John has started a sudoku puzzle and shows me his completed work, asking whether he's made any errors. There are no obvious errors (a number repeated in a row or subgrid). I know of two ways to determine whether he's erred:
- Continue solving the puzzle (without error) where John has left off, and see whether I arrive at an impossible state. If so, John erred. If not, I'll complete the puzzle, and John hasn't erred.
- Start the puzzle over again and solve it (without error) until either (a) I have filled in every square John has, and with the same numbers, in which case John hasn't erred; or (b) I have filled in some square John has, but with a different number, in which case John has erred (assuming that the puzzle has a unique solution).
Is there another way to determine whether John has erred? Specifically, is there a way that doesn't involve redoing or continuing the solution, but, rather, involves merely examining what John has done?