1992 AIME Problems/Problem 15

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Problem

Define a positive integer $n^{}_{}$ to be a factorial tail if there is some positive integer $m^{}_{}$ such that the decimal representation of $\displaystyle m!$ ends with exactly $\displaystyle n$ zeroes. How many positiive integers less than $\displaystyle 1992$ are not factorial tails?

Solution

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See also