{"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":"26f8d592-5838-569c-9184-826f4748f206","task_key":"test--26f8d592-5838-569c-9184-826f4748f206","task_revision_id":"1","upstream_id":"","short_description":"A ten-level 2-tree is drawn in the plane: a vertex $A_{1}$ is marked, it is…","config":"","split":"test","body":"{\"problem\":\"A ten-level 2-tree is drawn in the plane: a vertex $A_{1}$ is marked, it is connected by segments with two vertices $B_{1}$ and $B_{2}$, each of $B_{1}$ and $B_{2}$ is connected by segments with two of the four vertices $C_{1}, C_{2}, C_{3}, C_{4}$ (each $C_{i}$ is connected with one $B_{j}$ exactly); and so on, up to 512 vertices $J_{1}, \\\\ldots, J_{512}$. Each of the vertices $J_{1}, \\\\ldots, J_{512}$ is coloured blue or golden. Consider all permutations $f$ of the vertices of this tree, such that (i) if $X$ and $Y$ are connected with a segment, then so are $f(X)$ and $f(Y)$, and (ii) if $X$ is coloured, then $f(X)$ has the same colour. Find the maximum $M$ such that there are at least $M$ permutations with these properties, regardless of the colouring.\"}","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":[]}