{"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":"5c56bd0e-ca08-5f45-9a87-a82c554b541d","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--2127","task_revision_id":"1","upstream_id":"2127","short_description":"Let $n$ and $k$ be fixed positive integers of the same parity, $k \\geq n$. We…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Expression\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"Let $n$ and $k$ be fixed positive integers of the same parity, $k \\\\geq n$. We are given $2 n$ lamps numbered 1 through $2 n$; each of them can be on or off. At the beginning all lamps are off. We consider sequences of $k$ steps. At each step one of the lamps is switched (from off to on or from on to off).\\n\\nLet $N$ be the number of $k$-step sequences ending in the state: lamps $1, \\\\ldots, n$ on, lamps $n+1, \\\\ldots, 2 n$ off.\\n\\nLet $M$ be the number of $k$-step sequences leading to the same state and not touching lamps $n+1, \\\\ldots, 2 n$ at all.\\n\\nFind the ratio $N / M$.\",\"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":[]}