1997 AIME Problems/Problem 2
Problem
The nine horizontal and nine vertical lines on an 
checkeboard form 
rectangles, of which 
are squares. The number 
can be written in the form 
where 
and 
are relatively prime positive integers. Find 
Solution
For r, we can choose two out of 9 lines, and 2 out of nine lines again, to get 
For s, there are 8^2 unit squares, 7^2 2*2 squares, .... 1^1 8*8 squares. That gives us 
