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Curious Consecutive Cyphers II (Posted on 2009-02-23) Difficulty: 2 of 5
A positive integer T is defined as a factorial tail if there exists a positive integer P such that the decimal expansion of P! ends with precisely T consecutive zeroes, and (T+1)th digit from the right in P! is nonzero.

How many positive integers less than 1992 are not factorial tails?

No Solution Yet Submitted by K Sengupta    
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Computer Solution | Comment 1 of 7
a quick computer search shows that all numbers of the form 6k+5 for k>=0 are not factorial tails, thus the number of non factorial tails less than 1992 are simply 6k+5<1992 6k<1987 k<=332 thus there are 332 non factorial tail numbers less than 1992

  Posted by Daniel on 2009-02-23 11:55:33
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