{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"olympiadbench","formal_name":"OlympiadBench","introduction":"OlympiadBench 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","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"adacba10-89d7-5c30-9798-ace5d9175922","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--1810","task_revision_id":"3","upstream_id":"1810","short_description":"An integer $n \\geqslant 3$ is given. We call an $n$-tuple of real numbers…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Expression\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"An integer $n \\\\geqslant 3$ is given. We call an $n$-tuple of real numbers $\\\\left(x_{1}, x_{2}, \\\\ldots, x_{n}\\\\right)$ Shiny if for each permutation $y_{1}, y_{2}, \\\\ldots, y_{n}$ of these numbers we have\\n\\n$$\\n\\\\sum_{i=1}^{n-1} y_{i} y_{i+1}=y_{1} y_{2}+y_{2} y_{3}+y_{3} y_{4}+\\\\cdots+y_{n-1} y_{n} \\\\geqslant-1\\n$$\\n\\nFind the largest constant $K=K(n)$ such that\\n\\n$$\\n\\\\sum_{1 \\\\leqslant i<j \\\\leqslant n} x_{i} x_{j} \\\\geqslant K\\n$$\\n\\nholds for every Shiny $n$-tuple $\\\\left(x_{1}, x_{2}, \\\\ldots, x_{n}\\\\right)$.\",\"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":[]}