Sudoku Solving Techniques

XY-Wing

Consider the following partial Sudoku puzzle:

a partial Sudoku with XY-Wing pattern

The red, green and yellow cells form a XY-Wing pattern. If the red cell is X, then the yellow cell must be Z and therefore the blue cell cannot be Z. If the red cell is Y, then the green cell must be Z and again the blue cell cannot be Z. So in either case, the blue cell cannot be Z.

In the case above, the cells XZ and YZ share a common row or a common column with the cell XY. Actually one of them can be in the common 3x3 box with XY. In the following case:

another partial Sudoku with XY-Wing pattern

The yellow cell XZ share a common 3x3 box with the red cell XY and the green cell YZ share a common row with the red cell XY. If the red cell is X, then the yellow cell must be Z and all blue cells cannot be Z. If the red cell is Y, then the green cell must be Z and again all blue cells cannot be Z. In either case, all blue cells cannot be Z.

Example:

a Sudoku with XY-Wing pattern

This Sudoku puzzle is the same as the one we used in the Swordfish section. Actually the figure above is the immediate step right after the Swordfish technique was applied. In the figure above, the three yellow cells form a XY-Wing pattern. The digit 1 in the blue cell now can be safely eliminated as a candidate. After that, this puzzle can be solved very easily.