{"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":"8082a1f1-0d87-5800-9de9-2f73261b05d4","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--1782","task_revision_id":"1","upstream_id":"1782","short_description":"Let $n \\geqslant 3$ be an integer. An integer $m \\geqslant n+1$ is called…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Expression\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"Let $n \\\\geqslant 3$ be an integer. An integer $m \\\\geqslant n+1$ is called $n$-colourful if, given infinitely many marbles in each of $n$ colours $C_{1}, C_{2}, \\\\ldots, C_{n}$, it is possible to place $m$ of them around a circle so that in any group of $n+1$ consecutive marbles there is at least one marble of colour $C_{i}$ for each $i=1, \\\\ldots, n$.\\n\\nProve that there are only finitely many positive integers which are not $n$-colourful. Find the largest among them.\",\"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":[]}