XYZ-Wing
An XY-Wing with a three-candidate pivot — the shared digit is eliminated from cells that see all three wing cells.
The XYZ-Wing extends the XY-Wing by giving the pivot three candidates instead of two. A pivot cell showing {x,y,z} sees two pincer cells, one showing {x,z} and one showing {y,z}. Whichever value the pivot takes, z is forced into one of the three cells — so z can be removed from any cell that sees all three.
Because the pivot itself carries z, the elimination zone is the cells that can see the pivot and both pincers at once — usually only a couple of cells.
How to spot it
Find a three-candidate pivot {x,y,z}. Look for two cells it sees, one {x,z} and one {y,z}, sharing the digit z with the pivot. Any cell that simultaneously sees the pivot and both pincers cannot hold z.
- Pivot with exactly three candidates {x,y,z}.
- Two pincers it sees: {x,z} and {y,z}.
- Remove z from cells that see the pivot and both pincers.
Why z is forced
If the pivot is x, the {x,z} pincer becomes z. If it is y, the {y,z} pincer becomes z. If it is z, the pivot is z. In every case one of the three holds z, so a cell seeing all three cannot.
Worked example
- A pivot cell shows {2,5,9}.
- It sees a pincer {2,9} in its box and a pincer {5,9} in its row.
- The shared digit is 9.
- One cell sees the pivot, the box pincer and the row pincer together.
- Remove 9 from that cell.
Try it yourself
Tap a cell, then a number, to practise.
Frequently asked questions
- How is XYZ-Wing different from XY-Wing?
- The pivot has three candidates instead of two, so the pivot is also part of the elimination logic. The eliminated cell must see all three cells, not just the two pincers.
- Is it stronger than an XY-Wing?
- It triggers in different positions but eliminates fewer cells on average, because the cell must see three cells rather than two.
Related techniques
Practice: XYZ-Wing
Put the XYZ-Wing to work on a live board — free puzzles with notes, hints and four difficulty levels.
Try it on a live board