How to Solve Munraito Puzzles
Munraito (Sun and Moon) is one of over 400 types of puzzle invented by Japanese designer Naoki Inaba. Several “moons” appear in a grid, and your goal is to place stars and clouds in each row and column to light the moons as shown. Because of the theme described for the symbols, some publications renamed the puzzle to Star Clusters.
Rules
Initially, only the moons are given. Some are completely in shadow, and others have part or all of their surface lit. Your goal is to place exactly one star and one cloud in each row and column through deductive reasoning.
A star’s light travels horizontally and vertically, unless blocked by a cloud or moon. Because a star lights up the moons, you may not place one next to the unlit side of a moon.
A cloud blocks any light that reaches it. As a result, you can’t place a cloud directly adjacent to the lit side of a moon, nor can you put it between a star and the lit side of a moon.
Again, each row and column contains exactly one cloud and one star – no more or less. In most abstractions of the puzzle, the cloud is represented by a simple black square. Some star and cloud placements may not affect any of the moons.
Basic Techniques to Solve
- Look for moons with lit sides facing each other.
- Focus on the stars first.
- Block light where needed.
- Remember the limits for each symbol.
Start with Lit Moons
Anytime the lit face of two moons point toward each other, you can be certain that a star must be between them. First, search for lit moons with a gap of only one cell. When you see this, place a sun in that empty cell.
When there is a gap of more than one cell, try to eliminate options by looking at other clues. Shadowed faces adjacent to a potential cell can help to eliminate it as an option.
Focus on Star Placement
Light sources are the key to solving a Munraito puzzle. Because the goal is to place stars based on how the moons are lit, your best bet is to focus your efforts first on where that light must originate. Search along the row or column next to a lit face, and eliminate any cells where unlit surfaces nearby prevent a star.
You might not find all the stars at this stage, but this will still reveal many of them.
For now, don’t worry about accidentally lighting shadowed moons, if there is at least one empty cell between it and the star. We can block that extra light in a moment.
Place Clouds to Block Light
Now that you’ve placed a few stars, it’s time to start looking for shadows and adding clouds to the grid.
Find unlit or partially-lit moons facing your stars. In order to prevent a star’s light from reaching the moon, you must place a cloud between them. In some cases, this is easy – there will be only one possible cell for the cloud.
Sometimes, you will find a range of cells that must contain a cloud, but you can’t narrow your options down to one. You will have to use other methods to discover the correct placement.
Use Limits for Symbols
Remember, each row and column may only contain one of each symbol. This helps the solution process in two ways.
First, you can use known placements to eliminate options along a range where simple adjacency hasn’t resolved a cloud or moon. Once you determine the possible set of cells, check rows and columns that cross it to see if that symbol already exists. If so, you may eliminate that cell as an option.
Second, use this rule to deduce cells where neither a sun nor cloud can exist. Knowing that certain cells must be empty can assist you when thinking about the paths light and shadow may take.
Solving the Puzzle
Now that we’ve seen the basic techniques, let’s solve the rest of our example puzzle.
Locate the Remaining Stars
In this range, you can only place a star in the bottom right corner to light this moon. 
The board is filling up, so let’s take stock for a moment. These moons still require a star for light. 
Use the existing stars and shadowed moons to eliminate cells along the ranges required. We can eliminate the yellow cell, because a star there would mean the moon above it could not be lit.
Placing that star begins a chain reaction. Row 3 now has only one possible placement for a star. 
This leaves one option for a star in row 2. 
Now we place our last star in Row 1.
Find the Rest of the Clouds
Now we turn our attention to the clouds. There must be a cloud in this 2-cell range to leave the moon in shadow. 
But, a cloud must be placed in this range, too. Now we can eliminate one cell, and we know where one cloud is. 
In this range, we can eliminate this cell because there is already a cloud in the column.
Now we can narrow down this range to one option for a cloud. 
In the bottom row, a red X marks columns that already have a cloud. We can’t put it in the dark X position, because it would block light we need. 
When we eliminate columns with clouds in the top row, we’re left with one cell.
We can finally block the extra light to the last moon. 
This is the last cell without a cloud in its row or column. 
We’ve solved the Munraito puzzle!
