Saturday, May 22, 2010

Polyomino equation solutions

See the original puzzle

See solution 1
See solution 2

You can ask a more general question: given two kinds of polyominoes, is there some figure you can tile with either one?  In other words, are the two kinds of polyominoes "compatible"?

I know of two websites which try to address this question.  It turns out that some polyomino pairs are compatible, but require large numbers of pieces.  Other polyomino pairs are incompatible.  For many others, it's not known whether they're compatible.