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XY-Wing

Three two-candidate cells that trap a digit, whichever way the pivot goes.

The XY-Wing (also called the Y-Wing) uses three cells that each have exactly two candidates. The pivot holds {X,Y}. One wing, which shares a unit with the pivot, holds {X,Z}; the other wing, also seeing the pivot, holds {Y,Z}. If the pivot is X, the first wing must be Z; if the pivot is Y, the second wing must be Z. Either way, one wing is Z — so Z can be removed from any cell that sees both wings.

Worked example

The pivot {1,2} sees the wings {1,3} (same row) and {2,3} (same box). One of the wings must be 3, so 3 is removed from every cell that sees both wings (shaded).

How to apply it

1

Find a cell with exactly two candidates — call them X and Y. This is the pivot.

2

Look for a two-candidate cell the pivot can see that holds X and a new digit Z.

3

Look for another two-candidate cell the pivot can see that holds Y and the same Z.

4

Make sure the two wings are not the same cell and do not both contain X or both contain Y.

5

Remove Z from every cell that sees both wings.

When to use it

The XY-Wing is one of the most useful expert-level techniques because two-candidate cells are common late in a hard solve. On Sudoku.tips, many expert puzzles need it at least once.

Frequently asked questions

Is the XY-Wing the same as the Y-Wing?
Yes, the two names describe the same pattern. Its close relative, the XYZ-Wing, uses a pivot with three candidates and needs a target cell that sees all three cells.