Techniques

In this article we explain some techniques to solve sudoku games, from the simplest to the most complex.

1. Unique number to place in a cell

The first and easiest trick to solve the game is the unique number to place in a cell. Look at the examples in the diagram.

In example 1, we see a highlighted cell in row 2 and column 2, where we must put a number. In the same row we have placed numbers 1, 2, 3, 4, 6 and 7. In the same column we have placed numbers 1, 3, 4, 5 and 7. In the same region we have placed numbers 2, 3, 4, 5, 6, 7 and 8. In summary we have :

In the Row	1	2	3	4		6	7
In the Column	1		3	4	5		7
In the Region		2	3	4	5	6	7	8

Consequently, the only possible number to locate in the indicated cell is number 9. Any other is already present in the row, column, or region, and would be incompatible.

Let’s review example 2, we see a highlighted cell in row 7 and column 4, where we must put a number. In the same row we have placed numbers 7 and 9. In the same column we have placed numbers 2, 3, and 8. In the same region we have placed numbers 1, 5, 6, 5, 7 and 8. In summary we have :

In the Row							7		9
In the Column		2	3					8
In the Region	1				5	6	7	8

Consequently, the only possible number to locate in the indicated cell is number 4. Any other is already present in the row, column, or region, and would be incompatible.

2. Unique cell to locate a number

The second and equally easy trick to solve the game is the only cell to place a number. Apparently it could be interpreted as the same as the previous one -although they can coincide sometimes- but they are not the same. Look at the examples in the diagram.

In Example 1, we see the highlighted number 7 in the board. If we try to place that number in the lower left region, we will see that the only possible cell in that region to put the number 7 is the one indicated in the diagram highlighted , the cell in row 8 and column 3. That cell would also allow the numbers 3, 5, 6, 8 and 9, all of them compatible with the row, column and region, but it is the only one that allows the number 7 to be placed.

In the Row	1
In the Column	1	2		4
In the Region		2

In Example 2, we see the highlighted number 4 in the board. If we try to place that number in the central left region, we will see that the only possible cell in that region to put the number 4 is the one indicated in the diagram highlighted , the cell in row 5 and column 3. That cell would also allow the number 9, which is also compatible with the row, column and region, but it is the only one that allows the number 4 to be placed.

In the Row	1		3			6
In the Column	1	2	3		5		7	8
In the Region	1		3		5	6	7	8

3. Using the pencil for possible numbers in each cell

Using the pencil to write down possible numbers in each cell you can see the board with all the options. Always you will find cells with only one option to fill, so is a good idea to begin placing that cells with that numbers.

In the following diagram you can see two examples of the use of the pencil to complete options for each cell.

As you complete the cells that have a single option, those numbers from other cells begin to be discarded, which allows you to advance in the solution of the game until it is completed.

The following diagram shows how to advance in the solution of the game by choosing cells with a single option to place.

4. Single option discards

Single option discards

5. Pairwise discards

Pairwise discards

Other topics

CrossGames21	Presentation
The Sudoku Game	Explanation of the sudoku game
Games	Explanation of all games in CrossGames21.com
Levels	Difficulty levels of the games
Rules	Use of options / board and keyboard in CrossGames21.com
Techniques	Tricks to solve sudoku games
Statistics	Statistics of games in CrossGames21.com