How to Solve Lighthouse Puzzles
Lighthouses is another puzzle with an unknown history. This is unfortunately common with many types of games. The author puts something out there, possibly for a friend, and it gets passed around. Then it catches on, and by then, nobody remembers where it came from.
In a lighthouses puzzle, you will be using number clues to find single-cell ships hidden in the grid. I like to use tugboats in my theming.
Rules
Find all tugboats hidden in the grid, using number clues in the lighthouses.
- Each boat occupies a single cell.
- Lighthouses reveal all boats that share a row and column with it. Nothing blocks the lighthouse’s view..
- Numbers indicate how many boats are revealed by that lighthouse.
- Tugboats may not be adjacent to any other boat or lighthouse in any direction, including diagonally.
- Each boat is lit by at least one lighthouse.
Some puzzle setters ignore the last rule and include “hidden” ships, which are not revealed by any lighthouse. If that is the case, they will usually tell you the total number of ships in the grid, so you can be sure you’ve found them all.
Basic Techniques to Solve
- Mark all the water first.
- Count cells in pairs. Any 2×2 region only contains one boat.
- Start with larger clues.
- Mark water around stripes of cells that must contain a boat.
Mark the Water
In puzzles where the goal is to find hidden objects, it’s always important to mark cells that you know to be unoccupied. Every extra constraint on what you’re looking for helps. In this case, you know that boats may not touch each other or any lighthouse, even diagonally.
- First, mark all cells surrounding lighthouses as water.
- If you have any lighthouses that see zero boats, mark all cells in their row and column as water.
- In most puzzles, you can also eliminate all cells not seen by a lighthouse. The exception is if you’re given a boat total, implying that some may be hidden from view.
- Later, when you find boats, you can mark all the cells surrounding them as water.
- Finally, once you’ve revealed all the tugboats for a lighthouse, mark all the remaining cells in that row and column as water.
Adding water severely reduces the possibilities for cells containing boats.
Count in Pairs
Because no two ships are adjacent, it can be useful to count cells in pairs when you’re examining a row or column. In any two adjacent cells, if one is occupied, the other must be empty. This especially helps when you have a few single cells that are already surrounded by water – you might be able to prove that they hold a boat.
Similarly, remember that any 2×2 area of cells can only contain one tugboat. This point is tricky to elaborate on without seeing it in practice. It’s mostly used to find general areas that must contain a boat and compare them to earlier deductions with dominoes. When you know the general areas that boats have to be, you can use that to mark more water cells.
By counting in pairs, we narrow down five cells to three regions. This shows us one certain boat placement. 
In this grid, counting dominoes for this lighthouse limits boat placement to these 5 areas. We see one boat’s position for certain. 
Because there can only be one boat in each of these 2×2 areas, the adjacent cells must be water.
Large Clues are More Limited
In general, start with the larger clues. After you’ve marked the initial water cells, these will be the most constrained. As a result, you should be able to at least determine groups of cells that must contain a boat. If you’re lucky, you might even locate some of the tugboats for certain. You just saw an example of this above with the lighthouse showing a 5 clue.
Search for Stripes
The biggest reason that finding just the general area of boats is that you can create more constraints. There are a few patterns you can use when you have a stripe of cells that must contain boats. For simplicity, I’ll refer to “above and below” the stripe. However, if that stripe is vertical, then “left or right” would be the equivalent.
- Stripe of 2 cells that must contain 1 boat: Mark out the 4 cells above and below the stripe as water.
- Stripe of 3 cells containing 1 boat: Mark out the middle cell above and below the stripe as water.
Solving the Puzzle
Now that we have our techniques, we can walk through the solution of our example puzzle. If you want to attempt some of the example puzzles we’ve used, you can try them online.
First Steps
Here’s our example puzzle again. The first thing we’re going to do is mark all the water around lighthouses. 
Additionally, these cells aren’t seen by any lighthouse, so they must be water. Remember, not everyone uses this rule, so be careful with other puzzles. 
We want to start with one of the larger clues, and this lighthouse is the most restricted. It sees these four zones. Three are a single cell, so they contain boats.
Now, the blue cells must be water. This reveals the location of the fourth tugboat. We also solved this 2 lighthouse, so the rest of its column is water. 
Now here’s something interesting. This lighthouse only sees one boat. It can’t be in the row, so it must be in one of these two cells. 
That means it’s also seen by the 2 lighthouse. It’s already seen its second boat, so the remaining cells in its row must all contain water.
Revealing Boats
Next, we move on to this 4 lighthouse. We’ve found one boat, and it sees these three zones for the rest. That means two must fit in a stripe of three cells. 
There’s only one way to fit them. Then, we place water in the rest of the 2×2 area containing the last boat. 
Oh look! We just found the boat to solve these two lighthouses!
This lighthouse also sees only two cells, so they must both contain tugboats. 
Finally, we can place the last boat for both of these 4 lighthouses. Then, the water gives us the last boat. 
We’ve completed this Lighthouses puzzle!
