{"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":"967b1ef9-d5c7-5042-9de3-5cbb61605b20","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f17","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_17","short_description":"How many $4 \\times 4$ arrays whose entries are $0$s and $1$s are there such that…","config":"default","split":"train","body":"{\"problem\":\"How many $4 \\\\times 4$ arrays whose entries are $0$s and $1$s are there such that the row sums (the sum of the entries in each row) are $1, 2, 3,$ and $4,$ in some order, and the column sums (the sum of the entries in each column) are also $1, 2, 3,$ and $4,$ in some order? Output the remainder when the answer is divided by 100.\\n\\nFor example, the array\\n\\\\[\\\\left[   \\\\begin{array}{cccc}     1 & 1 & 1 & 0 \\\\\\\\     0 & 1 & 1 & 0 \\\\\\\\     1 & 1 & 1 & 1 \\\\\\\\     0 & 1 & 0 & 0 \\\\\\\\   \\\\end{array} \\\\right]\\\\]\\nsatisfies the condition.\"}","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":[]}