Contradiction

How it works

1. Say one 3-ship is all that's left, and the open cells form an L: three along the top, two more running down from the corner.
2. Suppose the corner cell were water, and follow it. The top row would be down to two open cells in a row, and the column to two — neither long enough for a 3-ship.
3. The last ship would have nowhere on the board to go. That can't be, so the supposition was wrong: the corner is a ship.
4. That's the whole method — assume, propagate, and if a line overflows or a ship runs out of homes, take the opposite. It only ever looks a few steps ahead, matching what a person could trace by hand.
5. Note the solver would never actually need it here: every placement of that 3-ship passes through the corner, so Placement Overlap gets there first and more cheaply. Contradiction is the last resort, reached only once every constructive rung has run dry.