An XY-Wing is a three-bivalue-cell pattern.
It contains:
- a pivot
{X,Y}; - one pincer
{X,Z}; - another pincer
{Y,Z}.
Both pincers must see the pivot.
The pincers do not need to see each other.
The key conclusion is:
At least one pincer must be Z.
So candidate Z can be removed from any cell that sees both pincers.
Quick pattern
Pivot {X,Y}
Pincer A {X,Z}
Pincer B {Y,Z}Requirements:
- every pattern cell is bivalue;
- both pincers see the pivot;
- both pincers share the same Z;
- elimination target sees both pincers.
The two-case proof
Use a concrete example:
- pivot
{2,7}; - pincer A
{2,5}; - pincer B
{7,5}.
The pivot must be either 2 or 7.
Case 1 — Pivot = 2
Pincer A sees the pivot and cannot also be 2.
So pincer A = 5.
Case 2 — Pivot = 7
Pincer B sees the pivot and cannot also be 7.
So pincer B = 5.
In both cases, one pincer is 5.
Therefore any candidate 5 that sees both pincers is impossible.
Step-by-step board example
Why the pincers do not need to see each other
The logic runs through the pivot.
Each pivot value forces one corresponding pincer to Z.
Nothing in that proof requires the pincers to share a unit.
What matters for an elimination target is different:
The target must see whichever pincer becomes Z.
Because either pincer may be the true Z, the target must see both.
Common XY-Wing geometries
There is no single mandatory shape.
A common arrangement is:
- pivot and pincer A share a row;
- pivot and pincer B share a box;
- target sees the two pincers through another combination of row/column/box.
Other peer configurations are possible.
Always verify the relationships instead of relying on orientation.
XY-Wing as a short XY-Chain
XY-Wing can be written as a very short chain.
The pattern teaches:
one endpoint candidate is forced under either pivot state.
Longer XY-Chains extend the same kind of bivalue propagation through more cells.
So XY-Wing is not an isolated trick.
It is the smallest memorable doorway into XY-Chain reasoning.
XY-Wing vs Naked Triple
Both can involve:
- three cells;
- three candidate digits.
But a Naked Triple requires the three cells to share one unit and collectively contain only three digits.
XY-Wing does not require all three cells to share one unit.
Its proof comes from peer relationships through the pivot.
If {XY}, {XZ}, {YZ} all share one unit, test the simpler Naked Triple explanation first.
XY-Wing vs XYZ-Wing
XY-Wing
Pivot {X,Y}.
Z must be in one of the two pincers.
Target needs to see both pincers.
XYZ-Wing
Pivot {X,Y,Z}.
Z can be in the pivot or either pincer.
Target needs to see all three pattern cells.
How to search for XY-Wings
This is a bivalue-cell search.
1. Highlight bivalue cells
2. Choose a pivot {X,Y}
3. Search its peers for {X,Z}
4. Search its peers for {Y,Z}
The same Z must appear in both pincers.
5. Check common peers of the pincers
Any common peer containing Z is a possible elimination.
6. Verify both pivot cases
Do not delete until the proof works cleanly.
What if there is no Z target?
You can have a valid XY-Wing structure with no current elimination.
That makes it unproductive.
Named patterns should be treated as solving moves only when they change the board.
Common mistakes
Choosing a trivalue pivot
That belongs to XYZ-Wing logic.
Using pincers with different third candidates
Both must share the same Z.
Requiring pincers to see each other
Not required.
Eliminating from a cell that sees only one pincer
Invalid.
Treating any three bivalue cells with three digits as XY-Wing
The candidate-role and peer relationships must match {XY} / {XZ} / {YZ}.
Recognition drill
Pick a bivalue cell and name it {X,Y}.
Then ask:
Can I find one peer that turns X into Z and another peer that turns Y into the same Z?
That question is much more reliable than visually hunting “wing shapes.”
FAQ
What is the pivot?
The {X,Y} cell seen by both pincers.
What is eliminated?
Z, the candidate shared by the pincers.
Do the pincers have to see each other?
No.
Is XY-Wing a chain?
It can be represented as a short XY-Chain.
What to learn next
Learn XYZ-Wing to see how adding Z to the pivot changes the proof and target visibility.
Later, XY-Chain generalizes the bivalue inference beyond three cells.