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Factorial Difference Digits (Posted on 2014-01-12) Difficulty: 3 of 5
Determine the last two non-zero digits of 36! - 24!

Extra Challenge: Solving this puzzle without a computer program.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Hints/Tips A thought | Comment 1 of 6

36! includes factors of 25, 30 and 35 not found in 24! and therefore its prime factorization has four more 5's, and therefore the number itself has four more terminal zeros.

As a result, the answer should depend only on 24!, by subtracting the last two digits before the terminal zeros, from 100. Hopefully the first of these is not a zero itself--nothing prevents internal zeros.

  Posted by Charlie on 2014-01-12 12:19:41
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