{"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":"e90976e7-626e-5d60-90d3-fb9b040befc6","task_key":"test--e90976e7-626e-5d60-90d3-fb9b040befc6","task_revision_id":"1","upstream_id":"","short_description":"Let $P_1,P_2,\\dots,P_n$ be $n$ distinct points over a line in the plane…","config":"","split":"test","body":"{\"problem\":\"Let $P_1,P_2,\\\\dots,P_n$ be $n$ distinct points over a line in the plane ($n\\\\geq2$). Consider all the circumferences with diameters $P_iP_j$ ($1\\\\leq{i,j}\\\\leq{n}$) and they are painted with $k$ given colors. Lets call this configuration a ($n,k$)-cloud.\\n\\nFor each positive integer $k$, find all the positive integers $n$ such that every possible ($n,k$)-cloud has two mutually exterior tangent circumferences of the same color.\"}","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":[]}