[math-fun] Tiling a square

Hi all, I've found out, through sheer playing around, that a 15x15 square can be tiled exactly using 4 5x5 squares, 9 3x3 squares, and 11 2x2 squares. No big deal. What I'd like to do is determine whether or not a certain combination of smaller squares will tile a larger square, without actually finding the tiling. For example, will 2 5x5s, 11 3x3s and 19 2x2s also tile a 15x15? I've already figured out that the areas need to match. :-) Any pointers or pearls of wisdom? Thanks, Kerry Mitchell -- lkmitch@gmail.com www.fractalus.com/kerry