Everyone knows Battleship the duel: two players, two hidden fleets, and volleys of called-out coordinates — a folk game played on graph paper since the early twentieth century, long before Milton Bradley boxed it in plastic pegs in 1967. It is a fine game, and it is almost entirely luck dressed as strategy.
Fewer people know that Battleships has a second life as a pure logic puzzle — no opponent, no guessing, no luck at all. The solitaire version was developed for an Argentine puzzle magazine in the early 1980s and introduced to the wider world at the first World Puzzle Championship in 1992, where it was an immediate hit; it has been a championship staple ever since. One of the great pleasures of the genre, it takes the childhood game's vocabulary — fleet, water, hits — and rebuilds it on the same foundation as Sudoku: a single solution, reachable by deduction alone.
The rules of the hunt
A fleet hides in the grid: classically one battleship (four cells long), two cruisers (three), three destroyers (two), and four submarines (single cells), though sizes vary. Ships lie in straight lines, horizontal or vertical. Two laws govern everything:
- Ships never touch — not even diagonally. Every vessel floats in its own halo of water.
- The border numbers are a census: each row and column clue counts the ship segments it contains.
Some cells may be revealed at the start — water, a submarine, a ship's middle, or a ship's end.
Water is worth more than ships
The novice hunts ships. The expert hunts water, because in Battleships, water is where the certainty lives.
Zeros first. A row clued 0 is pure ocean — ten cells resolved by one number. Fill them.
The halo rule is a machine. Every time any ship cell appears, its diagonal neighbors become water instantly and unconditionally (no ship may touch it corner-to-corner), and its along-axis neighbors resolve the moment you know the ship's extent. A single placed submarine paints up to eight cells of ocean around it. Placing water, in turn, constrains the counts, which places more ships, which paints more water. The game is a chain reaction, and water is the propellant.
Saturated rows. When a row's placed ship segments equal its clue, everything else in the row is water — the same "count is met, close it out" move you know from filling a Sudoku row's last candidates or completing a Nonogram block. Cross-hatching saturated rows against unsaturated columns is where midgame progress comes from.
The census and the shapes
Two more pillars complete the method.
Fleet accounting. The clues must add up: total segments in the fleet equal the sum of all row clues (and all column clues). Keep a running tally of what remains — "the battleship and one destroyer still unplaced" — because endgames are usually decided by pure bookkeeping: the only remaining shape that fits the only remaining counts.
Segment grammar. Revealed cells come with shapes, and each shape speaks. A rounded end-cap says: the ship continues exactly one way — away from the curve. A square middle segment is the loudest clue on the board: the ship extends in both directions along one axis, which means both perpendicular neighbors are water, and the ship is at least three long — consult the fleet list to see what it can still be. A submarine says: I am complete; ring me with ocean.
Where can the big one live? The most powerful global move mirrors Nonogram overlap logic. Scan the grid asking a single question: where can the four-cell battleship possibly fit? Rows with small clues, scattered water, and tight quarters eliminate stretch after stretch; often only two or three berths survive, and every candidate berth may share a cell — which is then certainly a ship segment, even before you know which berth is real. Big, awkward things are informative precisely because so few worlds have room for them. (Movers and Tetris players know.)
Why this puzzle feels different
Battleships trains a flavor of reasoning the number grids mostly don't: spatial exclusion with irregular pieces. Sudoku's citizens are identical digits; here the citizens have length, orientation, and personal space, and the constraint "these two things cannot be adjacent" does as much work as any count. Solvers of Tents — where every tent refuses to touch another — will recognize the muscle immediately. It is the logic of packing: airplanes boarding, warehouses filling, transistors on a die. There is honest computer science here, too: the general problem of packing constrained shapes to satisfy row-and-column counts scales viciously, which is why published puzzles, as ever, are the hand-picked solvable garden of a wild space.
And there is a small aesthetic miracle worth naming. The duel version of Battleship is a game of information starvation — you fire blind and learn one cell per turn. The solitaire version hands you total information from the start and asks only that you notice what it implies. Same fleet, same ocean, opposite epistemology. One is a slot machine; the other is a proof.
A worked instinct
If you retain a single move, take this one: whenever anything becomes a ship, immediately draw its diagonal water, then re-check every affected count. That two-beat rhythm — place, propagate — solves easy fleets outright and is the metronome under hard ones. It is also, incidentally, the deep pattern of all constraint puzzles: every placement is two moves, the mark you make and the shadow it casts. Battleships merely makes the shadow visible, cell by painted cell, until the ocean itself has told you where the last ship must be sleeping.
