What decimal digit occurs most often in the sequence of factorials from 77777! to 77877! inclusive?
Note: This can be solved by logic. No computer is needed.
(In reply to Guess
77777 has about 15555 multiples of 5
3111 multiples of 25
622 multiples of 125
124 multiples of 625
24 multiples of 3125
5 multiples of 15625
That's 19441 trailing zeros.
The factorial itself has 346621 digits.
That leaves about 327180 digits other than the trailing zeros, but that includes other zeros, presumably randomly. On average one would expect 32,718 of each digit, including the zeros with a standard deviation of less than 200. The 19441 advantage that zero has is many many times that standard deviation, and this would apply to each of the other factorials in the given range.
Posted by Charlie
on 2019-01-16 15:20:02