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

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

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.

19 October 2020

by Don

by Don

RE: Comments and feedback for xyWing

I see that you cover X Wing and XY Wing but not the XYZ Wing. Could you add an explanation of XYZ Wing?

I see that you cover X Wing and XY Wing but not the XYZ Wing. Could you add an explanation of XYZ Wing?

Sudoku Rules and Techniques

Sudoku Rules

Acknowledgments

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

SudokuWiki.Org by Andrew Stuart

PaulsPages.co.uk by Paul Stevens

Sudoku Rules

Cross Hatching

Counting

Naked Set

Hidden Set

Claiming

Remote Pairs

X Wing

XY Wing

Simple Coloring

Fishy Things

Unique Rectangle

X Chain

Aligned Pair Exclusion

Forcing Chains

Finned Fishy Things

Almost Locked Sets

Counting

Naked Set

Hidden Set

Claiming

Remote Pairs

X Wing

XY Wing

Simple Coloring

Fishy Things

Unique Rectangle

X Chain

Aligned Pair Exclusion

Forcing Chains

Finned Fishy Things

Almost Locked Sets

Acknowledgments

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

SudokuWiki.Org by Andrew Stuart

PaulsPages.co.uk by Paul Stevens