XY-Wing Sudoku Strategy (Y-Wing) Explained
The XY-Wing, also called a Y-Wing, uses three bivalue cells. A pivot {X,Y} sees one pincer {X,Z} and another pincer {Y,Z}. The pincers do not need to see each other. Whichever value the pivot takes, one pincer must contain Z, so any cell that sees both pincers cannot keep Z.
The pivot chooses the branch; both branches force the same candidate at one of the two pincers.
What is an XY-Wing?
An XY-Wing is a three-cell chain with exactly three digits. Every involved cell must be bivalue: the pivot contains X and Y, while the pincers contain X/Z and Y/Z. Each pincer must see the pivot. A valid elimination target must see both pincer cells, because Z is guaranteed in one of them.
How to verify an XY-Wing
- Find a bivalue pivot. Start from a cell with exactly two candidates, X and Y.
- Find two matching pincers. One visible bivalue cell must be X/Z and another visible bivalue cell must be Y/Z.
- Check the three-digit structure. The cells must use only X, Y, and Z in the required pairs.
- Find common peers of the pincers. Remove Z only from cells that share a house with each pincer.
Example: pivot {2,5}, pincers {2,8} and {5,8}
If the pivot becomes 2, the {5,8} pincer must be 8. If the pivot becomes 5, the {2,8} pincer must be 8. Candidate 8 is therefore true in one pincer.
- Check visibility. Both pincers see the pivot; they may sit in different houses.
- Follow both pivot outcomes. Pivot 2 forces one pincer to 8, while pivot 5 forces the other to 8.
- Remove the shared candidate. Delete 8 from any unsolved cell that sees both pincers.
Common XY-Wing mistakes
Using a three-candidate cell
The standard XY-Wing requires all three cells to be bivalue.
Making the pincers see each other
That is not required; only each pincer-to-pivot link is required.
Deleting from a partial peer
The target cell must see both pincers, not merely the pivot or one pincer.
XY-Wing practice checklist
- List bivalue cells after simpler eliminations stop.
- Choose a pivot and look for one partner for each of its two candidates.
- Name Z and highlight only cells that see both pincers.
The easiest way to trust an XY-Wing is to test the pivot’s two outcomes aloud. If both outcomes force the same Z conclusion and the target sees both pincers, the elimination is logical.
XY-Wing FAQ
Are XY-Wing and Y-Wing the same technique?
Yes. Both names commonly describe the same three-bivalue-cell pattern.
Must the two pincers see each other?
No. Each pincer must see the pivot, and the elimination target must see both pincers.
Can the pivot and pincers be in one box?
They can, but the required visibility and bivalue candidate pairs must still hold.
