{"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":"51e0c1a9-47cd-5601-aab6-11ffd4a60d3a","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--2012","task_revision_id":"1","upstream_id":"2012","short_description":"Let $\\mathbb{Z}_{\\geqslant 0}$ be the set of non-negative integers, and let $f:…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Numerical\",\"is_multiple_answer\":true,\"language\":\"English\",\"question\":\"Let $\\\\mathbb{Z}_{\\\\geqslant 0}$ be the set of non-negative integers, and let $f: \\\\mathbb{Z}_{\\\\geqslant 0} \\\\times \\\\mathbb{Z}_{\\\\geqslant 0} \\\\rightarrow \\\\mathbb{Z}_{\\\\geqslant 0}$ be a bijection such that whenever $f\\\\left(x_{1}, y_{1}\\\\right)>f\\\\left(x_{2}, y_{2}\\\\right)$, we have $f\\\\left(x_{1}+1, y_{1}\\\\right)>f\\\\left(x_{2}+1, y_{2}\\\\right)$ and $f\\\\left(x_{1}, y_{1}+1\\\\right)>f\\\\left(x_{2}, y_{2}+1\\\\right)$.\\n\\nLet $N$ be the number of pairs of integers $(x, y)$, with $0 \\\\leqslant x, y<100$, such that $f(x, y)$ is odd. Find the smallest and largest possible value of $N$.\",\"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":[]}