The XYZ-Wing Technique in Sudoku
The XYZ-Wing is a short-chain technique that cracks grids the pairs and fish cannot. It centres on a pivot cell holding three candidates — X, Y and Z — flanked by two cells that share one of them, letting you eliminate that digit from a cell all three can see. It sounds fiddly, but it is just careful bookkeeping of what each cell can be.
How to use the XYZ-Wing, step by step
- Find a pivot cell with exactly three candidates — call them X, Y and Z.
- Find a pincer in the pivot’s row, column or box with just two candidates that are two of those three, including Z.
- Find a second pincer the pivot can see, also two candidates including Z, covering the third of X/Y/Z.
- Locate cells that can see the pivot and both pincers at once.
- Eliminate Z from those shared cells — one of the three must be Z, so Z cannot live where all three see it.
- Re-scan for the singles the elimination opens up.
What is an XYZ-Wing?
An XYZ-Wing is a three-cell pattern: a pivot cell with three candidates {X, Y, Z} and two pincer cells, each with two candidates that share the digit Z. Between the pivot and the two pincers, the digit Z is guaranteed to appear in at least one of them. So any cell that can see all three at once cannot be Z — and you remove it there.
How to spot an XYZ-Wing
Start from cells with exactly three candidates and check whether two nearby bi-value cells “pincer” one of those digits. The pivot must be able to see both pincers; the two pincers need not see each other. The shared digit Z is the one you eliminate, and only from cells that see the pivot and both pincers.
- It is a close relative of the Y-Wing — there the pivot has two candidates, here three.
- Keep candidates tidy; like all wings, the XYZ-Wing is invisible without them. More moves in tips & strategy.
Why the elimination works
Whatever the pivot turns out to be, the digit Z ends up in the pivot or one of the pincers. A cell that sees all three therefore always has a Z among its neighbours, so Z can never go there. As with the X-Wing, you are not guessing — you are proving an impossibility.
XYZ-Wing in Sudoku: FAQ
What is an XYZ-Wing in Sudoku?
An XYZ-Wing is a three-cell technique: a pivot cell with three candidates {X, Y, Z} and two pincer cells of two candidates each that share the digit Z. Any cell that can see the pivot and both pincers cannot be Z, because one of the three must take Z.
What is the difference between a Y-Wing and an XYZ-Wing?
In a Y-Wing the pivot has two candidates and only the two pincers can hold the eliminated digit. In an XYZ-Wing the pivot has three candidates and can itself hold the digit, so the cell you eliminate from must see all three of pivot and pincers, not just the pincers.
How do you spot an XYZ-Wing?
Look for a cell with exactly three candidates, then check its peers for two bi-value cells that each share the same digit Z with it and cover its other two digits. If a cell exists that sees all three, you can remove Z from it.
Is the XYZ-Wing an advanced technique?
Yes — it sits above pairs, pointing pairs and the X-Wing, in the short-chain family with the Y-Wing. You will only need it on Expert and Evil puzzles once the simpler moves are exhausted.