I wrote a puzzle generator whose acceptance rate is 0.26% . It throws away 99.7% of everything it produces, and that is the design working as intended, not failing. Generating five valid puzzles takes 1,947 attempts and 84 milliseconds. The point is not the puzzles. The point is that the generator makes no correctness guarantee at all, and a verifier makes every one of them. Once you split those two responsibilities, "make the generator smarter" stops being the obvious optimisation — and tha...