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Let N = 2014 ! + 2015 ! + 2016 ! + + 9999 ! N = 2014!+2015!+2016!+· · ·+9999! How many zeros are at the end of the decimal representation of N N ?


The answer is 501.

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1 solution

Only the number of trailing zeros in 2014! is relevant, since the subsequent numbers will all have a greater number of trailing zeros. Number of trailing zeros in 2014! can be obtained by dividing 2014 with the powers of 5:

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