{"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":"e6284b57-fb45-5af2-a7f8-4f6804681c1a","task_key":"test--e6284b57-fb45-5af2-a7f8-4f6804681c1a","task_revision_id":"1","upstream_id":"","short_description":"Let $A B C$ be a triangle. The following diagram contains points $P_{1}, P_{2},…","config":"","split":"test","body":"{\"problem\":\"Let $A B C$ be a triangle. The following diagram contains points $P_{1}, P_{2}, \\\\ldots, P_{7}$, which are the following triangle centers of triangle $A B C$ in some order: - the incenter $I$; - the circumcenter $O$; - the orthocenter $H$; - the symmedian point $L$, which is the intersections of the reflections of $B$-median and $C$-median across angle bisectors of $\\\\angle A B C$ and $\\\\angle A C B$, respectively; - the Gergonne point $G$, which is the intersection of lines from $B$ and $C$ to the tangency points of the incircle with $\\\\overline{A C}$ and $\\\\overline{A B}$, respectively; - the Nagel point $N$, which is the intersection of line from $B$ to the tangency point between $B$ excircle and $\\\\overline{A C}$, and line from $C$ to the tangency point between $C$-excircle and $\\\\overline{A B}$; and - the Kosnita point $K$, which is the intersection of lines from $B$ and $C$ to the circumcenters of triangles $A O C$ and $A O B$, respectively. Compute which triangle centers $\\\\{I, O, H, L, G, N, K\\\\}$ corresponds to $P_{k}$ for $k \\\\in\\\\{1,2,3,4,5,6,7\\\\}$.\"}","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":[]}