Contradiction
Suppose the cell were ship (or water) and follow the consequences — if a line overflows or a ship has nowhere left to go, the opposite must be true.
How it works
- 1Say two 2-ships and two submarines are still to place. Nothing constructive moves here, so suppose the marked cell were a ship and follow it.
- 2Its four diagonal neighbours would go to water, and two of them are in the first column.
- 3The third row's clue is 1, so that row would already be full and its other three cells would be water too — one of them the first column's third cell.
- 4The first column would be down to a single open cell while its clue still asks for 2, which no fleet can satisfy.
- 5The supposition breaks the board, so the marked cell is water — assume, propagate, and take the opposite when a line starves or a ship runs out of homes.
- Water
- Cells that establish the pattern
- Where the conclusion lands