{"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":"47b116ca-62f0-57ea-8b8b-e2562344fc7b","task_key":"test--47b116ca-62f0-57ea-8b8b-e2562344fc7b","task_revision_id":"1","upstream_id":"","short_description":"On a board the following six vectors are written: \\((1,0,0), \\quad(-1,0,0),…","config":"","split":"test","body":"{\"problem\":\"On a board the following six vectors are written: \\\\((1,0,0), \\\\quad(-1,0,0), \\\\quad(0,1,0), \\\\quad(0,-1,0), \\\\quad(0,0,1), \\\\quad(0,0,-1)\\\\). Given two vectors \\\\(v\\\\) and \\\\(w\\\\) on the board, a move consists of erasing \\\\(v\\\\) and \\\\(w\\\\) and replacing them with \\\\(\\\\frac{1}{\\\\sqrt{2}}(v+w)\\\\) and \\\\(\\\\frac{1}{\\\\sqrt{2}}(v-w)\\\\). After some number of moves, the sum of the six vectors on the board is \\\\(u\\\\). Find, with proof, the maximum possible length of \\\\(u\\\\).\"}","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":[]}