Sudoku Solving Techniques

XYZ-Wing

Consider the following partial Sudoku puzzle:

a partial Sudoku with XYZ-Wing pattern

The yellow cell XZ shares a common 3x3 box with the red cell XYZ and the green cell YZ shares a common row with the red cell XYZ. These three cells form a XYZ-Wing pattern. If the red cell is X, then the yellow cell must be Z and therefore the blue cells cannot be Z. If the red cell is Y, then the green cell must be Z and the blue cells cannot be Z. If the red cell itself is Z, then again the blue cells cannot be Z. So in any of these three cases, the blue cells cannot be Z.

Note that this technique also works if the green cell YZ shares the common column with the red cell XYZ.

Example:

a Sudoku with XYZ-Wing pattern

The yellow cells in this Sudoku puzzle form a XYZ-Wing pattern. The digit 3 in the blue cell can be safely eliminated as a candidate. After that, this puzzle can be solved very easily.