{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"olympiadbench","formal_name":"OlympiadBench","introduction":"OlympiadBench evaluates scientific reasoning on Olympiad-level mathematics and physics problems. Its official description lists 8,476 English and Chinese problems with separate text-only and multimodal settings.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/OpenBMB/OlympiadBench","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"9a9418d8-258a-5c80-ba4b-a65f3e8fb960","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--1620","task_revision_id":"3","upstream_id":"1620","short_description":"Let $n \\geqslant 2$ be an integer, and let $f$ be a $4 n$-variable polynomial…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Expression\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"Let $n \\\\geqslant 2$ be an integer, and let $f$ be a $4 n$-variable polynomial with real coefficients. Assume that, for any $2 n$ points $\\\\left(x_{1}, y_{1}\\\\right), \\\\ldots,\\\\left(x_{2 n}, y_{2 n}\\\\right)$ in the plane, $f\\\\left(x_{1}, y_{1}, \\\\ldots, x_{2 n}, y_{2 n}\\\\right)=0$ if and only if the points form the vertices of a regular $2 n$-gon in some order, or are all equal.\\n\\n\\n\\nDetermine the smallest possible degree of $f$.\",\"question_type\":\"Open-ended\",\"subject\":\"Math\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/OpenBMB/OlympiadBench","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}