Big Ships First

How it works

1. Say the only ships still missing are the 4-ship and one 3-ship. Instead of taking a line at a time, fit both at once and keep whatever every joint fit agrees on.
2. The first column needs four ship cells. Two ships can't sit end to end — they'd be touching — so a single ship must supply all four, and only the 4-ship is long enough. It's standing in that column, either rows 1-4 or rows 2-5.
3. Try rows 2-5. That drops a ship cell into the bottom row, which needs exactly three. The 3-ship is all that's left: lying along the row it would bring the total to four, standing on end it would add just one. Neither reaches three, so this placement is dead.
4. So the 4-ship takes rows 1-4. Its foot is now directly above the bottom row's first cell, and ships never touch — not even at a corner — so the bottom row's first two cells are water.
5. That leaves the bottom row's last three cells as the only way to make its three, and the 3-ship fits them exactly. Both ships are placed from one joint fit.
6. Neither ship could be pinned down alone: the column allowed two spots and the row allowed three. It's the pair TOGETHER that has only one arrangement.