{"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":"77d15894-d527-54c8-9a42-cc10a24b3dfe","task_key":"test--77d15894-d527-54c8-9a42-cc10a24b3dfe","task_revision_id":"1","upstream_id":"","short_description":"All subscripts in this problem are to be considered modulo 6 , that means for…","config":"","split":"test","body":"{\"problem\":\"All subscripts in this problem are to be considered modulo 6 , that means for example that $\\\\omega_{7}$ is the same as $\\\\omega_{1}$. Let $\\\\omega_{1}, \\\\ldots \\\\omega_{6}$ be circles of radius $r$, whose centers lie on a regular hexagon of side length 1 . Let $P_{i}$ be the intersection of $\\\\omega_{i}$ and $\\\\omega_{i+1}$ that lies further from the center of the hexagon, for $i=1, \\\\ldots 6$. Let $Q_{i}, i=1 \\\\ldots 6$, lie on $\\\\omega_{i}$ such that $Q_{i}, P_{i}, Q_{i+1}$ are colinear. Find the number of possible values of $r$.\"}","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":[]}