{"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":"d8afe04e-5f3e-5764-bb01-9d84b35ea862","task_key":"test--d8afe04e-5f3e-5764-bb01-9d84b35ea862","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbb{Q}$ be the set of rational numbers. A function $f: \\mathbb{Q} \\to…","config":"","split":"test","body":"{\"problem\":\"Let $\\\\mathbb{Q}$ be the set of rational numbers. A function $f: \\\\mathbb{Q} \\\\to \\\\mathbb{Q}$ is called aquaesulian if the following property holds: for every $x,y \\\\in \\\\mathbb{Q}$,\\n\\\\[ f(x+f(y)) = f(x) + y \\\\quad \\\\text{or} \\\\quad f(f(x)+y) = x + f(y). \\\\]\\nShow that there exists an integer $c$ such that for any aquaesulian function $f$ there are at most $c$ different rational numbers of the form $f(r) + f(-r)$ for some rational number $r$, and find the smallest possible value of $c$.\"}","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":[]}