I've just stumbled across a game/concept called Moveless chess. The idea is that you defeat your opponent, not by moving pieces, but by transforming them. You are given a position, and a number of 'points' which can be used to turn one type of piece into another. The points match the standard value of chess pieces (Q=9, R=5 etc) and each transformation reduces the number of points you have. The idea is to checkmate your opponent by transforming your existing pieces. In the meantime your opponent can move, so it isn't as simple as it looks.
I've had a quick play with it, and even at the simplest level it took a couple of tries to solve the position. I'm sure with practice I can do better (like most things). It looks like a pleasant alternative to traditional chess problems, although the solving technique of 'I wish I had a queen instead of a knight here' doesn't neccesarily translate to real world chess.