data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
AI-MO/NuminaMath-CoT-processed | [
{
"content": "Compute the number of ordered quadruples of positive integers $(a,b,c,d)$ such that $$ a!\\cdot b!\\cdot c!\\cdot d!=24! $$ [list=1]\n[*] 4\n[*] 4!\n[*] $4^4$ [*] None of these\n[/list] Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "None \\text{ of these}",
"style": "rule"
} | {
"answer": "To solve the problem, we need to find the number of ordered quadruples \\((a, b, c, d)\\) of positive integers such that \\(a! \\cdot b! \\cdot c! \\cdot d! = 24!\\).\n\n1. **Prime Factorization of \\(24!\\)**:\n \\[\n 24! = 2^{22} \\cdot 3^{10} \\cdot 5^4 \\cdot 7^3 \\cdot 11^2 \\cdot 13 \\cdot 17 \... |
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