> Amazingly this means we can solve a Rubik's Cube without ever knowing what the original configuration is, as long as we can ask at any time if the cube is sol

> Amazingly this means we can solve a Rubik's Cube without ever knowing what the original configuration is, as long as we can ask at any time if the cube is solved or not. I think you mean current configuration? Otherwise it's kind of silly, the original configuration is irrelevant once you know the configuration you are currently at.