{"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":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"81fa79b7-cb0b-59d0-9b16-88663a6589fa","task_key":"test--81fa79b7-cb0b-59d0-9b16-88663a6589fa","task_revision_id":"3","upstream_id":"","short_description":"Let $a, b, c, p, q, r$ be positive integers with $p, q, r \\ge 2$. Denote","config":"","split":"test","body":"{\"problem\":\"Let $a, b, c, p, q, r$ be positive integers with $p, q, r \\\\ge 2$. Denote\\n\\\\[Q=\\\\{(x, y, z)\\\\in \\\\mathbb{Z}^3 : 0 \\\\le x \\\\le a, 0 \\\\le y \\\\le b , 0 \\\\le z \\\\le c \\\\}. \\\\]\\nInitially, some pieces are put on the each point in $Q$, with a total of $M$ pieces. Then, one can perform the following three types of operations repeatedly:\\n(1) Remove $p$ pieces on $(x, y, z)$ and place a piece on $(x-1, y, z)$ ;\\n(2) Remove $q$ pieces on $(x, y, z)$ and place a piece on $(x, y-1, z)$ ;\\n(3) Remove $r$ pieces on $(x, y, z)$ and place a piece on $(x, y, z-1)$.\\n\\nFind the smallest positive integer $M$ such that one can always perform a sequence of operations, making a piece placed on $(0,0,0)$, no matter how the pieces are distributed initially.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}