$ about the point $P_k$. Let $R$ denote the map obtained by applying, in order, $R_1$, then $R_2, \\\\dots$, then $R_n$. For an arbitrary point $(x,y)$, find, and simplify, the coordinates of $R(x,y)$.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}