{"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":"fe7ea94e-744e-52ad-b74f-2894c7531637","task_key":"test--fe7ea94e-744e-52ad-b74f-2894c7531637","task_revision_id":"1","upstream_id":"","short_description":"Let $n\\geq 3$ be a fixed integer. Each side and each diagonal of a regular…","config":"","split":"test","body":"{\"problem\":\"Let $n\\\\geq 3$ be a fixed integer. Each side and each diagonal of a regular $n$-gon is labelled with a number from the set $\\\\left\\\\{1;\\\\;2;\\\\;...;\\\\;r\\\\right\\\\}$ in a way such that the following two conditions are fulfilled:\\n\\n[b]1.[/b] Each number from the set $\\\\left\\\\{1;\\\\;2;\\\\;...;\\\\;r\\\\right\\\\}$ occurs at least once as a label.\\n\\n[b]2.[/b] In each triangle formed by three vertices of the $n$-gon, two of the sides are labelled with the same number, and this number is greater than the label of the third side.\\n\\n[b](a)[/b] Find the maximal $r$ for which such a labelling is possible.\\n\\n[b](b)[/b] [i]Harder version (IMO Shortlist 2005):[/i] For this maximal value of $r$, how many such labellings are there?\\n\\n[hide=\\\"Easier version (5th German TST 2006) - contains answer to the harder version\\\"]\\n[i]Easier version (5th German TST 2006):[/i] Show that, for this maximal value of $r$, there are exactly $\\\\frac{n!\\\\left(n-1\\\\right)!}{2^{n-1}}$ possible labellings.[/hide]\\n\\n[i]\"}","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":[]}