Proof by Contradiction
When nothing else advances the puzzle, try one cell's two possible states and follow the consequences a few steps ahead. If one choice breaks a rule, the other is forced.
How it works
- 1Every constructive technique above is stuck on this board, so pick an undecided cell and try one of its two states.
- 2Say the cell below the top-left corner is land: the corner is then boxed in by land on both sides, so it must be land too, and the 4 is one cell short.
- 3Everything neither clue can still reach turns to sea, and that new water in turn corners one square into being land — which completes the 4 and walls it in with sea of its own.
- 4That wall closes a 2×2 block of water, which is illegal, so the tested assumption was wrong and the cell is sea. The proof only looks a few steps ahead, matching what a person could actually trace by hand.
- Sea
- Cells that establish the pattern
- Where the conclusion lands