2006 AMC 10B Problems/Problem 11
Problem
What is the tens digit in the sum
Solution
Since is divisible by
, any factorial greater than
is also divisible by
. The last two digits of all factorials greater than
are
, so the last two digits of
is
.
(*)
So all that is needed is the tens digit of the sum
So the tens digit is
(*) A slightly faster method would have to take the residue of
Since
we can rewrite the sum as
Since the last two digits of the sum is
, the tens digit is