XY-Wing Sudoku Technique

Updated 11 August 2026

An XY-Wing links three cells that each hold exactly two candidates so that, whichever value the middle cell turns out to hold, a shared candidate can be erased from any cell that sees both of the other two.

When an XY-Wing applies

The fish patterns reason about one digit across several units. An XY-Wing reasons about three digits across three cells instead. Pick a pivot cell with exactly two candidates, X and Y. Find two pincer cells, each seeing the pivot, where one pincer holds X and a third value Z, and the other holds Y and the same Z. The pivot must hold either X or Y — there is no third option — and whichever it holds forces one of the two pincers to hold Z instead.

If the pivot turns out to hold X, the X-sharing pincer cannot also hold X, so it must hold Z. If the pivot holds Y, the same argument forces the other pincer to hold Z. Either branch ends with some cell in the wing holding Z, so any cell that sees both pincers — even though it sees neither branch specifically — cannot hold Z itself.

The pivot does not need to see both pincers through the same kind of unit. One pincer might share the pivot’s row, and the other its box; what matters is that both pincers see each other closely enough that a target cell can see them both, usually because all three cells share a row, column or box in some combination.

Worked example

r4c7 is the pivot, with candidates 1 and 4. r4c5 shares the pivot’s candidate 1 and also carries 9. r4c2 shares the pivot’s candidate 4 and also carries 9. The pivot must hold either 1 or 4. If it holds 1, r4c5 cannot, so r4c5 must hold 9. If the pivot holds 4, r4c2 cannot, so r4c2 must hold 9 instead. Either way, one of the two pincers ends up holding 9.

r4c4 sits in row 4 alongside both r4c5 and r4c2, so it sees both pincers directly. It was carrying 8 and 9 before the deduction. Since one of the two pincers must hold 9 regardless of which value the pivot takes, r4c4 cannot hold 9 either, and the solver removes it, leaving 8 behind as a naked single for the next pass.

How to spot an XY-Wing

1. Find a bivalue pivotLook for a cell with exactly two candidates, X and Y. Cells with only two candidates are the only useful pivots.
2. Find two pincers that each see the pivotEach pincer must share a row, column or box with the pivot, hold exactly two candidates, and include one of X or Y.
3. Check the pincers share a third valueBoth pincers must carry the same third candidate, Z, alongside their shared value with the pivot. If they do not match on Z, the wing does not close.
4. Erase Z from cells that see both pincersAny cell, other than the pivot and pincers themselves, that sees both pincers cannot hold Z and can have it removed.

Common mistakes

• Allowing a pivot or pincer with three or more candidates. Every cell in an XY-Wing must be strictly bivalue for the either/or argument to hold.
• Eliminating Z from the pivot or the pincers themselves. The elimination only reaches other cells that see both pincers.
• Accepting two pincers that do not actually share the same third value. If one pincer’s non-pivot candidate differs from the other’s, there is no shared Z to eliminate.
• Forgetting that a pincer only needs to see the pivot, not the other pincer. The target cell is what needs to see both pincers, not the pincers needing to see each other.