{"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":"62975369-4edd-5550-b20f-6649076ef35e","task_key":"test--62975369-4edd-5550-b20f-6649076ef35e","task_revision_id":"1","upstream_id":"","short_description":"There is a population $P$ of $10000$ bacteria, some of which are friends…","config":"","split":"test","body":"{\"problem\":\"There is a population $P$ of $10000$ bacteria, some of which are friends (friendship is mutual),\\nso that each bacterion has at least one friend and if we wish to assign to each bacterion a coloured\\nmembrane so that no two friends have the same colour, then there is a way to do it with $2021$\\ncolours, but not with $2020$ or less.\\nTwo friends $A$ and $B$ can decide to merge in which case they become a single bacterion whose\\nfriends are precisely the union of friends of $A$ and $B$. (Merging is not allowed if $A$ and $B$ are\\nnot friends.) It turns out that no matter how we perform one merge or two consecutive merges,\\nin the resulting population it would be possible to assign $2020$ colours or less so that no two\\nfriends have the same colour. Is it true that in any such population $P$ every bacterium has at\\nleast $2021$ friends?\"}","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":[]}