Battleship Solitaire Strategy: Water, Counting and the Big Ship First
Battleship solitaire techniques in the order you need them: zero lines, water rings, the battleship first, fleet accounting and a full 8x8 solve.
The best strategy for Battleship solitaire is to settle water first and ships second. Clear the zero lines, close every line whose number is met, fill every line whose open squares match its number, and put water around each ship square you find. Then place the biggest ship while it still has few places to go, and keep a tally of the fleet. This guide is for players who know the rules and want to solve Medium to Expert grids.
If you are new to the puzzle, start with how to play Battleship solitaire, which covers the rules and a first 6x6 grid. The techniques below come in the order solvers usually meet them, and the guide ends with a complete 8x8 puzzle that uses each of them.
The technique ladder at a glance
Battleship solitaire techniques form a ladder: the first few rungs solve Easy grids on their own, and the later ones are what Hard and Expert need. Puzzle makers describe the same core set: fill around known pieces, complete lines with water, complete lines with ships, place ships that fit only one way, use the overlap of possible positions, and reason by elimination (Conceptis: Battleships techniques).
| Rung | Technique | What to look for | What you get |
|---|---|---|---|
| 1 | Zero lines | A row or column marked 0 | The whole line is water |
| 2 | Finished lines | A line that already has its number | Every other square in it is water |
| 3 | Full lines | Open squares equal to what the line still needs | Every open square is ship |
| 4 | Corners | Any ship square | Its four diagonal neighbours are water |
| 5 | Closing ships | A run with water or the edge at both ends | A finished ship, and the ring of water around it |
| 6 | Biggest ship first | Lines with enough count left and a long open run | Where the battleship is, or part of it |
| 7 | Fleet accounting | Which ships are still missing | Runs that must stop, places that are ruled out |
| 8 | Counting what is left | Squares still needed against squares still open | Forced squares in tight lines |
| 9 | Trying every case | A line with only one water square left to place | Squares that are ship in every case |
Four of the first five rungs are about water, because in the classic 10x10 puzzle the fleet fills 20 of the 100 squares (Conceptis: Battleships rules), so four squares in five are water, and finding them is most of the work.
Zero lines, finished lines and full lines
The row and column numbers in Battleship solitaire give three deductions that never need anything else, and a good solve returns to them after every new square.
Zero lines. A 0 beside a row or under a column means every square in it is water. Mark them first. Two zero rows and two zero columns settle 28 of the 64 squares in an 8x8 grid before you think about a single ship.
Finished lines. When a line has as many ship squares as its number, the rest of it is water. This is easy to miss in the middle of a solve, because a line often gets finished by a ship you placed for a different reason, such as a vertical ship that completes three rows at once.
Full lines. When the number of open squares in a line equals the number of ship squares it still needs, every open square is ship. In a fresh grid this only fires on very high numbers (a 6 in a row of 6), but after a few water squares it fires all the time.
The habit that makes these work is one question, asked of every line: how many does it still need, and how many squares are still open? If the first answer is zero, the open squares are water. If both answers are equal, they are ship. Swiss puzzle publisher Küng Verlag, which prints the puzzle as Bimaru, gives the same advice in its instructions: start with the lines that contain only water, continue where the numbers are highest, and never guess (Bimaru: Instructions).
Water around every ship square
The no-touching rule in Battleship solitaire puts water around every ship, and you can use it long before a ship is finished. Three versions come up constantly.
Corners first. A single ship square tells you nothing about its direction, but it always tells you about its corners. Ships are straight, so the square diagonally next to it cannot be part of the same ship, and a different ship there would touch at a corner. So all four diagonal neighbours are water.
Sides of a run. As soon as two ship squares sit next to each other, you know the ship's direction. Every square alongside the run is then water: above and below a horizontal run, left and right of a vertical one.
Closing a ship. When a run has water or the edge at both ends, the ship is complete. Mark its whole ring: for a ship of length L lying along a line, that is up to 2L + 6 squares (12 for a three-square ship in open water), fewer against an edge.
Revealed pieces work the same way. A revealed submarine has water all round it. A revealed end piece has water on three sides and ship on the fourth. A revealed middle piece has ship on both sides along one axis, and if it touches the edge of the grid, that axis must run along the edge. There is a full table of pieces in reading ship pieces, and more corner tricks in why ships never touch.
Place the battleship first
The biggest ship in Battleship solitaire is the hardest to fit, so it usually has the fewest possible places, and finding it early prunes the rest of the grid. Küng Verlag's Bimaru tips put it in one line: "Try to place large ships first" (Bimaru: Instructions).
A four-square ship needs two things at once:
- A long enough open run. Four squares in a straight line, none of them water, with no other ship already next to the run.
- Enough count left. If it lies along a row, that row must still need at least four ship squares. If it stands in a column, that column must still need four, and each of the four rows it crosses must still need at least one.
The second condition is the one people forget. A column with an open run of five looks like a perfect home for the battleship, but if the column's number is 3, the battleship cannot be there at all.
Often you can only narrow the battleship down to a short stretch, and that is still enough. If it must lie somewhere in a run of five open squares, it covers either squares 1 to 4 or squares 2 to 5. Either way, squares 2, 3 and 4 are ship.
This "overlap" idea works for any ship and any run: if a ship of length L must lie in a run of R open squares, and L is more than half of R, then the middle 2L − R squares are ship. For the four in a run of five, that is 2 x 4 − 5 = 3 squares. For a three in a run of four, 2 x 3 − 4 = 2.
After the battleship, do the same for the cruisers (three squares). With two cruisers, the question becomes "where can both go at once without touching?", which is harder to see but often has a single answer.
Fleet accounting: know what is still missing
Fleet accounting in Battleship solitaire means keeping a running tally of which ships you have found and which are still hidden, and it turns runs of ship squares into finished ships. In Puzzle Picnic the fleet legend shows every ship to find; on paper, tick them off beside the grid.
The tally gives you three kinds of deduction:
- A run that reaches the longest missing ship is finished. If the battleship and both cruisers are found, the longest ship still hidden is two squares. So any two ship squares side by side are a whole destroyer: put water at both ends.
- A run with no ship left to fill it cannot happen. If both cruisers are found, no three ship squares can sit side by side unless they are part of the battleship. A line that needs three must then get them from several ships, or from ships crossing it.
- Only submarines left means every new ship square is a whole ship. Its eight neighbours are water as soon as you find it.
| Ship | Length | Expert fleet | Found | Still missing |
|---|---|---|---|---|
| Battleship | 4 | 1 | 1 | 0 |
| Cruiser | 3 | 2 | 2 | 0 |
| Destroyer | 2 | 3 | 1 | 2 |
| Submarine | 1 | 4 | 2 | 2 |
In a tally like this one (a moment from a 10x10 solve), the longest missing ship is two squares. Any run of two is closed on the spot, and a single ship square with an open square on each side can only grow by one in one direction.
In Puzzle Picnic, Easy (6x6) has six ships with a three as the biggest, Medium (8x8) adds the battleship, and Expert (10x10) has the classic ten from the table.
Counting what is left
Counting in Battleship solitaire means comparing how many ship squares are still needed with how many squares could still hold them, over a line, a few lines, or the whole grid. It is the same arithmetic as the full-line rule, applied more widely.
Whole-fleet counting. The squares still to find always equal the total length of the missing ships. Late in a solve, this is a strong check: if two submarines are missing, exactly two ship squares remain anywhere in the grid, and the row and column numbers must account for exactly two.
Line counting with the fleet. Three open squares in a row between water can only all be ship if a ship of exactly three is still missing, because three side-by-side ship squares are one ship. Once both cruisers are found, such a run holds at most two ship squares: two side by side at one end, or one at each end. The fleet sets the limit, not just the number of squares.
Line counting with limits. When a line still needs n squares and its open squares come in separate groups, each group can hold only so many: a single open square at most 1, two side by side at most 2, three side by side at most 3 (or 2, as above, if no cruiser is left). If the limits add up to exactly n, every group holds its limit, and the single squares and pairs are all ship.
Trying every case, without guessing
When the simpler rungs run out, Battleship solitaire still never needs a guess, but it sometimes needs you to try every case of a small question and see what they agree on. Conceptis calls this indirect logic: assume a square is water, follow the consequences, and if they break a rule, the square is ship (Conceptis: Battleships techniques). The difference from guessing is that you test every possibility, not one, and you only keep what is true in all of them.
The best candidates are lines with exactly one water square still to place, a case Küng Verlag's Bimaru techniques page also singles out (Bimaru: Techniques). Here is one: a row of a 6x6 Easy grid that needs 5, with no square known yet. In the Easy fleet, the longest ship has three squares.
Try each position for the one water square:
| Water at | Ship squares left over | Possible? |
|---|---|---|
| A | B to F, a run of 5 | No: no ship is that long |
| B | A, then C to F, a run of 4 | No: the longest Easy ship is 3 |
| C | A to B (2) and D to F (3) | Yes |
| D | A to C (3) and E to F (2) | Yes |
| E | A to D, a run of 4, then F | No |
| F | A to E, a run of 5 | No |
So the water is at C or D, and A, B, E and F are ship in every case. There is more: in both cases the row is filled with two side-by-side ships, so every square in the rows directly above and below is water, either beside one of the ships or at the corner where the ships meet the gap.
Keep these case checks short: two to four cases you can hold in your head. If a question splits into dozens of branches, there is a simpler step somewhere else. Battleship puzzles in general are hard for computers (Merlijn Sevenster proved the general problem NP-complete in 2004), yet the same paper sets that result against "the general experience of Battleship puzzles being well playable" (Sevenster, ICGA Journal, 2004).
A full 8x8 solve, rung by rung
Here is a complete Battleship solitaire puzzle on the Medium grid: 8x8 with the Medium fleet of one battleship (4), two cruisers (3), two destroyers (2) and three submarines (1), 17 ship squares in all. No squares are revealed. Columns are A to H from the left, rows 1 to 8 from the top. A brute-force search over every possible layout confirms it has exactly one solution.
Rung 1: four zero lines
Rows 2 and 4 and columns C and E are 0. Mark all of them as water: 28 squares.
Rung 3: row 3 is full
Row 3 needs 6. Its squares in columns C and E are water, which leaves exactly six open: A, B, D, F, G and H. All six are ship.
Rung 5: three ships close at once
Row 3 now holds three runs, and rows 2 and 4 are water above and below them. A3 and B3 run from the edge to the water at C3: a destroyer, complete. D3 has water on all four sides: a submarine. F3, G3 and H3 run from the water at E3 to the edge: a cruiser.
Column A needs 1, and A3 is it, so the rest of column A is water (rung 2). Fleet tally: found a 3, a 2 and a 1; still missing the battleship, one cruiser, one destroyer and two submarines.
Rung 6: the battleship has one home
No row can take the battleship lying flat: row 1 needs 2, and rows 5 to 8 need 2, 3, 3 and 1. So it stands in a column that still needs at least 4. Count what each column still needs: B needs 2 more, D needs 4, F needs 1, G needs 3 and H needs 1. Only column D is left. Its open squares are D1, D5, D6, D7 and D8, and the only four in a row are D5 to D8. The battleship is there, and column D, now at 5, is finished: D1 is water.
Rungs 2 and 6 again: the last cruiser
Row 8 needs 1, and D8 is it, so the rest of row 8 is water. Now the missing cruiser. Lying flat, it would need a row with 3 left: row 5 has 1 left, rows 6 and 7 have 2 each, row 1 has 2. Standing up, it needs a column with 3 left: only column G, with G3 already found. G2, G4 and G8 are water, so column G's open squares are G1, G5, G6 and G7, and the only run of three is G5 to G7. The cruiser is there, and column G is finished: G1 is water.
Rungs 5 and 3: the destroyer
The cruiser in column G has water along both sides, so F5, F6, F7, H5, H6 and H7 are water. Row 5 needs 2 and has D5 and G5, so B5 is water too. Row 6 needs 3 and has D6 and G6; its only open square is B6, so B6 is ship. Row 7 is the same: B7 is ship. B6 and B7 sit between water at B5 and B8: the second destroyer. Column B now has its 3 (B3, B6, B7), so B1 is water.
Rung 7: two submarines, two squares
The fleet tally says two submarines are missing, so exactly two ship squares remain. Row 1 needs 2, and its only open squares are F1 and H1. Both are ship, each with water all round: the two submarines. Column F (F1 and F3) and column H (H1 and H3) both reach 2.
The two moves that opened the middle of this puzzle were both "biggest ship first" moves, and both depended on the count condition, not the open run. Column G had a run of four open squares all along, but with only 3 left to fill, the battleship could never go there.
Frequently asked questions
What is the most important Battleship solitaire technique?
Marking water. Zero lines, finished lines and the water around every ship square do most of the work in every grid, because about four squares in five are water. The second most important is placing the biggest ship early.
Why do ship corners always count as water?
Ships are straight, so a square diagonally next to a ship square can never belong to the same ship. If it held a different ship, the two would touch at a corner, which the rules forbid. So the four diagonal neighbours of any ship square are water, whatever the ship's direction.
Is trying cases the same as guessing?
No. Guessing means picking one option and hoping. Trying cases means checking every option for a small question and keeping only what is true in all of them, so every square you mark is proven. The puzzle above never needed it, and short case checks are only for the tightest lines.
How do I get faster at Battleship solitaire?
Make a fixed loop: zeros, finished lines, full lines, corners, then the biggest missing ship, then the fleet tally. Repeat the loop after every new ship. Speed comes from not missing the easy steps, not from finding clever ones.
What should I do when I am completely stuck?
Recount every line, slowly, and check the fleet legend for the longest missing ship. Most stalls are a missed finished line. In Puzzle Picnic, a hint explains the next logical step.
Where to go next
A routine that works from Medium to Expert: mark the zeros; ask every line "needs how many, open how many?"; put water on the corners of every ship square; close every run that hits water or the edge; place the battleship by checking both the open run and the count; tick off the fleet; and only then look for a line with one water square left to place. Run the loop again after every ship.
For the rules again, see how to play Battleship solitaire. The corner and halo ideas get a full post in why ships never touch, and revealed pieces in reading ship pieces. If you are curious where the puzzle came from, Bimaru, Yubotu and Battleship solitaire tells the story of its many names. You can practise every level on the Ships page; every puzzle there has exactly one solution and never needs a guess.