[math-fun] Motley torus tilings

Inspired by Scott Kim’s work on motley dissections ( http://www.gathering4gardner.org/g4g13-videos/), I offer a puzzle that I know the answer to and ask a question I don’t know the answer to: Puzzle: Find a tiling of the square torus by two squares of unequal sizes. Question: Is there a tiling of some (not necessarily square) torus by more than two squares, all of unequal sizes? Jim Propp