XY-Wing

How It Works

XY-Wing involves a pivot cell with two candidates (XY) and two wing cells. One wing has candidates XZ and the other YZ. Any cell that sees both wings cannot contain Z.

Step by Step

1. Find a pivot cell with exactly two candidates (X, Y).
2. Find two wing cells that each share one candidate with the pivot and have a common third candidate Z.
3. Eliminate Z from any cell that can see both wing cells.

When to Use

Use XY-Wing when you have a pivot cell with two candidates (X and Y) and two wing cells: one with X and Z, the other with Y and Z. Any cell that sees both wings cannot contain Z.

Example

Pivot has 3 and 7. One wing has 3 and 9, the other has 7 and 9. Both wings share a row/column/box with a third cell. That third cell cannot be 9, because 9 must go in one of the two wings.

Common Mistakes

Forgetting that the target cell must 'see' both wing cells (share a row, column, or box with each). Also, the pivot and wings must have exactly two candidates each.

Tips

Look for cells with two candidates that could form a pivot. Then search for wings that share one candidate with the pivot and have a common third candidate. The elimination applies to cells that see both wings.