Interactive Sudoku Technique
How the XY-Wing Forces a Candidate Away
Three cells hold two candidates apiece. One cell connects the other two, and their shared candidate becomes certain in one pincer or the other—even before you know which one.
First, Separate the Families
This Wing Is Not an X-Wing
The XY-Wing is also commonly called a Y-Wing. Both names describe the same technique. The X and Y in its formal name stand for changing candidate values—not the crossed lines of an X-Wing.
X-Wing: a Fish
Follow one digit through matching rows and columns. Its strength comes from paired houses.
XY-Wing: a Wing
Follow three digits through cells containing two candidates each. Its strength begins inside the cells.
Fish organize one candidate across houses. Wings connect candidate choices through cells.
A New Two-Choice Search
From Two Places to Two Values
Earlier lessons searched for one candidate with exactly two possible places in a row, column, or box. Wings ask you to turn that search around and look for a cell containing exactly two candidates.
BLC
Bi-Local Candidate
One digit has exactly two possible places within one house.
BVC
Bivalue Cell
One cell contains exactly two possible values.
If this cell is not 2, it must be 7. If it is not 7, it must be 2. That forced either-or bond makes a BVC one of the most useful building blocks in the Wing family.
The familiar Strong-Link promise has moved inside the cell: the two candidates cannot both be true, cannot both be false, and one of them must eventually occupy the cell.
Build the Wing with Real Digits
A Pivot and Two Pincers
Begin with three BVCs using only the digits 2, 7, and 9. The center of the logic is called the pivot. It must see both of the other cells, called pincers.
Pivot
r4c4
27
Shares 2 with one pincer and 7 with the other.
Pincer A
r4c8
29
Sees the pivot across Row 4.
Pincer B
r8c4
79
Sees the pivot down Column 4.
See the Logical Y
The Shape Is Made by Relationships
The cells do not need to draw a perfect letter Y on the grid. What matters is that the pivot sees both pincers. The pincers are allowed to sit far apart and usually do not see each other.
Pivot: r4c4 (2,7)
Pincer A: r4c8 (2,9)
Pincer B: r8c4 (7,9)
Victim: r8c8 contains 9
The victim sees Pincer A in Column 8 and Pincer B in Row 8.
A Sudoku Paradise Case Study
First See the Crowd. Then See the Wing.
These images show the same puzzle at the same moment. In the first, every BVC is allowed to demand attention. The useful pattern is present, but it is camouflaged inside a crowd of other two-candidate cells.
What survives the filter
-
Blue pivot:
r1c4 (1,5)sees both green pincers—one down Column 4 and one across Row 1. -
Green pincer:
r2c4 (1,3)shares candidate 1 with the pivot. -
Green pincer:
r1c9 (3,5)shares candidate 5 with the pivot. - The two pincers share candidate 3. That 3 must be true in one pincer or the other.
-
Red victim:
r2c7 (1,3)sees the first pincer across Row 2 and the second inside Box 3.
If the pivot is 1
r2c4 cannot be 1 and must be 3. The victim sees it
across Row 2 and loses 3.
If the pivot is 5
r1c9 cannot be 5 and must be 3. The victim sees it
inside Box 3 and loses 3.
The XY-Wing removes 3 from r2c7. Its remaining
candidate, 1, is then ready for the Naked Single to place.
Do not ask which BVC looks interesting. Ask which three BVCs rotate the same three candidates and connect through one pivot. The other BVCs remain on the grid; they simply leave your attention.
Interactive Proof
Give the Pivot Either Value
The pivot must be either 2 or 7. Test both possibilities. One pincer becomes 9 in either case, so the victim receives the same verdict along both roads.
Both roads force a pincer to be 9: remove 9 from
every candidate cell that sees both pincers, including
r8c8.
Interactive Geometry Check
Which Cell Can Be the Victim?
A victim must contain the shared pincer candidate—9 in this example—and must see both pincers. Seeing only one is not enough.
Choose the cell that sees both pincers.
Interactive Candidate Practice
Do These Three Pairs Fit?
For this exercise, assume the pivot sees both pincers. Decide whether the three candidate pairs form the candidate structure of an XY-Wing. Geometry and victim placement are checked afterward.
0 of 4 examples mastered
Now Give It Its Formal Language
The XY-Wing Formula
You have already proved the technique. The letters merely let us describe the same relationship without choosing particular digits.
Any outside cell that sees both pincers cannot contain Z.
| Role | Cell | Candidates | Formal pair |
|---|---|---|---|
| Pivot | r4c4 |
2, 7 | (X,Y) |
| Pincer A | r4c8 |
2, 9 | (X,Z) |
| Pincer B | r8c4 |
7, 9 | (Y,Z) |
| Victim | r8c8 |
9 removed | Z eliminated |
The Wing Family Ahead
BVCs Keep Returning in Different Arrangements
An XY-Wing is the cleanest introduction to Wings because all three working cells are bivalue. Later Wing techniques reuse that two-choice power in different ways.
XY-Wing
Three BVCs pass one forced candidate to either pincer.
XYZ-Wing
A three-candidate pivot works with two BVC pincers.
W-Wing
Matching BVCs gain power from an outside Strong Link.
BVCs are the recurring joints of the family, but each Wing has its own geometry and proof. Do not transfer one Wing's rules to another by appearance alone.
Before You Eliminate
Check the Entire Wing
- The pivot must be a true BVC and see both pincers.
- Each pincer must share a different pivot candidate.
- The two pincers must share the same third candidate.
- For a basic XY-Wing, the three working cells use only three digits altogether.
- The pincers do not need to see each other.
- The victim must contain the shared pincer candidate and see both pincers.
- A cell seeing only one pincer cannot be touched.
Common Questions
XY-Wings Clarified
Are XY-Wing and Y-Wing the same strategy?
Yes. Y-Wing is a popular short name. XY-Wing is the formal name used here because its X, Y, and Z candidate roles explain the proof.
Must the three cells look like a letter Y?
No. The logical branches matter, not the drawing. The pivot must see both pincers; the victim must see both pincers.
Must the pincers see each other?
No. They usually do not. Their shared candidate becomes useful because the pivot guarantees that one pincer or the other must contain it.
Can an XY-Wing eliminate more than one candidate?
Yes. Remove the shared candidate from every cell that sees both pincers. A compact arrangement may produce more than one victim.
Continue Through the Wing Family
Let the Pivot Carry the Third Candidate
The XY-Wing uses three BVCs. The XYZ-Wing keeps two BVC pincers, gives the shared candidate to the pivot as a third possibility, and opens one more road to the same elimination.