{"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":"57b0cf75-d26e-5f8d-8c0b-7de2d3802c64","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--1968","task_revision_id":"1","upstream_id":"1968","short_description":"For a sequence $x_{1}, x_{2}, \\ldots, x_{n}$ of real numbers, we define its…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Numerical\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"For a sequence $x_{1}, x_{2}, \\\\ldots, x_{n}$ of real numbers, we define its price as\\n\\n$$\\n\\\\max _{1 \\\\leqslant i \\\\leqslant n}\\\\left|x_{1}+\\\\cdots+x_{i}\\\\right|\\n$$\\n\\nGiven $n$ real numbers, Dave and George want to arrange them into a sequence with a low price. Diligent Dave checks all possible ways and finds the minimum possible price $D$. Greedy George, on the other hand, chooses $x_{1}$ such that $\\\\left|x_{1}\\\\right|$ is as small as possible; among the remaining numbers, he chooses $x_{2}$ such that $\\\\left|x_{1}+x_{2}\\\\right|$ is as small as possible, and so on. Thus, in the $i^{\\\\text {th }}$ step he chooses $x_{i}$ among the remaining numbers so as to minimise the value of $\\\\left|x_{1}+x_{2}+\\\\cdots+x_{i}\\\\right|$. In each step, if several numbers provide the same value, George chooses one at random. Finally he gets a sequence with price $G$.\\n\\nFind the least possible constant $c$ such that for every positive integer $n$, for every collection of $n$ real numbers, and for every possible sequence that George might obtain, the resulting values satisfy the inequality $G \\\\leqslant c D$.\",\"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":[]}