Reading from left to right, what is the last non - zero digit in ((20!)!)!? (That is, the factorial of factorial of 20 factorial).
I guess I took too simple an approach. I think the chance that my answer (8) is correct is about 1 in 4.
I will decline to elaborate on my flawed thinking, except to give one indication of where I went wrong. Because multiplying by 2 and 5 does not change the last digit, I took the leap of inferring (incorrectly) that multiplying by 12 and 15 would also not change the last-non-zero digit. This simplified the problem significantly. :-)