How to Solve Retrograde Battleships Puzzles
Retrograde Battleships is similar to the standard Battleships puzzle, but leans harder into the trial-and-error aspect.
This time, the grid is pre-filled with ship segments, and your goal is to color in the correct pieces to place all the ships in the fleet, so that no ship touches another, not even diagonally.
While it can sometimes vary with different puzzles, this is the most common fleet. One 4-segment battleship, two 3-segment carriers, three 2-segment destroyers, and four single-cell submarines.
Unlike the standard Battleships puzzle, which has number clues showing how many segments are in a row or column, but may belong to different ships, Retrograde Battleships shows you multiple possible placements of all the different ships. You challenge is to find which ones are correct, in that they allow all the other ships to be placed without touching.
The best way to work this puzzle is to start with the larger ship placements and work your way down to the small ones. It will eliminate dead-end options more quickly that way.
In our example, we have two possible positions of the battleship. To start our elimination process, we will begin with the vertical option, because it will eliminate the most cells around it.
With pen and paper, you will typically use a dot to mark your current chosen segments, and an X to mark the cells you eliminate. Here, I’ll color eliminated cells blue purely are a stylistic choice.
Here we have the vertical battleship with all the cells around it are filled to prevent other ships being placed adjacent to it.
Notice that we have a few other cells filled in addition to those directly next to the battleship. This is because ships from the fleet must be placed complete, so if we eliminate one segment, we must eliminate all of them.
The next-largest ship is the 3-segment cruisers, and there are two of them in the fleet. Here are the remaining options for placement.
Either of the options in the bottom right corner will eliminate the other one, so those would be the best place to start to check options for this branch of testing. I’m going to use the vertical one, because again, that will affect the most cells around it, which can lead to contradictions more quickly.
And here we are, left with two options for the second cruiser. Trying the one on the top right covers three cells around it, rather than the one that the vertical option on the left will eliminate, so I’ll try that for our next step.
Once we block out all the water spaces that would be created, including the other cruiser spot, since there can only be two, we discover that there would be exactly four submarine options.
Because there are four submarines in the fleet, we would have to use all of them, which would result in turning all the segments highlighted in blue into water.
This would leave us only one option for our destroyers. Since there need to be three in the fleet, that means that this combination of cruisers is invalid.
Looks like that’s even worse! Again, we end up with only four places left for submarines, but this time, they eliminate all the destroyer positions.
Now we know that the vertical placement of the two cruiser options on the bottom right is definitely incorrect.
Next, we’ll try the horizontal one, and try the two options for the cruisers at the top one more time.
Well, that gives us a few more options. There are 6 options for submarines, and 7 for destroyers.
Rather than testing combinations, we’re going to take advantage of the fact that the destroyers are mostly clustered together. We know that we need to place three of them, so I’m going to try one at a time and see what cells it eliminates, to find out if there would still be enough room for the others.
To save space, if an option leaves exactly enough places for the other two ships, I’ll go ahead and fill those out, too. That way, we can check if there would be options left for the 4 submarines.
The pink destroyer started out good, forcing the other two positions (in yellow), but the result leaves us with only three spaces for submarines, so along this branch, these two cells would have to be water, no matter what other destroyers we place.
This destroyer placement also can’t work. As you see here, we would be left with five positions for submarines.
Option 4 can’t be used, because it would eliminate two out of the three remaining destroyer positions, leaving us with only one spot for the two other desroyers in the fleet.
This leaves us with four definite submarine spots. However, both positions 2 and 5 eliminate a destroyer, again giving us only one place left for two remaining destroyers.
This placement only leave us with 3 submarines, so it’s no good, either.
With this option, we eliminate not only the ships directly adjacent, but also the third destroyer option on row 5, which we just proved can’t be an option with the last test.
This leaves us with only two options for destroyers, and we fill in the submarine cells next to them.
Now we only have 4 submarine cells left, and if we count it all up, we have 1 battleship, 2 cruisers, 3 destroyers, and 4 submarines on the grid, none of them touching another.
We have solved the puzzle!
Here is how the completed puzzle will normally look.
