# ALS-XY-Wing

The ALS-XY-Wing rule is a solving technique that uses three Almost Locked Sets.

Make sure you understand the concept of Almost Locked Sets before you proceed.

### How it works

Say we have three Almost Locked Sets A, B and C. Suppose

- The digit Y is a restricted common of A and C, and
- The digit Z is a restricted common of B and C.

Then for any digit X that is a common candidate for A and B, we can eliminate X from any cell that sees all cells belonging to either A or B and having X as a candidate.

Observe that this technique is very similar to XY-Wing, and hence its name. The similarity can be illustrated by treating A, C and B as nodes in a chain of length three, with C being the pivot.

### Note on notation

Unlike ALS-XZ and XY-Wing, which eliminates the digit Z, the ALS-XY-Wing eliminates the digit X instead. Unfortunately, this inconsistent notation is widely used by the Sudoku community.

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