{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"571ff1f5-9b48-5a44-960e-83e1e19062cf","task_key":"test--571ff1f5-9b48-5a44-960e-83e1e19062cf","task_revision_id":"1","upstream_id":"","short_description":"(a) Can 1000 queens be placed on a $2017 \\times 2017$ chessboard such that every…","config":"","split":"test","body":"{\"problem\":\"(a) Can 1000 queens be placed on a $2017 \\\\times 2017$ chessboard such that every square is attacked by some queen? A square is attacked by a queen if it lies in the same row, column, or diagonal as the queen. (b) A $2017 \\\\times 2017$ grid of squares originally contains a 0 in each square. At any step, Kelvin the Frog chooses two adjacent squares (two squares are adjacent if they share a side) and increments the numbers in both of them by 1. Can Kelvin make every square contain a different power of 2? (c) A tournament consists of single games between every pair of players, where each game has a winner and loser with no ties. A set of people is dominated if there exists a player who beats all of them. Does there exist a tournament in which every set of 2017 people is dominated? (d) Every cell of a $19 \\\\times 19$ grid is colored either red, yellow, green, or blue. Does there necessarily exist a rectangle whose sides are parallel to the grid, all of whose vertices are the same color? (e) Does there exist a $c \\\\in \\\\mathbb{R}^{+}$such that $\\\\max (|A \\\\cdot A|,|A+A|) \\\\geq c|A| \\\\log ^{2}|A|$ for all finite sets $A \\\\subset \\\\mathbb{Z}$? (f) Can the set $\\\\{1,2, \\\\ldots, 1093\\\\}$ be partitioned into 7 subsets such that each subset is sum-free (i.e. no subset contains $a, b, c$ with $a+b=c)$?\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}