Why Ships Never Touch: The Diagonal Rule in Battleship Puzzles
Ships never touch, not even diagonally. Learn the diagonal rule, the water ring around a finished ship, and how both clear most of a Battleship grid.
In Battleship solitaire, ships never touch each other, not even at a corner. That one rule means every ship square has water on its four diagonal neighbours, two ship squares side by side always belong to the same ship, and a finished ship sits inside a closed ring of water. Most of any grid is water, so these three consequences do a large share of the solving.
This guide is for players who know the basic rules and want to use the no-touch rule on purpose. If you are brand new, start with how to play Battleship solitaire and come back. Squares are named by row and column, counted from the top left: R2C3 is row 2, column 3.
The no-touch rule in Ships, exactly
The no-touch rule says that no square of one ship may share a side or a corner with a square of another ship. Ships lie in straight lines, horizontally or vertically, and the fleet is always given in full. Those are the classic rules of the puzzle, which goes by many names: Battleship solitaire, Solitaire Battleships, Bimaru, Yubotu. The Wikipedia article on the puzzle) lists them, and our post on Bimaru, Yubotu and the puzzle's other names has the story behind each one.
In Puzzle Picnic's Ships the rule is written the same way: ships never touch, not even diagonally. The numbers beside each row and column say how many ship squares that line holds, and the fleet legend shows every ship you still have to find.
Two things follow straight away, and the rest of this guide builds on them:
- A square that touches a ship square at a corner can never be a ship square, because it would belong to a second ship, or bend the first one.
- A square that touches a ship square along a side is either part of the same ship or water. Never part of another ship.
Why most of a Ships grid is water
Water fills between 72 and 80 percent of a Ships grid, so every deduction that marks water is doing the bulk of the work. You can check this from the fleets: add up the ship squares, and the rest is water.
| Level in Puzzle Picnic | Grid | Fleet | Ship squares | Water squares | Share that is water |
|---|---|---|---|---|---|
| Easy | 6x6 | 3 x 1, 2 x 2, 1 x 3 | 10 | 26 | 72% |
| Medium | 8x8 | 3 x 1, 2 x 2, 2 x 3, 1 x 4 | 17 | 47 | 73% |
| Hard | 9x9 | 3 x 1, 3 x 2, 2 x 3, 1 x 4 | 19 | 62 | 77% |
| Expert | 10x10 | 4 x 1, 3 x 2, 2 x 3, 1 x 4 | 20 | 80 | 80% |
The Expert fleet is the classic one from newspapers and puzzle books: one battleship of four, two cruisers of three, three destroyers of two and four submarines. Four out of five squares in that grid are water. A solver who only hunts for ships is searching the smallest part of the grid. A solver who marks water as soon as it is certain watches the ships appear in whatever is left.
The diagonal rule: every ship square has four water corners
The diagonal rule is the most useful consequence of no-touch: the moment you know a square is a ship, its four diagonal neighbours are water. You do not need to know which ship it is, how long it is or which way it points.
The reason is short. A diagonal neighbour cannot be part of the same ship, because ships are straight, and it cannot be part of a different ship, because ships never touch. So it is water.
This is worth doing every single time, even when it feels small. Here is the kind of chain it starts. The fragment below is part of a larger puzzle. Row 3 needs exactly one more ship square, its open squares are R3C2, R3C4 and R3C5, and you have just worked out that R2C3 is a ship square.
R3C2 and R3C4 are diagonal neighbours of R2C3, so both are water. That leaves R3C5 as the only open square in row 3, so it is the ship square. And R3C5 now has diagonal neighbours of its own: R2C4, R2C6, R4C4 and R4C6 are water too.
One fact about a square in row 2 decided five squares in these two rows, plus two more in row 4. That is the usual pattern: each diagonal mark narrows a row or column count, and the count then forces a new ship square with four new diagonals.
Two squares in a line: water along both sides
When two ship squares share a side, they are the same ship, and that ship runs in their direction. Two side-by-side squares cannot belong to two different ships, because those ships would touch. So the pair tells you the ship's direction, and with it a lot of water.
Take two ship squares stacked vertically. Every square to their left and right is water: the side squares would make the ship bend if they were ships, and the corner squares are covered by the diagonal rule anyway.
The end squares are the exception, and they are where solvers slip. The squares directly above and below the pair are still open: the ship might be two, three or four long. You can only put water at an end once you know the ship is complete.
The same idea gives a handy 2x2 rule. In any 2x2 block of squares there are at most two ship squares, and if there are two, they share a side. Two diagonal ship squares would touch at a corner, and three would need a bend. So when a 2x2 block already holds one ship square, the square diagonally opposite it is water, and at most one of the other two can join it.
The water ring around a finished ship
A finished ship is surrounded on every side and corner by water. Once you know a ship is complete, you can mark the whole ring in one go.
The ring is large. In open water a ship of length L has 2L + 6 neighbours, and the edge of the grid trims that down:
| Ship | Ring in open water | Lying along an edge | Tucked into a corner |
|---|---|---|---|
| Submarine (1) | 8 | 5 | 3 |
| Destroyer (2) | 10 | 6 | 4 |
| Cruiser (3) | 12 | 7 | 5 |
| Battleship (4) | 14 | 8 | 6 |
A ship is complete when one of these is true:
- Both ends are capped: each end touches water or the edge of the grid.
- It has reached the length of the longest ship you have not found yet. If the battleship is already placed and you have three squares in a line on Expert, that line is a cruiser and both ends are water.
- It is a single square with water or the edge on all four sides, which makes it a submarine.
The fleet legend helps here. Crossing off each ship as you place it tells you the longest length still possible, and that tells you when to cap. Our Battleship solitaire strategy guide covers this fleet accounting in more depth, including why placing the biggest ship first pays off.
A worked 6x6: watching the rule clear the grid
Here is a complete Easy-sized puzzle, solved step by step, so you can see how much the no-touch rule does alongside the row and column counts. The fleet is Puzzle Picnic's Easy fleet: one ship of three, two ships of two and three submarines.
Step 1: the zero lines. Rows 4 and 6 and columns 2 and 6 have a count of 0, so all 20 of their squares are water.
Step 2: the submarine's ring. A submarine is a complete ship of one square, so everything around R1C5 is water. R1C6 and R2C6 are already water, which leaves three new marks: R1C4, R2C4 and R2C5.
Step 3: column 3. Column 3 needs four ship squares and only four of its squares are still open (R1C3, R2C3, R3C3, R5C3). All four are ships.
Step 4: the first finished ship. R1C3, R2C3 and R3C3 are three ship squares in a line, with the top edge above and water in R4C3 below. Both ends are capped, so this is the ship of three, and it is complete. Its ring adds one new water square, R3C4. The fourth ship square, R5C3, gets its four diagonals as water, but they are already water from the zero rows.
Step 5: the counts take over. Row 1 needs two and already has R1C3 and the submarine, so R1C1 is water. Row 2 needs two: R2C3 is one, and the only open square left is R2C1, so it is a ship. Row 3 needs three: R3C3 is one, and the open squares are exactly R3C1 and R3C5, so both are ships.
Step 6: read the new ships. R3C5 has water above, below, left and right, so it is a submarine. R2C1 and R3C1 are a vertical pair with water above (R1C1) and below (row 4), so they make a finished ship of two.
Step 7: finish the counts. Column 1 needs three and has two, and R5C1 is its last open square, so it is a ship: a submarine, since row 4, row 6 and column 2 surround it with water. Column 5 needs two and has the two submarines, so R5C5 is water. Row 5 needs three: R5C1 and R5C3 are two, and R5C4 is the only open square left, so it is the third. R5C3 and R5C4 make the second ship of two.
Count where the 26 water squares came from: 20 from the zero lines, 4 from the no-touch rule (the submarine's ring and the cruiser's side), and only 2 from rows and columns filling up. On an Easy grid the zero lines do the heavy lifting. On Hard and Expert there are fewer zeros and fewer revealed squares, and the diagonal rule and the rings carry a much bigger share.
Where the no-touch rule trips people up
Most mistakes with this rule come from using it too little or too early. These are the ones to watch for.
- Forgetting the diagonals. Players mark water beside a ship and miss the corners. Make it a habit: every new ship square gets four corner marks before you look anywhere else.
- Capping an end too soon. A pair of ship squares on Medium could still be a ship of two, three or four. Only cap an end when it touches water or the edge, or when the fleet legend says no longer ship is left.
- Treating side neighbours as water. A side neighbour of a ship square is open until you know the ship's direction. If you mark it as water and the ship actually ran that way, the grid will stop adding up later.
- Leaving the ring out of a ship's footprint. When you test where a ship can go, count its ring too. If the ship fits in only one place once its ring is kept clear of every known ship square, it goes there.
In Puzzle Picnic you can tap a square to cycle between water and ship, or drag to paint several squares at once, which makes marking a full ring quick. The same habits apply on paper: mark water in a way you can see at a glance, so a missing corner stands out.
Frequently asked questions
Can ships touch diagonally in Battleship puzzles?
No. In Battleship solitaire, ships may not touch at all, which includes touching at a corner. This is the standard rule in puzzle books and newspapers, and in Puzzle Picnic's Ships. It is different from the two-player Battleship game, where you choose where to put your own ships.
Why is every diagonal neighbour of a ship square water?
Ships are straight, so a diagonal square cannot be part of the same ship. Ships never touch, so it cannot be part of another ship either. That leaves water, whatever kind of ship the first square turns out to be.
When can I put water at the end of a ship?
Only when you know the ship is complete. That happens when both ends already touch water or the edge, when the ship has reached the length of the longest ship you still have to find, or when a single square is boxed in on all four sides, which makes it a submarine.
Does the no-touch rule work the same in Star Battle?
Yes. Star Battle uses the same no-touching rule for its stars, corners included, so the habit of marking all eight neighbours carries straight over. Our guide on how to play Star Battle shows it at work.
Where to go next
Take the diagonal rule into your next grid and make one promise: every ship square gets its four corners marked the moment you find it. After a few puzzles you will do it without thinking, and the counts will start forcing ships much earlier. When revealed squares show a ship's shape, our guide to reading ship pieces explains what each end, middle and submarine forces around it.
The Ships page has the rules and a Play button, and the web app plays in the browser with no account. Easy reveals a few squares to start; Expert usually reveals none, and there the no-touch rule is where nearly every solve begins.