First, we can exclude all the spaces around the 0s:
----------------------------------------- | 2 | | 1 | . | 1 | | 3 | | | | ----------------------------------------- | | | . | 0 | . | | | | 2 | 1 | ----------------------------------------- | 2 | | . | . | 1 | . | . | | | | ----------------------------------------- | | | 1 | | . | 0 | . | | 3 | . | ----------------------------------------- | | | | | . | . | . | | . | 0 | ----------------------------------------- | | | 3 | | 3 | | | | . | . | ----------------------------------------- | | | | | 2 | | | 1 | | | ----------------------------------------- | . | . | | 4 | | | 1 | . | . | 2 | ----------------------------------------- | 0 | . | | | | | . | 0 | . | | ----------------------------------------- | . | . | | 3 | | 2 | . | . | 2 | | -----------------------------------------
The 2 in the bottom right only has two open spaces next to it, so we can fill those in. We also have some squares in the top left with only one possibility.
----------------------------------------- | 2 | . | 1 | . | 1 | | 3 | | | | ----------------------------------------- | < | > | . | 0 | . | | | | 2 | 1 | ----------------------------------------- | 2 | . | . | . | 1 | . | . | | | | ----------------------------------------- | . | . | 1 | | . | 0 | . | | 3 | . | ----------------------------------------- | | | | | . | . | . | | . | 0 | ----------------------------------------- | | | 3 | | 3 | | | | . | . | ----------------------------------------- | | | | | 2 | | | 1 | | | ----------------------------------------- | . | . | | 4 | | | 1 | . | . | 2 | ----------------------------------------- | 0 | . | | | | | . | 0 | . | ^ | ----------------------------------------- | . | . | | 3 | | 2 | . | . | 2 | v | -----------------------------------------
The 3 above the 2 in the center requires that there is some part of a ship in the space above and to the left of it:
----------------------------------------- | 2 | . | 1 | . | 1 | . | 3 | | | | ----------------------------------------- | < | > | . | 0 | . | ? | | | 2 | 1 | ----------------------------------------- | 2 | . | . | . | 1 | . | . | | | | ----------------------------------------- | . | . | 1 | . | . | 0 | . | | 3 | . | ----------------------------------------- | | . | . | ? | . | . | . | | . | 0 | ----------------------------------------- | | | 3 | | 3 | | | | . | . | ----------------------------------------- | | | | | 2 | | | 1 | | | ----------------------------------------- | . | . | | 4 | | | 1 | . | . | 2 | ----------------------------------------- | 0 | . | | | | | . | 0 | . | ^ | ----------------------------------------- | . | . | | 3 | | 2 | . | . | 2 | v | -----------------------------------------
Now the 3 in the top row has only one possibility that works with the 2-1 to its right, and the 3 below those is left with only 3 spaces around it:
----------------------------------------- | 2 | . | 1 | . | 1 | . | 3 | . | . | | ----------------------------------------- | < | > | . | 0 | . | < | x | > | 2 | 1 | ----------------------------------------- | 2 | . | . | . | 1 | . | . | . | . | o | ----------------------------------------- | . | . | 1 | . | . | 0 | . | ^ | 3 | . | ----------------------------------------- | | . | . | ? | . | . | . | ? | . | 0 | ----------------------------------------- | | | 3 | | 3 | | | | . | . | ----------------------------------------- | | | | | 2 | | | 1 | | | ----------------------------------------- | . | . | | 4 | | | 1 | . | . | 2 | ----------------------------------------- | 0 | . | | | | | . | 0 | . | ^ | ----------------------------------------- | . | . | | 3 | | 2 | . | . | 2 | v | -----------------------------------------
At this point, there is only one possible location for the flagship:
----------------------------------------- | 2 | . | 1 | . | 1 | . | 3 | . | . | | ----------------------------------------- | < | > | . | 0 | . | < | x | > | 2 | 1 | ----------------------------------------- | 2 | . | . | . | 1 | . | . | . | . | o | ----------------------------------------- | . | . | 1 | . | . | 0 | . | ^ | 3 | . | ----------------------------------------- | | . | . | ? | . | . | . | ? | . | 0 | ----------------------------------------- | | | 3 | | 3 | | | | . | . | ----------------------------------------- | | | | | 2 | . | . | 1 | | | ----------------------------------------- | . | . | . | 4 | . | . | 1 | . | . | 2 | ----------------------------------------- | 0 | . | < | x | x | > | . | 0 | . | ^ | ----------------------------------------- | . | . | . | 3 | . | 2 | . | . | 2 | v | -----------------------------------------
The space between the two 3s and the 4 must have a ship part, otherwise it becomes impossible to place enough parts in that area.
----------------------------------------- | 2 | . | 1 | . | 1 | . | 3 | . | . | | ----------------------------------------- | < | > | . | 0 | . | < | x | > | 2 | 1 | ----------------------------------------- | 2 | . | . | . | 1 | . | . | . | . | o | ----------------------------------------- | . | . | 1 | . | . | 0 | . | ^ | 3 | . | ----------------------------------------- | | . | . | ? | . | . | . | ? | . | 0 | ----------------------------------------- | | | 3 | | 3 | | | | . | . | ----------------------------------------- | | | . | ? | 2 | . | . | 1 | | | ----------------------------------------- | . | . | . | 4 | . | . | 1 | . | . | 2 | ----------------------------------------- | 0 | . | < | x | x | > | . | 0 | . | ^ | ----------------------------------------- | . | . | . | 3 | . | 2 | . | . | 2 | v | -----------------------------------------
If the space between the 3s is empty, we find that it is not possible to place all the remaining ships (either we need 5 caravels, or there is nowhere for the other frigate). So the frigate is between the 3s.
----------------------------------------- | 2 | . | 1 | . | 1 | . | 3 | . | . | | ----------------------------------------- | < | > | . | 0 | . | < | x | > | 2 | 1 | ----------------------------------------- | 2 | . | . | . | 1 | . | . | . | . | o | ----------------------------------------- | . | . | 1 | . | . | 0 | . | ^ | 3 | . | ----------------------------------------- | | . | . | ^ | . | . | . | v | . | 0 | ----------------------------------------- | | . | 3 | x | 3 | . | . | . | . | . | ----------------------------------------- | | . | . | v | 2 | . | . | 1 | | | ----------------------------------------- | . | . | . | 4 | . | . | 1 | . | . | 2 | ----------------------------------------- | 0 | . | < | x | x | > | . | 0 | . | ^ | ----------------------------------------- | . | . | . | 3 | . | 2 | . | . | 2 | v | -----------------------------------------
And all that's left is to place the remaining 3 caravels:
----------------------------------------- | 2 | | 1 | | 1 | | 3 | | | | ----------------------------------------- | < | > | | 0 | | < | x | > | 2 | 1 | ----------------------------------------- | 2 | | | | 1 | | | | | o | ----------------------------------------- | | | 1 | | | 0 | | ^ | 3 | | ----------------------------------------- | o | | | ^ | | | | v | | 0 | ----------------------------------------- | | | 3 | x | 3 | | | | | | ----------------------------------------- | o | | | v | 2 | | | 1 | o | | ----------------------------------------- | | | | 4 | | | 1 | | | 2 | ----------------------------------------- | 0 | | < | x | x | > | | 0 | | ^ | ----------------------------------------- | | | | 3 | | 2 | | | 2 | v | -----------------------------------------