{"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":"a450231c-6472-5f4e-9bed-6208e8a06f8b","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--1613","task_revision_id":"3","upstream_id":"1613","short_description":"Determine all positive integers $n$ satisfying the following condition: for…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Numerical\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"Determine all positive integers $n$ satisfying the following condition: for every monic polynomial $P$ of degree at most $n$ with integer coefficients, there exists a positive integer $k \\\\leq n$, and $k+1$ distinct integers $x_{1}, x_{2}, \\\\ldots, x_{k+1}$ such that\\n\\n\\n\\n$$\\n\\nP\\\\left(x_{1}\\\\right)+P\\\\left(x_{2}\\\\right)+\\\\cdots+P\\\\left(x_{k}\\\\right)=P\\\\left(x_{k+1}\\\\right) .\\n\\n$$\\n\\n\\nNote. A polynomial is monic if the coefficient of the highest power is one.\",\"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":[]}