XY-Wing
Three bi-value cells forming a hinge that eliminates a shared candidate from cells seeing both wings.
An XY-Wing uses three cells that each hold exactly two candidates. A "pivot" cell with candidates {X,Y} sees two "wing" cells: one with {X,Z} and one with {Y,Z}. Whatever the pivot becomes, one wing is forced to Z — so Z can be eliminated from any cell that sees both wings.
It is one of the most useful advanced chains because the pattern is compact and frequent.
How to spot it
Find a bi-value pivot {X,Y}. Look among the cells it sees for two bi-value cells {X,Z} and {Y,Z} sharing a third digit Z. Any cell seeing both wings cannot be Z.
- Pivot {X,Y} sees wing {X,Z} and wing {Y,Z}.
- One wing must be Z regardless of the pivot.
- Eliminate Z from cells seeing both wings.
Worked example
- Pivot cell shows {4,7}.
- One wing it sees shows {4,2}; another shows {7,2}.
- If the pivot is 4 the first wing is 2; if 7 the second wing is 2.
- Either way a 2 appears in one wing.
- Any cell seeing both wings loses its 2.
Try it yourself
Tap a cell, then a number, to practise.
Frequently asked questions
- What is a bi-value cell?
- A cell with exactly two candidates. XY-Wings are built entirely from bi-value cells.
- How is XY-Wing related to Y-Wing?
- They are the same pattern; "Y-Wing" is just another common name for the XY-Wing.
Related techniques
Practice: XY-Wing
Put the XY-Wing to work on a live board — free puzzles with notes, hints and four difficulty levels.
Try it on a live board