{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"数学オリンピック水準の問題を通じて、数学的推論能力を評価するベンチマークです。公式データは4,428問を収録し、分野や難易度の情報を伴います。\n\nOmni-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"},"task_id":"3f5d9e33-0756-5fa0-a621-5dc5629414be","task_key":"test--3f5d9e33-0756-5fa0-a621-5dc5629414be","task_revision_id":"2","upstream_id":"","short_description":"Two rational numbers $\\frac{m}{n}$ and $\\frac{n}{m}$ are written on a…","config":"","split":"test","body":"{\"problem\":\"Two rational numbers $\\\\frac{m}{n}$ and $\\\\frac{n}{m}$ are written on a blackboard, where $m$ and $n$ are relatively prime positive integers. At any point, Evan may pick two of the numbers $x$ and $y$ written on the board and write either their arithmetic mean $\\\\frac{x+y}{2}$ or their harmonic mean $\\\\frac{2xy}{x+y}$ on the board as well. Find all pairs $(m,n)$ such that Evan can write $1$ on the board in finitely many steps.\"}","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":[]}