1. Fill in what you know around given ship segments

Let’s start with the puzzle on the right, which contains five given squares: three with ship segments and two with water segments.

Since submarines consist of one segment, all neighboring squares of H8 must be filled with water by marking them with an “X”.

Square C4 contains the end segment of a ship, which means there is another part of the ship in C5. Since the count of row C is two, this ship must be a destroyer. We can now place the other end segment and fill in the ten squares surrounding the destroyer with water by marking them with an X.

Square F10 is a middle segment of a ship so it must be part of a battleship or a cruiser and must be oriented vertically. Therefore the squares above and below are ship segments denoted by dots, and three more squares are filled with water.

2. Remaining empty squares in a row or column are water

This strategy helps complete rows and columns where ship segments denoted by the row and column counts are fully accounted for.

Row A, column 2, and column 7 have a count of zero. This means there are no ship segments and all their squares are water.

Row C has a count of two, which is accounted for in C4 and C5. Therefore all other squares are water.

Row F has a count of one, which is accounted for in F10 so all other squares in the row are water.

Columns 4 and 5 have counts of one, which are accounted for in C4 and C5. Therefore all remaining cells are water.

3. Remaining empty squares in a row or column are ship segments

Continuing with the grid we left off with in the previous strategy, the present strategy helps us find rows and columns whose remaining empty squares contain ship segments.

Let’s look at column 3 which has a count of four. No ship segments have been found yet so we need to place all four segments in this column. Since there are exactly four empty squares, all of them must contain a ship segment. This means that a submarine is placed in E3 and a cruiser in H3, I3 and J3.

We can now go back and use Basic Strategy 2 in row E. Since the count of two is accounted for, all the remaining squares in row E must be water.

The resulting puzzle can be seen in the diagram on the right.

Advanced Strategies for Solving Battleship Puzzles

4. Remaining ships of one type can be placed in one way only

This strategy is used when there’s only one way to place all remaining ships of a particular type.

In this puzzle we need to place three destroyers. There are seven valid positions to place a single destroyer:D3-E3, D10-E10, E9-E10, G3-H3, G10-H10, J2-J3, and J9-J10.

This may seem daunting, but some candidate destroyer positions will exclude others. For example, D10-E10 and E9-E10 are mutually exclusive.

5. Overlapping cells when placing a ship

This strategy is used when there are common squares for positioning a ship. In this puzzle the battleship, which has four segments, can only be placed in row C.

There are exactly three valid positions to place the battleship: C1-C 4, C2-C5, or C3-C6.

No matter where the Battleship is placed, the overlapping squares C3 and C4 are common to all three positions which means they must contain battleship segments. Since we don’t know at this stage which segments of the battleship these squares are going to be, we will mark them temporarily with dots.

6. Indirect logic (process of elimination)

Indirect logic can be used in many forms to prove a cell must have a specific content such as water or ship segment. The indirect logic can be simple or complicated. Here is an example of using indirect logic.

Let’s show that square H10 must be a ship segment and not water. We’ll do this by assuming for the moment that H10 is water, in which case the grid would look like the next diagram below.

If square H10 is water, then according to basic strategy 3 (see above) we must fill the rest of row H with ship segments. This will create two new cruisers, as shown in the next diagram below.

Do you notice something wrong? There are three cruisers in the puzzle… but this is one more than the number allowed according to the rules!

The conclusion is clear: We have eliminated the possibility that square H10 is water. Assuming square H10 is water led us to a non-valid solution and therefore H10 must be a ship segment.

We used indirect logic to show that an assumption leads to a contradiction. This means the assumption is incorrect and tells us what the square should contain.