{"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":"ff7cdbc4-9ca0-570f-8a11-fba02c61ad51","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--1873","task_revision_id":"3","upstream_id":"1873","short_description":"Let $\\mathcal{A}$ denote the set of all polynomials in three variables $x, y, z$…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Numerical\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"Let $\\\\mathcal{A}$ denote the set of all polynomials in three variables $x, y, z$ with integer coefficients. Let $\\\\mathcal{B}$ denote the subset of $\\\\mathcal{A}$ formed by all polynomials which can be expressed as\\n\\n$$\\n(x+y+z) P(x, y, z)+(x y+y z+z x) Q(x, y, z)+x y z R(x, y, z)\\n$$\\n\\nwith $P, Q, R \\\\in \\\\mathcal{A}$. Find the smallest non-negative integer $n$ such that $x^{i} y^{j} z^{k} \\\\in \\\\mathcal{B}$ for all nonnegative integers $i, j, k$ satisfying $i+j+k \\\\geqslant n$.\",\"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":[]}