How to Solve Battleships Puzzles
Battleships began as a 2-player pen and paper game at least a century ago, long before the plastic board and peg game we know today. The solitaire puzzle version first appeared in an Argentinian puzzle magazine called Humor and Juegos in 1982.
Rules
Use the clues to locate the given fleet on the grid. Ships may not touch each other in any direction, including diagonally.
Number clues along the side and bottom of the grid indicate how many ship segments exist in that row or column. In some hand-crafted puzzles, a row or column without a clue contains an unknown number of segments, which you must deduce.
The fleet refers to all of the ships you must find in the grid. The exact makeup will change in different puzzles, but the possible ships include: Carriers (5 segments), Battleships (4 segments), Cruisers (3 segments), Destroyers (2 segments), and Submarines (1 segment). You might see them as triangles, squares, circles, etc.
The most common fleet consists of: 1 Battleship, 2 Cruisers, 3 Destroyers, and 4 Submarines.
Any given end-segments will be in the correct orientation. Some grids will use wavy lines to indicate a known water cell which does not contain any part of a ship.
Basic Techniques to Solve
- Fill in all known water cells as you solve.
- Mark pieces next to given segments, where possible.
- Combine clues where there are few unknown cells.
- Find the Battleship early.
- Pay attention to your remaining fleet.
Fill in Known Water Cells
As you work through the puzzle, keep marking all cells that you know can’t contain a ship segment. It helps to visualize the available space, especially for larger ships. Marking water cells also reveals rows and columns that have a number of available cells that exactly matches the clue. A cell is definitely water if:
- All ship segments for a clue are found – mark the rest of that row or column as water. Usually, your first move will be to fill in any 0 clues.
- It is one of the 8 cells around a submarine.
- It is diagonally adjacent to an unknown single segment. You don’t know its type or orientation, but nothing can touch it diagonally.
- It runs beside 2 or more adjacent ship segments. Even if you don’t know their type, you know the ship orientation
- It’s around the tip of an end-segment. A given end-segment provides many known cells – one definite segment to extend it, and all the water around them.
Given Segments
As you saw above, a given end-segment reveals many cells around it. This is because you know there must be at least one more segment in the direction of its flat side. Sometimes, you will be given a square mid-ship piece. If it’s in the middle of the grid, you will only know that the diagonal cells around it are water. However, when it is against the border, or if you’ve already found a group of water cells beside it, you now know its orientation. Mid-ship segments must have at least one more segment on each end, so once you know which direction those ends are, you may fill in many cells.
Combine Clues
A useful, but somewhat more advanced, technique is grouping clues where there are a limited number of unknown cells. This method is similar to trial and error, but more focused in its logic. First, find adjacent columns or rows where the sum of the clues is close to the number of available cells.
Use the individual clues to eliminate options. Perhaps a particular placement for one clue causes the other clue to be impossible. Look for cells that must contain ship segments or water by process of elimination. You might not completely solve the row or column, but every deduction helps in the overall grid.
Find the Battleship
Because the exact makeup of the fleet varies between puzzles, a more exact wording would be to look for the largest ship early. Longer ships have more restricted placement options. When the grid starts getting crowded with eliminated cells, that’s the best time to note options for the largest ship in your fleet.
If you have more than one possible placement, look at other clues. The Battleship options may all cause certain cells to be eliminated. If there is more than one option in a single row or column, check if there is overlap between them. Overlap between all possibilities marks cells that must contain a ship segment.
Keep Track of Your Fleet
Cross out ships as you find them. By looking over what is left, you can determine if a particular placement is possible. It might eliminate your ability to place certain ships, or force more of them than you have left.
In our example puzzle, we have found one Cruiser, but we have a second one to place. We already know that the single Battleship must be in either the 5 row or the 4 row at the bottom of the grid.
For a moment, let’s imagine that the Battleship is in the bottom row. When we mark the resulting water cells, we find that there is no longer anywhere that our second Cruiser can fit. Therefore, the Battleship belongs in the 5 row.
Solving the Puzzle
Now that we know some basic strategies, let’s start over with the example puzzle so you can see the entire solving process.
First, we’ll fill in the water for the 0 clues. 
We were given end pieces, so we can place a segment next to each of them and fill in water around them. In addition, we’ve completed these three clues. 
You may recognize the combined clues from before. The 3 column cannot have 2 adjacent segments without making the 5 clue impossible.
This shows the only configuration of the 3 column before noting the 2 possible placements of our Battleship. Either option fulfills the 1 columns, so we can mark all other cells as water. 
The remaining cells in this row match the clue, so we can solve it. We’ve located one of the Cruisers. 
As we noted in our earlier example, if the Battleship is i the yellow position, we can’t place the second Cruiser. So the Battleship must be in Row 5.
We can only place the second Cruiser here, which will solve these three clues. 
We found two Submarines! Now, there are only two possible placements for a Destroyer, and we conveniently have 2 left. This solves these three clues.
These final cells must hold our other two Submarines. 
We’ve found the fleet and solved the Battleships puzzle!
