How to Solve Lighthouse Battleships Puzzles
Some of the most interesting puzzles combine concepts from two simpler puzzles to present a new challenge. In this case, we’re placing a Battleships fleet into a grid, but we’re not using clues outside the board to count segments. Instead we use the Lighthouses rules to find them from cells inside the grid that essentially create known “islands” of water cells in the process.
Rules
Use number clues in lighthouses to locate a hidden fleet of ships.
- Numbers indicate how many total ship segments that lighthouse sees in its row or column. Nothing blocks their view.
- No ship touches a lighthouse or other ship in any direction, including diagonally.
- Ships may be rotated.
- Any given ship segments are exactly the type shown (barrel, end, or middle) and in the correct orientation.
- Some segments may be “hidden,” not seen by any lighthouses.
Numbers count segments. Note you see through lighthouses and ships. 
Lighthouses and ships must be completely surrounded by water. 
Some segments or ships may be hidden from the lighthouses’ view.
The fleet refers to all of the ships you must find in the grid. The exact makeup will change in different puzzles. I like theming this puzzle with pirates, so I use names from the age of sail. Possible ships include: Dreadnoughts (5 segments), Caravels (4 segments), Sloops (3 segments), Rowboats (2 segments), and Barrels (1 segment). You might see them as triangles, squares, circles, etc.
The most common fleet consists of: 1 Caravel, 2 Sloops, 3 Rowboats, and 4 Barrels.
Basic Techniques to Solve
- Always mark any known water cells.
- Extend from known segments.
- Search for the largest ships early.
- Big clues light the way.
- Mark out any completed clue or found ship.
Find the Water
Water cells create restrictions for possible ship placements, so it’s important to mark them when you find them. When solving any variation of a battleship puzzle, marking the known water cells is always a good first step. Cells that must be water include:
- All 8 cells surrounding a lighthouse or known submarine.
- All 4 diagonally adjacent cells to any known ship segment
- The 3 orthogonally adjacent cells at the tip and sides of a known end segment.
Surround lighthouses and barrels with water. 
Ships are never placed diagonally, so regardless of orientation, these cells must be water. 
A tip has a known orientation, so surround the end and sides with water.
Extend Known Segments
Any ship segments in the initial puzzle are always the correct type. Take advantage of this to immediately place more segments and some extra water cells.
- Add an unknown segment next to an end-piece.
- A mid-ship segment could be oriented vertically or horizontally, but as soon as you have an adjacent water cell (or it’s against the grid edge), you can add two more unknown segments. Plus, you get to add a whole stripe of water!
Here, we have a known barrel, end piece, and mid-ship segment.As always, the first step is to add water. 
This water cell from the lighthouse reveals the orientation of the mid-ship segment. So we can mark another water cell on the other side. 
Then, we extend the known segments. The mid-ship piece ran into a dead-end below it, so that must be an end segment.
Look for Big Ships
Long ships always have the fewest possible placements once you’ve filled in all the water. So they will usually be the easiest to deduce. Look at each area of the grid with enough cells to fit the long ship, and imagine it in place. Most critically, imagine the water that must surround it. Did you just make it impossible to complete a lighthouse clue or fit one of the remaining ship types? Then you know the long ship must not belong there, and you can try another spot.
One thing to keep in mind – if you don’t see a conflict quickly, move on to another area of the grid. The goal here is to use the process of elimination, not take a guess and find out 15 steps later that you have to back up. Occasionally, you’ll find a placement that doesn’t immediately cause a conflict. In those cases, test it with the next-largest ship.
Large Clues Matter
You just saw how a large ship is restricted in its placement options by the conflicts it creates. Now let’s do the same with large clues. Look for one that has greatest restriction to fill its remaining quota. Count the number of cells left open to a large clue, and subtract the number of segments required. The lowest total shows you where you should begin testing.
The 7 lighthouse needs 6 more segments, and only has 7 open cells left. That means only one water cell. 
We can’t fill all 3 of these cells, because a Sloop would prevent the 5 lighthouse from being solvable. Therefore, the one empty cell must be along this stripe. 
The other cells must be segments, making a Sloop and a barrel (because that cell solves the 1 lighthouse). Adding the water proves the bottom ship is a Rowboat.
Mark Completed Clues
When you track what you’ve solved, you narrow your focus. You’ve found all the segments for a lighthouse? Great! Mark the rest of the cells in that row and column as water, and now you have one fewer option for any clues that look across them. While you’re at it, mark the lighthouse itself so you know which ones haven’t been completed yet.
You discovered both halves of a 2-segment ship? Wonderful! Cross it out from the fleet. When you’re considering other ships, you could find that placing one of them eliminates all remaining 2-segment ship options. If you still have one 2-segment ship left, you know it’s an invalid placement. You’ve probably noticed me making these markings in the examples above.
Solving the Puzzle
Now that we know how it’s done, we can move on to the walkthrough of our main example puzzle. If you’d like to try it yourself, here are the puzzles used in this tutorial:
Water and First Steps
Once again, this is our original example puzzle from the top. The first thing to do is fill in the known water. 
We don’t have any known segments to extend, and there are too many options to test large ships. So we’ll first look at this 5 lighthouse, with only 7 open cells. 
If we fill all four of these cells, we’d complete the 4 lighthouse. But once we mark all the water that would create, the 3 lighthouse can’t be solved.
Similarly, placing a Sloop and a Barrel solves the 4 lighthouse, and blocks the 3. 
In fact, any combination that completes the 4 lighthouse on this row will prevent the 3 lighthouse from being solved. 
So we know that Row 3 has a maximum of three segments. Therefore, the other two must be here to complete the 5 lighthouse. We found a Rowboat!
A Rising Tide
Continuing the thought, if we place all three segments along this stripe, the 3 lighthouse must place all its segments in Column 10, overfilling the 4. 
So after all that, we’ve proved that there must be a segment here, and two more segments somewhere along this stripe. 
Taking that a step further, that means that Column 10 can only contain one segment, so two segments must be in this stripe for the 3 lighthouse.
Any configuration of two segments along the stripes which don’t line up would cause a conflict. So we’re left with one of these two pairings. Can we eliminate one? 
Yes we can! Placing this pair forces the 5 lighthouse at the bottom to be solved, creating a conflict with the 2 lighthouse in the corner by giving it four segments.. 
By marking the water around these now known segments, we conveniently also solve the 2 lighthouse.
Find the Caravel
Now that we’ve filled so much of the grid, we can start to look for the 4-segment Caravel. We can immediately eliminate these areas, because placement there would overflow the lighthouses nearby. 
This option is out simply because it prevents the 2 lighthouse at the bottom from being solved. 
Placing here forces a Barrel at the top to complete the lighthouses in Column 10. This fills the 2 lighthouse, and prevents the 3 from being solvable.
Here, placement of a Caravel forces a Sloop in Column 4. Then we’d complete the 3 lighthouse, and both 2s at the bottom. Notice we no longer have space for all the ships we’d still have to place from the fleet. 
This option looks promising. Let’s try it for now. If we run into a conflict later, we know the onloy remaining position for the Caravel is horizontally on Row 8. 
Something important to note now, in order to save a lot of repetition in a moment. There must be one segment in Row 10, to satisfy the 5 and 2 lighthouses. That means there can only be one segment in Column 1.
Searching for Sloops
I drew a quick diagram with all the possible positions for Sloops which don’t immediately conflict with a lighthouse. Currently, we have 7. Can we remove some? 
A Sloop here blocks the 5 and 2 lighthouses from being solved, while overloading Column 1, which we know holds only one segment. 
This placement, on the other hand, solves the 5 and 2 lighthouses, but it still forces Column 1 to have an extra segment because of the 3 lighthouse.
That leaves 5 positions. Because 3 of them conflict with each other, we only have 7 possible combinations. 
This pair forces two more Barrel placements, and seems to satisfay clues. But there isn’t enough room for all the remaining ships. 
This option also looks good, until you notice that you can’t place the last Rowboat and Barrel in Row 1 without overflowing the 2 lighthouse.
Nope. This pair doesn’t leave room for two more Rowboats and three more Barrels. 
Here, we have no valid placement for the final Rowboat. 
Yet again, this pair doesn’t leave room for the remaining Rowboats and Barrels.
Once again, we have no valid placement for the last Rowboat. 
This is harder to see, but remember the lines must hold exactly one segment each. You can’t place two Rowboats without blocking at least one of the 3 Barrels. 
After eliminating all those pairs, we’ve proven the Caravel can’t be in Column 4. That means it must be in Row 8. We also confirmed a Sloop in Column 4.
A Wave of Revelations
To complete the 3 lighthouse, we must place a Rowboat here. This solves Column 10, and reveals a segment in Row 10. 
There are only two options for the second Sloop. It can’t be here, because it forces a Rowboat at the top, and now we can’t place the last 3 Barrels. 
Mark the last Sloop. We can’t solve the 2 lighthouse with a Rowboat, because we couldn’t then place 3 Barrels. Therefore, Row 1 is two Barrels.
We resolved all the lighthouses, but we still have 2 ships to place. A Rowboat here blocks the final Barrel. 
Therefore, we must place the last Rowboat here, and the last mystery segment is a Barrel. 
We’ve solved the Lighthouse Battleships puzzle!
