{"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":"3ee4533f-ac0e-58c3-92c5-5ad3e4bbbc1d","task_key":"test--3ee4533f-ac0e-58c3-92c5-5ad3e4bbbc1d","task_revision_id":"1","upstream_id":"","short_description":"Two rational numbers \\(\\tfrac{m}{n}\\) and \\(\\tfrac{n}{m}\\) are written on a…","config":"","split":"test","body":"{\"problem\":\"Two rational numbers \\\\(\\\\tfrac{m}{n}\\\\) and \\\\(\\\\tfrac{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 \\\\(\\\\tfrac{x+y}{2}\\\\) or their harmonic mean \\\\(\\\\tfrac{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":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}