Sudoku Made and maintained by Brian Hamilton and Karan Hamilton.
Brian builds the playable puzzle tools, while Karan helps test clarity, difficulty feel, and the player experience.
Playable puzzles and controls are tested in the browser for rule accuracy, usability, and a clear solving experience. See how we make and test puzzles, our editorial standards, or report a problem.
What is Battleship Sudoku?
Battleship Sudoku is two puzzles on one grid. Fill it so that:
- every row, column and 3×3 box holds 1 to 9 exactly once, as in ordinary sudoku;
- and find the hidden fleet: one battleship four squares long, two cruisers of three, three destroyers of two and four submarines of one — twenty ship squares in ten straight ships, no two of them touching, not even at a corner.
The number to the right of each row and under each column says how many of its squares are ship. A few squares are shown as ship from the start. Below the grid the fleet is listed by size, each ship’s digits hidden behind question marks until you have found it.
The digits say nothing about where the ships are, and the ships say nothing about the digits: the fleet list keeps its digits hidden until a ship is found, so it gives nothing away. You can solve the sudoku first, the fleet first, or both at once. That is a simpler rule than the original puzzle’s, where each ship’s digits are printed in the fleet list and a ship can only sit where its digits fit.
How do you find the fleet?
Mark water as eagerly as ships. Every ship square makes its four corners water, since ships never touch; a row or column whose count is already met is water everywhere else; and one that needs every open square it has left is ship there. Those rules, applied over and over, are most of the fleet:
Then think in whole lines, and in whole ships. A row of count 3 with four open squares in a block can only fall a few ways, and any square they all agree on is settled. And the fleet itself is a clue: the four-square battleship needs four open squares in a straight line, clear of everything else, and late in a puzzle there are rarely many such runs left.
Across 40 boards per level, counts and corners settle a median of 68 to 70 of the 81 squares from the six or so shown at the start. The last ten or so are where the puzzle is: counts and corners alone finish only 3 to 6 boards in 40, and on 29 to 35 boards in 40 nothing short of reasoning about which ships are still missing finishes the fleet.
Why are some squares shown?
Because the counts alone almost never fix the fleet. On the board above they allow hundreds of fleets:
The game accepts one fleet and one grid of digits, so a board is only fair if each half has exactly one answer. This page used to deal boards without checking either. We measured 160 of them, 40 per level: only 15 had a single answer for the digits and only 8 a single fleet, and just 5 — all on Easy — had both. On Hard and Expert the digits had a median of over 200 answers, and an Expert board’s counts allowed a median of 330 fleets. You could solve one of those correctly and never be told you had won.
The generator now proves both halves. It removes digits one at a time, keeping a removal only while the sudoku still has exactly one answer. Then it places a fleet, shows every ship square that is not already a given digit, and takes those away one at a time, keeping each only while the fleet can still be worked out with the steps above — counts, corners, whole lines and the fleet — without trial and error. A separate search then confirms that exactly one fleet fits. We re-checked 160 fresh boards with a sudoku solver and a fleet counter written separately from the page: every one has one grid and one fleet, and a board takes a median of 4 to 21 milliseconds to deal.
How do the four levels differ?
We ran 40 fresh boards per level through a sudoku solver that knows one technique at a time, and through the fleet steps above, then took steps away to see which boards stopped.
| Level | Given digits | Ship squares shown | Digits: singles finish it | Digits: beyond our solver | Fleet: counts and corners finish it |
|---|---|---|---|---|---|
| Easy | 38 | 6 (6–10) | 100% | 0% | 15% |
| Medium | 30 | 6 (3–10) | 88% | 13% | 8% |
| Hard | 27 | 6 (2–10) | 65% | 20% | 15% |
| Expert | 22–25 | 6 (2–11) | 58% | 23% | 8% |
40 boards per level from this page’s generator, fixed seed; medians with ranges, and shares rounded. The sudoku solver knows naked and hidden singles, locked candidates, naked pairs and triples, and the X-Wing; “beyond our solver” digits still have exactly one answer. Every fleet at every level is finished by counts, corners, whole lines and the fleet, with no trial and error.
The levels are about the digits. Every level shows about six ship squares, because that is roughly what it takes for the fleet to be worked out at all, so the fleet is much the same puzzle on Easy as on Expert. The digits step up: all 40 Easy boards fall to singles, Medium 35 and Hard 26, while Expert gives two to five fewer digits than Hard and a few more of its boards need locked candidates or pairs. Hard and Expert are close, and every board at both has exactly one answer.
The digits are dug one removal at a time with a check after each that the grid still has exactly one answer; a check that runs out of search answers “not proven” and the digit stays. The fleet’s shown squares are chosen so the fleet can be reasoned out, and a separate search then confirms that no second fleet fits; the deepest of those searches in 160 boards took 57,177 steps of the 60,000 it is allowed.
Which level should you play?
Start on Easy even if you know sudoku well. The digits will not hold you up, which leaves you free to learn the fleet: marking water, reading the counts, and spotting where the battleship can still go. That skill carries straight up the levels, because the fleet does not get harder.
Choose the level after that by the sudoku you want. Medium is a comfortable ordinary sudoku; Hard and Expert need the odd locked candidate or pair, and about one board in five goes beyond everything our solver knows, though it still has exactly one answer.
What goes wrong on a Battleship Sudoku
- Marking only ships. Water is most of the grid — 61 of the 81 squares — and every square you cross off narrows where the ships can go. Use Miss as freely as Ship.
- Forgetting the corners. Ships never touch, not even diagonally, so every ship square makes its four corners water the moment you find it.
- Letting a ship bend or grow. Ships are straight. A square beside the middle of a known ship is water, and a run already as long as the longest ship still missing is closed at both ends.
- Losing track of the fleet. Count what you have finished. Once the battleship and both cruisers are found, no run of three or more can appear anywhere else.
- Expecting the digits to help. On this page they do not: a ship’s digits stay hidden in the fleet list until the ship is found, so the fleet has to be worked out from the counts and the shown squares.
Where does Battleship Sudoku come from?
The fleet puzzle came first. Solitaire Battleship was invented in Argentina by Jaime Poniachik and first appeared in 1982 in his magazine Humor & Juegos; it reached a wider audience at the first World Puzzle Championship, in New York in 1992. Its fleet of one battleship, two cruisers, three destroyers and four submarines is the one used here. It is not the fleet of Milton Bradley’s 1967 Battleship board game, whose five ships run from a five-square carrier down to a two-square destroyer.
Battleship Sudoku was created by the American puzzler Thomas Snyder, who, according to his site GMPuzzles, first made it for his blog The Art of Puzzles in 2006. It became his first book, Battleship Sudoku, published by Sterling in 2008 with 150 puzzles. In his version each ship’s segments carry digits, and those digits must also fit the sudoku; this page keeps them hidden until a ship is found.
What do the buttons do?
Select a square, then a digit from 1 to 9; the page opens on Medium. Selecting a square highlights its row, column and box, and a wrong digit is marked the moment it goes in. To mark the fleet, press Ship or Miss and then tap squares; tap a square again to clear its mark. The buttons:
- Notes turns pencil marks on and off, and switches off Ship and Miss. A correct digit clears itself from the notes of its row, its column and its box.
- Ship marks squares as ship with an anchor, and Miss marks them as water with a cross; either mark replaces the other. The squares shown from the start cannot be changed. Ship marks are not checked as you go: when every ship square of one ship is marked and its digits are right, that ship lights up in the fleet list and shows its digits.
- Erase clears the digit in the selected square, and pressing the same digit twice does the same.
- Undo takes back the last change, ship and miss marks included, though not the notes a correct digit cleared elsewhere, and not the Mistakes count, which counts wrong digits only.
- Hint fills one square’s digit, picked at random; it never places a ship.
- Solve asks first, then fills the grid and the fleet and stops the timer.
- New Game deals another board at the level you are on; the level buttons deal one at theirs.
The board is won when every digit and every ship square is right. Digits 1–9, the arrow keys, Backspace or Delete and Ctrl+Z all work from a keyboard, and S and M mark the selected square as ship or water. The board is saved in this browser after every move.
Where to go next
If the fleet was the part you enjoyed, the clues outside the grid are the link to Sandwich Sudoku, where the number beside each row and column is the sum of the digits between its 1 and its 9 — and there, unlike here, the clues and the digits are one puzzle. Killer Sudoku swaps given digits for sums inside the grid, and pencil marks are worth a look before the harder digit levels.