{"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":"654425b2-2c8d-56ab-a79a-d959c29d9737","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--2300","task_revision_id":"1","upstream_id":"2300","short_description":"The numbers $a_{1}, a_{2}, a_{3}, \\ldots$ form an arithmetic sequence with…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Numerical\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"The numbers $a_{1}, a_{2}, a_{3}, \\\\ldots$ form an arithmetic sequence with $a_{1} \\\\neq a_{2}$. The three numbers $a_{1}, a_{2}, a_{6}$ form a geometric sequence in that order. Determine all possible positive integers $k$ for which the three numbers $a_{1}, a_{4}, a_{k}$ also form a geometric sequence in that order.\\n\\n(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3, 5, 7, 9 are the first four terms of an arithmetic sequence.\\n\\nA geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a non-zero constant. For example, $3,6,12$ is a geometric sequence with three terms.)\",\"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":[]}