{"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":"9d67ea2e-c76e-5415-a153-4c60c368804f","task_key":"test--9d67ea2e-c76e-5415-a153-4c60c368804f","task_revision_id":"1","upstream_id":"","short_description":"Consider a regular 2n-gon $P$ , $A_1,A_2,\\cdots ,A_{2n}$ in the plane ,where $n$…","config":"","split":"test","body":"{\"problem\":\"Consider a regular 2n-gon $P$ , $A_1,A_2,\\\\cdots ,A_{2n}$ in the plane ,where $n$ is a positive integer . We say that a point $S$ on one of the sides of $P$ can be seen from a point $E$ that is external to $P$ , if the line segment $SE$ contains no other points that lie  on the sides of $P$ except $S$ .We color the sides of $P$ in 3 different colors (ignore the vertices of $P$ ,we consider them colorless), such that every side is colored in exactly one color, and each color is used at least once . Moreover  ,from every point in the plane external to $P$ , points of most 2  different colors on $P$ can be seen .Find the number of distinct such colorings of $P$ (two colorings are considered distinct if at least one of sides is colored differently).\"}","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":[]}