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?

(In reply to re: Computer Solution by Charlie)

By direct calculation in UBASIC the factorials of 124 and 125 have 28 and 31 terminal zeros respectively:

?!(124):?!(125)
 1506141741511140879795014161993280686076322918971939407100785852066825250652908
79093506346311596738506917124356744046192504129535473104478255106766046837644419
4611004520057054167040000000000000000000000000000

 1882677176888926099743767702491600857595403648714924258875982315083531563316135
98866882932889495923133646405445930057740630161919341380597818883457558547055524
326375565007131770880000000000000000000000000000000

Posted by Charlie on 2009-02-23 12:45:50