{"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":"c10c2865-34ea-5df3-9570-e8354a9dd363","task_key":"test--c10c2865-34ea-5df3-9570-e8354a9dd363","task_revision_id":"1","upstream_id":"","short_description":"For a point $P = (a, a^2)$ in the coordinate plane, let $\\ell(P)$ denote the…","config":"","split":"test","body":"{\"problem\":\"For a point $P = (a, a^2)$ in the coordinate plane, let $\\\\ell(P)$ denote the line passing through $P$ with slope $2a$ . Consider the set of triangles with vertices of the form $P_1 = (a_1,  a_1^2)$ , $P_2 = (a_2, a_2^2)$ , $P_3 = (a_3, a_3^2)$ , such that the intersections of the lines $\\\\ell(P_1)$ , $\\\\ell(P_2)$ , $\\\\ell(P_3)$ form an equilateral triangle $\\\\triangle$ . Find the locus of the center of $\\\\triangle$ as $P_1P_2P_3$ ranges over all such triangles.\"}","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":[]}