No. Their only purpose is to act as a kind of receipt: "look, I actually really did waste all this energy". The solution to the puzzle itself is irrelevant - i

No. Their only purpose is to act as a kind of receipt: "look, I actually really did waste all this energy". The solution to the puzzle itself is irrelevant - it's an operation that would be extremely simple but that's made very, very hard on purpose. And the sole purpose is to align incentives by using lots of energy.