{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"olympiadbench","formal_name":"OlympiadBench","introduction":"OlympiadBench evaluates scientific reasoning on Olympiad-level mathematics and physics problems. Its official description lists 8,476 English and Chinese problems with separate text-only and multimodal settings.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/OpenBMB/OlympiadBench","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"fd0d4a3a-185a-58dc-8fc9-b9c34e65d3c1","task_key":"OE~5fTO~5fmaths~5fen~5fCOMP--train--1914","task_revision_id":"3","upstream_id":"1914","short_description":"Let $n$ be a positive integer. Harry has $n$ coins lined up on his desk, each…","config":"OE_TO_maths_en_COMP","split":"train","body":"{\"answer_type\":\"Expression\",\"is_multiple_answer\":false,\"language\":\"English\",\"question\":\"Let $n$ be a positive integer. Harry has $n$ coins lined up on his desk, each showing heads or tails. He repeatedly does the following operation: if there are $k$ coins showing heads and $k>0$, then he flips the $k^{\\\\text {th }}$ coin over; otherwise he stops the process. (For example, the process starting with THT would be THT $\\\\rightarrow H H T \\\\rightarrow H T T \\\\rightarrow T T T$, which takes three steps.)\\n\\nLetting $C$ denote the initial configuration (a sequence of $n H$ 's and $T$ 's), write $\\\\ell(C)$ for the number of steps needed before all coins show $T$. Show that this number $\\\\ell(C)$ is finite, and determine its average value over all $2^{n}$ possible initial configurations $C$.\",\"question_type\":\"Open-ended\",\"subject\":\"Math\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/OpenBMB/OlympiadBench","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}