Since we know 9 is a factor we can make the digit sum a multiple of 9: 52+x+y
The only attainable sums are 54 and 63
So x+y=2 or x+y=11
Since we know 11 is a factor we can make the differences of the even and odd numbered digits a multiple of 11:
Odds 41+y
Evens 11+x
Difference 30+yx
The only attainable differences are 22 and 33
So xy=8 or xy=3
There are four combinations to check.
Two won't give integer solutions.
x+y=2 and xy=8 has a negative solution.
x+y=11 and xy=3 has the only viable solution x=4, y=7
A quick web search confirms
21! = 510909
421
71709440000

Posted by Jer
on 20130701 11:20:38 