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Factorial Tremors (Posted on 2019-01-16) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: Guess | Comment 2 of 4 |
(In reply to Guess by armando)

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
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