The commonly used sudoku techniques are classified into Direct Elimination Techniques and Candidates Elimination Techniques. When the puzzle is relatively simpler, usingDirect Elimination Techniques can always get you very good results. If the puzzle is somewhat complex, however, you may dislike Direct Elimination Techniques due to its limitations. In this situation, Candidates Elimination Techniques can give you a big help. What's more, Candidates Elimination Techniques is much easier to be programmed and has an even higher efficiency in solving sudoku puzzles.

Before you start to use Candidates Elimination Techniques, you have to prepare a possible-candidates-grid like this:

On initialization, every cell includes all digits from 1 to 9. These digits represent the numbers that are possible to be filled into the cell. It is obvious that digits not listed in these candidates cannot be placed. According to sudoku rule, if a cell is filled with a certain number, then this number should be removed from the possible candidates of all cells in the column, row and block where the cell lies. For the following puzzle:

As soon as a number is placed in a cell, all possible candidates in this cell will be eliminated. In addition, the column, row and block where this cell lies should be updated immediately by removing this number from the candidates. For example, when we place number 3 in [A1]:

We remove all candidates at [A1] and update the candidates of the other cells in Row A, Column 1 and Block at [A1]:

Similarly, when other initial values are filled into the puzzle, we have to remove the number from the possible candidates of the corresponding cells in the columns, rows and blocks. After we have processed all the initial numbers, we finally get the following grid:

Please note that the order of placing numbers have no effects on the final grid.

Now we find that the possible candidates in each cell are greatly reduced. This is really an exciting start. We can use other techniques to reduce more candidates in a cell until only one candidate is left. And this sole candidate is the final solution to this cell. In the example above, we are happy to find that sole candidate 1 is left at cell [I1]. Now we can use Naked Single Technique.

In Candidates Elimination Techniques, most commonly used techniques include:

• Naked Single Technique
• Hidden Single Technique
• Intersection Removal Technique
• Naked Pair Technique
• Naked Triplet Technique
• Naked Quad Technique
• Hidden Pair Technique
• Hidden Triplet Technique
• Hidden Quad Technique
• X-Wing Technique
• XY-Wing Technique
• XYZ-Wing Technique
• Swordfish Technique
• WXYZ-Wing Technique

See Also:

• What is Sudoku: rules, history and terminology
• Sudoku Strategies
• Direct Elimination Techniques