{"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":"1e2c0855-2df7-5adc-acd8-ab4406aff151","task_key":"test--1e2c0855-2df7-5adc-acd8-ab4406aff151","task_revision_id":"1","upstream_id":"","short_description":"Let $n$ be the product of the first 10 primes, and let $$S=\\sum_{x y \\mid n}…","config":"","split":"test","body":"{\"problem\":\"Let $n$ be the product of the first 10 primes, and let $$S=\\\\sum_{x y \\\\mid n} \\\\varphi(x) \\\\cdot y$$ where $\\\\varphi(x)$ denotes the number of positive integers less than or equal to $x$ that are relatively prime to $x$, and the sum is taken over ordered pairs $(x, y)$ of positive integers for which $x y$ divides $n$. Compute $\\\\frac{S}{n}$.\"}","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":[]}