n is a multiple of 3 and n factorial is equal to:

arithmetic/digits/zeros/factorial.given New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

n is a multiple of 3 and n factorial is equal to:

    1405006117752879898543142606244511569936384000000000

What is n?  (No calculator is needed.)

Show solution

Hmmm, there are 9 zeros at the end of the number and the preceding
digit is not a 5 so there must be 9 factors of 5 in n! ... so
5.10.15.20.25..(count twice)30.35.40. = the nine factors.  So
40 <= n <= 44 ('cos 45 would be 10 5's) ... and as n is multiple of 3
that only leaves 42.  ;)

-- Mike Fee <M.Fee@irl.cri.nz>

[ Editor: the puzzle was posed by Mark van Hoeij
<hoeij@sci.kun.nl>.  The number has 52 digits, which also fits 42!
(about 1.4 x 10^51). ]