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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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An observation | Comment 3 of 4 |
The numbers below 100000 are small enough that the answer is almost certainly zero.  However, the proportion of zeros at the end of n! does tend to decrease toward zero as n increases.

http://perplexus.info/show.php?pid=7319&cid=45884

If I get a chance I may do a bit of statistical analysis on the likelihood a digit can surpass zero for some large n! assuming the digits in the non-trailing zeros portion.

(It can also be mentioned the first digit and digit before the trailing zeros are not zero.)



  Posted by Jer on 2019-01-16 22:45:17
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