{"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":"f5f860eb-2f0f-5e5e-a2a3-acfffa23b1c0","task_key":"test--f5f860eb-2f0f-5e5e-a2a3-acfffa23b1c0","task_revision_id":"1","upstream_id":"","short_description":"Lucy starts by writing $s$ integer-valued $2022$-tuples on a blackboard. After…","config":"","split":"test","body":"{\"problem\":\"Lucy starts by writing $s$ integer-valued $2022$-tuples on a blackboard. After doing that, she can take any two (not necessarily distinct) tuples $\\\\mathbf{v}=(v_1,\\\\ldots,v_{2022})$ and $\\\\mathbf{w}=(w_1,\\\\ldots,w_{2022})$ that she has already written, and apply one of the following operations to obtain a new tuple:\\n\\\\begin{align*}\\n\\\\mathbf{v}+\\\\mathbf{w}&=(v_1+w_1,\\\\ldots,v_{2022}+w_{2022}) \\\\\\\\\\n\\\\mathbf{v} \\\\lor \\\\mathbf{w}&=(\\\\max(v_1,w_1),\\\\ldots,\\\\max(v_{2022},w_{2022}))\\n\\\\end{align*}\\nand then write this tuple on the blackboard.\\n\\nIt turns out that, in this way, Lucy can write any integer-valued $2022$-tuple on the blackboard after finitely many steps. What is the smallest possible number $s$ of tuples that she initially wrote?\"}","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":[]}