XYZ-Wing Sudoku Technique

Updated 11 August 2026

An XYZ-Wing tightens the XY-Wing by giving the pivot cell all three candidates involved, X, Y and Z, so the elimination only reaches cells that all three cells of the wing see at once.

When an XYZ-Wing applies

An XY-Wing’s pivot has only two candidates, so it never itself carries the value being eliminated. An XYZ-Wing’s pivot carries all three: X, Y and Z. Two pincers each see the pivot and each hold one of X or Y alongside the shared value Z. The pivot must end up holding X, Y or Z. If it holds X, one pincer is forced to Z. If it holds Y, the other pincer is forced to Z. If it holds Z itself, the pivot is Z. Every branch ends with the pivot or one of the pincers holding Z.

Because the pivot itself is one of the three cells that might hold Z, any target cell has to see all three — the pivot and both pincers — for the elimination to be safe. That usually means the wing sits inside a single box, with the pivot and pincers close enough together that a target cell shares a unit with all of them.

This is stricter than an XY-Wing, which only needs a target cell to see the two pincers. The payoff is that an XYZ-Wing can fire in positions where the pivot’s extra candidate rules out a plain XY-Wing but the three-way agreement on Z still holds.

Worked example

r7c6 is the pivot, carrying 1, 5 and 9. r7c4 shares the pivot’s row and holds 5 and 9. r9c5 shares the pivot’s box and holds 1 and 5. Both pincers agree with the pivot on 5, so every one of the pivot’s three possible values leads to 5 landing somewhere in the wing. If the pivot itself is 5, that is immediate. If the pivot is 9 instead, r7c4 cannot also be 9, so r7c4 must be 5. If the pivot is 1 instead, r9c5 cannot also be 1, so r9c5 must be 5.

r8c6 sits in the same bottom-middle box as all three wing cells, so it sees the pivot and both pincers at once. It was carrying 1, 5 and 6 before the deduction. Since 5 lands somewhere in the wing no matter which value the pivot takes, r8c6 cannot hold 5, and the solver removes it, leaving 1 and 6 behind.

How to spot an XYZ-Wing

1. Find a tri-value pivotLook for a cell with exactly three candidates, X, Y and Z, sitting inside a box with room for two pincers nearby.
2. Find two pincers that each see the pivotEach pincer must share a unit with the pivot, hold exactly two candidates, include Z, and include one of X or Y.
3. Confirm all three cells share a unit with the targetThe elimination only applies to cells that see the pivot and both pincers, which usually means all four cells share a box.
4. Erase Z from that shared cellRemove Z from any cell, other than the wing’s own three cells, that sees the pivot and both pincers.

Common mistakes

• Using a pivot with only two candidates. That is an XY-Wing, not an XYZ-Wing; the pivot here must carry all three values.
• Eliminating Z from a cell that sees only the pincers but not the pivot. All three wing cells must see the target for an XYZ-Wing elimination.
• Mixing up which pincer shares which value with the pivot. Each pincer needs exactly one of X or Y in common with the pivot, plus the shared Z.
• Assuming the wing always fits in a single row or column. It is most often confined to a single box because that is usually the only unit all three cells share.