Problem:
A standard six-sided die is rolled, and is the product of the five numbers that are visible. What is the largest number that is certain to divide ?
Answer Choices:
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Solution:
Since , the prime factors of can consist of at most 's, 's, and 's. The least possible number of 's is two, which occurs when is not visible. The least possible number of 's is one, which occurs when either or is not visible, and the least number of 's is zero, when is not visible. Thus must be divisible by , but not necessarily by any larger number.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions