Here is a riddle someone has been asked in a job interview: How many zero digits are there in $100!$?
Well, I found the first $24$ quite fast by counting how many times five divides $100!$ ($5$ divides $20$ times and $25$ divides it $4$ times).
However, there are more zero digits in the middle of the number (these can be found by hand, by typing
factorial(100) in sage).
My question is whether there is a smart way to determine the number of zero digits in $100!$, and more generally in $n!$.
By the way, this will not affect the job interview as it was finished some time ago.