{"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":"65282ae9-5b1f-5fbe-8a48-19a4862b095c","task_key":"test--65282ae9-5b1f-5fbe-8a48-19a4862b095c","task_revision_id":"1","upstream_id":"","short_description":"Let \\(n \\geq 3\\) be a fixed integer. The number 1 is written \\(n\\) times on a…","config":"","split":"test","body":"{\"problem\":\"Let \\\\(n \\\\geq 3\\\\) be a fixed integer. The number 1 is written \\\\(n\\\\) times on a blackboard. Below the blackboard, there are two buckets that are initially empty. A move consists of erasing two of the numbers \\\\(a\\\\) and \\\\(b\\\\), replacing them with the numbers 1 and \\\\(a+b\\\\), then adding one stone to the first bucket and \\\\(\\\\operatorname{gcd}(a, b)\\\\) stones to the second bucket. After some finite number of moves, there are \\\\(s\\\\) stones in the first bucket and \\\\(t\\\\) stones in the second bucket, where \\\\(s\\\\) and \\\\(t\\\\) are positive integers. Find all possible values of the ratio \\\\(\\\\frac{t}{s}\\\\).\"}","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":[]}