2010 AIME II Problems/Problem 1
Problem
Let be the greatest integer multiple of
all of whose digits are even and no two of whose digits are the same. Find the remainder when
is divided by
.
Solution
If assume to include all the even digits for the greatest integer multiple, we find that it is impossible for it to be divided by or
.
The next logical try would be
, and this happens to be divisible by
. Thus