{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"olympiadbench","formal_name":"OlympiadBench","introduction":"数学と物理のオリンピック水準の問題で、科学的推論を評価するベンチマークです。公式紹介では英語・中国語の8,476問を収録し、テキストのみと画像付きの設定を区別します。\n\nOlympiadBench 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"},"task_id":"63c97aa8-eef1-509a-89fd-6cee3c85adac","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--2177","task_revision_id":"1","upstream_id":"2177","short_description":"Find the smallest positive integer $k$ for which there exist a colouring of the…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Numerical\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"Find the smallest positive integer $k$ for which there exist a colouring of the positive integers $\\\\mathbb{Z}_{>0}$ with $k$ colours and a function $f: \\\\mathbb{Z}_{>0} \\\\rightarrow \\\\mathbb{Z}_{>0}$ with the following two properties:\\n\\n(i) For all positive integers $m, n$ of the same colour, $f(m+n)=f(m)+f(n)$.\\n\\n(ii) There are positive integers $m, n$ such that $f(m+n) \\\\neq f(m)+f(n)$.\\n\\nIn a colouring of $\\\\mathbb{Z}_{>0}$ with $k$ colours, every integer is coloured in exactly one of the $k$ colours. In both (i) and (ii) the positive integers $m, n$ are not necessarily different.\",\"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":[]}