TECHNIQUES FOR SOLVING AKARI PUZZLES

In this discussion, the following cell types will be referred to:-
  • PATTERN These are the black cells, some of which will contain numbers indicating the number of adjacent cells (horizontal and vertical) which contain lamps.

  • LAMP Cells which have had a lamp inserted into them.

  • LIT Cells which have been illuminated by a previously inserted lamp. They are colored white.

  • NOLAMP Cells which will NOT contain a lamp, but have not yet been illuminated. They are colored yellow.

  • DARK Uncommited cells waiting to be designated as LAMP, LIT, or NOLAMP. They are colored light gray.

  • When specific cells need to be referred to, they will be designated as C4-R3 which means the 4th cell in row 3.
The following presents a number of strategies which you should apply in turn. Note that the successful application of a strategy opens up new opportunities which permit the successful application of other strategies within the list. Consequently, if the puzzle is not solved after the first pass through the list, you should continue to repeat the process, until the puzzle is solved.

For a description of AKARI puzzles, refer to  Building Akari Puzzles 

Required Lamp(s)

This is the most fundamental strategy available for the solving of Akari puzzles. If you make a puzzle having a difficulty level of 1, then you will be able to solve it completely using only this strategy.

The three cells highlighted in blue draw your attention to the pattern cell containing a 3. This cell requires 3 lamps in its horizontally and vertically adjacent cells, and only three such cells are available. You have no option but to place a lamp into each of these 3 cells.


Type 1 Prohibited Lamp(s)

There are three strategies which can be used to identify cells which are not permitted to contain a lamp (Prohibited Lamp cells). This is the simplest of those strategies.

The two cells highlighted in blue draw your attention to the pattern cell containing a 2. This cell requires 2 lamps and closer inspection reveals that it already has its complement of 2. Consequently, the two highlighted cells may be designated as Prohibited Lamp cells.


Orphan Cell(s)

Sometimes it happens that the only way in which a cell can be illuminated is to place a lamp into that cell. The highlighted cell shown here is such a cell. It is shielded from other cells in the same column by the two pattern cells. Other cells in the same row are shielded from it by pattern cells, or are already designated as either Illuminated or Prohibited.

The highlighted cell is referred to quite appropriately as an Orphan Cell, and there is no option but to fill it with a lamp.


Type 2 Prohibited Lamp(s)

The two cells highlighted in blue draw your attention to the pattern cell containing a 3. This cell already has one lamp, so two additional lamps must be placed into the three remaining vacant cells. There is no way of knowing just yet which two cells they will be, but a little thought will convince you that regardless of which two cells contain the lamps, the two highlighted cells will end up being illuminated. Since an illuminated cell may not also contain a lamp, the two highlighted cells must be designated as Prohibited Lamp Cells.

Illuminate Prohibited Lamps(s)

In this case, the single highlighted cell draws your attention to the Prohibited Lamp Cell at C5-R3. This cell is not yet illuminated, and is not permitted to contain a lamp. It must be illuminated by a lamp in some other cell, and the only cell capable of doing this is the highlighted cell. Consequently, it must be filled with a lamp.

Type 3 Prohibited Lamp(s)

The single highlighted cell draws your attention to the Prohibited Lamp Cell at C7-R6. This cell is not yet illuminated, and is not permitted to contain a lamp, so it must be illuminated by some other lamp. It is easy to see that there are exactly two cells which could complete this task, viz. C7-R5 and C8-R6. Regardless of which of these cells contain the lamp, the highlighted cell will be illuminated by it. This being the case, it qualifies as a Prohibited Lamp

Three and One configuration

The two highlighted cells draw your attention to the pattern cell containing a 3. This cell requires three lamps, but has four vacant adjacent cells. We need to determine which of the four will contain lamps. The diagonally adjacent pattern cell containing a 1 gives us the answer. Of the two cells C6-R4 and C7-R3, only on is permitted to contain a lamp, thus forcing the two highlighted cells to contain a lamp.

Two and One configuration

The highlighted cell draws your attention to the pattern cell containing a 2. This cell requires two lamps, but has three vacant adjacent cells. We need to determine which of the three will contain the lamps. The diagonally adjacent pattern cell containing a 1 gives us the answer. Of the two cells C2-R6 and C3-R5, only on is permitted to contain a lamp, thus forcing the highlighted cell to contain a lamp.

Astute solvers may find other, more obscure strategies which they can apply. However, the strategies listed here are guaranteed to solve any AKARI puzzle created by Magnum Opus.