I like this. The puzzles are cool even in the abstract, and the framing story makes it significantly better than, for example, just matching colours would.
It would be interesting to try to construct a level which has only one solution. (Actually, that's trivial. What would be interesting would be to find a level of reasonable complexity - on the order of the puzzle-game levels, say - but with only one solution. Precisely what "only one solution" means also becomes relevant....)