{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"amc","formal_name":"AMC (AIMO validation set)","introduction":"83 AMC 12 problems assembled by Project Numina as a validation set for the AIMO competition. They sit a step below AIME in difficulty, which makes them a useful lower rung on the same scale.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/AI-MO/aimo-validation-amc","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"c092d4b9-00e3-5f97-93b4-2318d9c88c0a","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f18","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_18","short_description":"Each square in a $5 \\times 5$ grid is either filled or empty, and has up to…","config":"default","split":"train","body":"{\"problem\":\"Each square in a $5 \\\\times 5$ grid is either filled or empty, and has up to eight adjacent neighboring squares, where neighboring squares share either a side or a corner. The grid is transformed by the following rules:\\n\\nAny filled square with two or three filled neighbors remains filled.\\nAny empty square with exactly three filled neighbors becomes a filled square.\\nAll other squares remain empty or become empty.\\nA sample transformation is shown in the figure below.\\n\\nSuppose the $5 \\\\times 5$ grid has a border of empty squares surrounding a $3 \\\\times 3$ subgrid. How many initial configurations will lead to a transformed grid consisting of a single filled square in the center after a single transformation? (Rotations and reflections of the same configuration are considered different.)\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/AI-MO/aimo-validation-amc","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}