Sudoku HowTo

XY Wing

The XY Wing strategy uses three cells that contain two and only two candidates and have common values in the cells. Even though the name is similar, the XY Wing strategy is not related to the X Wing strategy.

The Pattern. Find a cell that has only two candidates. Call this the XY cell. Now find a buddy cell that also only has two candidates one of which is X. Call this the XZ cell. Now find another buddy cell that only has two candidates one of which is Y and the other is Z. Call this the YZ cell.

If this pattern is found, Z can be removed from any cells that are buddy cells to both XZ and YZ. Why?. In this pattern it does not matter which value you choose from the XY cell, it will cause Z to be placed in either the XZ or the YZ cell.

The XY Wing is the minimal version of the more generic XY Chain. The logic used here can be extended to a chain of any length.
The XY Wing pattern in Figure 1 shows an XY cell in green and the XZ and YZ cells in blue.

If the value 2 is placed in the XY cell then the XZ cell has to contain the value 6. If the value 3 is placed in the XY cell then the value 6 has to be placed in the YZ cell. No matter what is chosen for the XY cell there will be a value 6 in either the XZ or the YZ cell.

The value 6 can be removed from any cell that is a buddy cell to both the XZ and the YZ cells. The grey cells in this example.
The XY Wing pattern in Figure 2 shows an XY cell in green and the XZ and YZ cells in blue.

If the value 2 is placed in the XY cell then the XZ cell has to contain the value 9. If the value 1 is placed in the XY cell then the value 9 has to be placed in the YZ cell. No matter what is chosen for the XY cell there will be a value 9 in either the XZ or the YZ cell.

The value 9 can be removed from any cell that is a buddy cell to both the XZ and the YZ cells. The grey cells in this example.

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Acknowledgments

I would like to acknowledge these sites referenced for strategy ideas and solving techniques.

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