How to Solve Akari Puzzles
Akari, which means “light” in Japanese, is a logic challenge which first appeared in 2001 in Nikoli. A reader named going by the name Asaokitan submitted it among several new puzzle ideas. Originally, they named Akari “Bijutsukan”, meaning “museum,” and that is still the name of the puzzle in Japan today. Elsewhere, another common name is “Light Up.”
Why museums? Art and sculpture in museums benefit from complete, even lighting, and the goal in Akari is to light every cell , using number clues printed on the walls.
Rules
Place light bulbs in the puzzle in such a way to illuminate all of the unlit cells in the grid, using number clues and walls. Numbers on the walls indicate how many bulbs are placed orthogonally adjacent to them. Walls also block light.
- Bulbs shine as far as they can in all four orthogonal directions, unless blocked by a wall or the border. They do not light up any cells in diagonal directions.
- You may not place a bulb in the light path of another bulb.
- Numbered walls limit how many bulbs may be placed orthogonally adjacent to them. For example, a wall numbered 4 will have a bulb above, below, and to its left and right.
- Bulbs placed diagonally adjacent to a numbered cell do not count toward the limit.
- Not all walls are numbered. A wall without a number may have any amount of bulbs placed next to it, as long as all other rules are followed.
Basic Techniques to Solve
- Place bulbs where the number clue matches available spaces.
- Mark cells where a bulb can’t be.
- Find cells with limited lighting options.
- Use known clue patterns.
- Force an invalid chain reaction.
Clue Matches Space
The first thing to look for are clues that have that exact number of unlit cells adjacent to them. A 4 clue will have a bulb in all spaces around it, as will a 3 on the border, or a 2 in the corner. Periodically, look for clues in your puzzle that have had their placement options narrowed down to match the limit.
Mark Non-Bulb Cells
Whenever you can, mark where a bulb cannot be placed. Doing so helps you narrow down cells that are available to you. For example, when you see a wall with a clue of 0, cross out all of its orthogonally adjacent cells. Once you’ve placed a number of bulbs that satisfy a clue, cross out the remaining spaces, if any.
In addition, when you have a 3 surrounded by empty cells, a 2 on the border, or a 1 in the corner, you might not know the exact placement of the bulbs, but you can still cross out the diagonally adjacent spaces. This is because placing a bulb on these cells would shine on any legal bulb put in the orthogonally adjacent cells.
Finally, when you do place a bulb, draw lines to help you remember what cells it illuminates. Online, I simply change their color to show they are lit, but most pen and paper solvers use lines.
Limited Light Options
After you’ve marked and eliminated cells with the tips above, start looking for areas that only have one way to light them. Search for a cell surrounded on three or four sides by walls or eliminated spaces, and scan along the remaining direction for an open cell where you can put a bulb that will illuminate it. Sometimes, it will be the surrounded cell itself.
Let’s look at our example puzzle. After eliminating all of the cells around the 0 clues, I was able to cross out the diagonals around a few more numbers. Next, I placed a couple of bulbs next to some 1 clues which only had one space remaining. From this point, I stopped looking at just the clue numbers and examined the puzzle layout.
Zoom in on the right side of the board to see a cell which is surrounded by walls on three sides. The only direction out has one eliminated space before it runs into another wall. Therefore, it must contain a bulb, because that’s the only way to light it. That satisfies the 1 clue, and we mark out the remaining cells around it.
Use Clue Patterns
As you get more proficient and start to work on more complex and intricate Akari puzzles, you will find it useful to learn patterns of clues that force bulb placement and cell elimination. Two of the most common patterns you might see include:
- A pair of 3 clues in the same row or column with one cell between them. That cell must contain a bulb. Otherwise, the bulb placement in the remaining three cells around each clue forces bulbs to shine on each other. In addition, we can conclude that a bulb must be at both ends of the clue row (or column), to avoid the same issue of one bulb lighting another. This pattern of clues can only result in two possible configurations.
- A clue of 2 with one side blocked off, and a 1 diagonally adjacent to the clue, but not the eliminated cell. A walled off or eliminated cell next to the 2 but not the 1 forces one of the bulbs around the 2 to be adjacent to the 1. As you can see, both clues share two of the three possible placements around the 2. Because there must be a bulb in one of the shared cells, we can eliminate any other spaces around the 1 clue. Finally, we can also deduce that the second bulb around the 2 must be in the cell not shared with the 1.
Force Invalid Chains
Sometimes, you just get stuck, and can’t simply find the next step with basic logic. In that case, look for a clue or an unlit region with only 2 possible bulb placements. Try to find a single cell that you can mark with a bulb or an X and change the state of a lot of nearby cells. You’re trying to create a series of chain reactions that will create an invalid placement, so that you can eliminate one of the options. Once you reach that point, simply back up, mark that cell as the opposite option to the one you chose, and move forward with the other possibility.
Sometimes, you will reach another branching choice instead. Do not make another choice and continue, because you might be on the wrong path. If you move forward, you will overcomplicate your path back to the original choice. Instead, back up, and try the other option, to see if you can eliminate it. If that leads to a branching choice as well, back up again, and try a different area of the puzzle.
Solving the Puzzle
Now that we’ve seen examples of solution techniques, let’s start over with our example puzzle. To keep things neat, once a cell is lit by a bulb, I will remove red X’s that marked an eliminated cell in earlier steps. Whenever I reach a branch point, I will also demonstrate the incorrect placement each time, so you can see why it’s wrong, rather than solving the puzzle by luck.
First Steps
Starting the example Akari puzzle 
We don’t start with easy bulb clues, but we can eliminate all cells around 0s. 
These 1s have only one space left to place a bulb.
These cells must contain a bulb, or they can’t be lit. 
Eliminating cells around the solved 1 reveals a cell that must hold a bulb to be lit 
Next, let’s eliminate some diagonal cells around limited clues.
You can’t light these cells from another position, so they must contain bulbs 
Place a bulb to the right to light this cell.
First Branch
We’ve reached out first branch point. Eliminating this cell would force 3 bulbs, so let’s try that.. 
We can only light these cells by placing bulbs that shine on each other. This branch is invalid, so we know a bulb is in the original cell. 
That new known cell didn’t move us forward much. Next, we’ll try placing a bulb here to solve the 2.
That forces these three cells to hold bulbs. 
Now we’re unable to light this cell, so we know the original bulb goes in the other cell next to the 2. 
A bulb in the purple cell blocks the blue cell from being lit, so we must place it in the other position to solve the 2.
That forces bulbs into these two spaces. 
We’ve solved the 2, and we must place a bulb in the other cell to light it. 
We can only light the circled cells by solving the 3 in this configuration.
We can eliminate another diagonal cell, but we reached another branch point. Place a bulb here to test it. 
We force these two bulbs to light the circled cells. Bulbs can’t shine on each other, so the initial bulb is invalid. 
We’ve solved the other 1 clue.
If we place a bulb in this corner, we can’t light the blue cell, so we can eliminate it. 
Place bulbs here to light the remaining cells in this area.
The Last Region
Another branch point, so try eliminating this cell for the largest change. 
That forces bulbs into these three cells. 
By marking eliminated spaces around solved clues, we reveal two more bulbs.
Now you can’t light the remaining spaces without putting a bulb in both blue cells. The purpla cell must be a bulb.. 
Solve the 1 with a. bulb in this cell. 
That forces these two bulbs and completes their clues.
Now, place the last two bulbs here. 
We’ve solved the example Akari puzzle!
