# Solving a Squared Battleships Puzzle

Let’s try our hand at solving a Squared Battleships puzzle.

When solving Squared Battleships the solver has an additional tidbit of information: all ships are square, rather than rectangular.  This redundancy gives the puzzle a flavor of its own.

 We will attempt to place the battleship on the board.  Since the battleship is a 4x4 square, only rows with a minimal row tally of four can contain a battleship segment.   Examining the puzzle, we see that the only four consecutive rows with tallies of four or more are rows C, D, E, and F. Similarly, the only four consecutive column tallies with a value of four or more are columns 6 through 9. The 4x4 area where rows C to F intersect columns 6 to 9 (surrounded by the dashed lines) is the only possible position for the battleship. We’ve surrounded the battleship with water because no ship can be adjacent to another.   We can fill in the rest of both row D and column 8 because the battleship fills up their tally of 4. We’re making good progress!   Looking at column 7 with a tally of eight, we know that all remaining cells along the column are ship segments. The single ship segment at (A,7) can only be a submarine.  Therefore, (A,6) is water.   This allows us to fill the three cells (H,6), (I,6), and (J,6) with ship segments. Notice the 2x3 partial ship at (H‑J,6‑7). This must be a 3x3 ship, and the remaining three segments must be (H‑J,5).  Surrounding the newly found cruiser with water gives us the next frame. Row G can be filled in with three ship segments.   A brief examination will show that the only place the remaining cruiser can be placed is (F-H,1-3). Filling the rest of row C with ship segments, and completing the obvious destroyer at (B-C,1,2), we get the next frame. We can fill in the rest of row H with ship segments.  Once again, these segments can only belong to a destroyer at (H‑I,9‑10). Completing the obvious destroyer at (I‑J,1‑2) and the submarines at (A,4) and (A,10) gives us the final solution: Solved!