XY-Wing

An XY-Wing is a three-cell pattern built entirely from bivalue cells.

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 important conclusion is:

At least one pincer must be Z.

Therefore candidate Z can be removed from any cell that sees both pincers.

XY-Wing is also commonly called Y-Wing. The names describe the same standard pattern.

XY-Wing at a glance

Pivot      {X,Y}
Pincer A   {X,Z}
Pincer B   {Y,Z}

For the standard pattern:

• all three pattern cells are bivalue;
• both pincers see the pivot;
• the pincers share the same third candidate Z;
• the elimination target contains Z;
• the target sees both pincers.

The letters X, Y, and Z are roles, not fixed digits. An actual XY-Wing might use {2,7}, {2,5}, and {7,5}, or any other three distinct digits arranged in the same logical structure.

Why XY-Wing works

Use this example:

• pivot {2,7};
• pincer A {2,5};
• pincer B {7,5}.

The pivot must eventually be either 2 or 7.

If the pivot is 2

Pincer A sees the pivot, so pincer A cannot also be 2.

Because pincer A is bivalue {2,5}, it must therefore be 5.

If the pivot is 7

Pincer B sees the pivot, so pincer B cannot also be 7.

Because pincer B is bivalue {7,5}, it must therefore be 5.

Those are the only two possibilities for the pivot.

So in every valid solution:

pincer A is 5 or pincer B is 5.

A candidate 5 that sees both pincers would conflict whichever branch becomes true. That candidate can be eliminated.

Step-by-step board example

When reading an XY-Wing board, prove the pattern in a fixed order:

1. identify the bivalue pivot;
2. assign its candidates X and Y;
3. find an {X,Z} pincer that sees it;
4. find a {Y,Z} pincer that also sees it;
5. confirm the same Z appears in both pincers;
6. find cells containing Z that see both pincers;
7. eliminate Z only from those common peers.

That order prevents the most common error: noticing three attractive bivalue cells and assuming they form a Wing before checking their peer relationships.

Why the pincers do not need to see each other

The logical connection runs through the pivot.

If the pivot is X, the {X,Z} pincer becomes Z.

If the pivot is Y, the {Y,Z} pincer becomes Z.

Nothing in that proof requires the two pincers to share a row, column, or box.

The target has a different requirement. Because either pincer may become Z, a candidate Z can be eliminated only if it sees both possible Z locations.

This distinction is central to XY-Wing:

• pivot ↔ pincer visibility creates the implication;
• pincer ↔ target visibility creates the elimination.

XY-Wing geometry

There is no single mandatory visual shape.

A pivot may see one pincer through a row and the other through a box. It might instead use a column and a box, or two different houses in another arrangement.

The pattern is defined by peer relationships, not by looking like a literal letter Y.

This is why candidate highlighting is often more useful than shape memorization.

How to find an XY-Wing

XY-Wing is best searched cell-first, beginning with bivalue cells.

1. Highlight bivalue cells

Cells with exactly two candidates are the natural starting points.

2. Choose a possible pivot {X,Y}

Do not decide that it is a Wing yet. Treat it as a search anchor.

3. Search the pivot's peers for {X,Z}

The first pincer shares X with the pivot and introduces a third digit Z.

4. Search the pivot's peers for {Y,Z}

The second pincer shares Y with the pivot and must contain the same Z as the first pincer.

5. Intersect the pincer peer regions

Look for cells that see both pincers.

6. Check whether those common peers contain Z

If none does, the structure may be valid but it produces no elimination now.

7. Verify the two pivot cases

Before deleting anything, mentally test:

• pivot = X → first pincer = Z;
• pivot = Y → second pincer = Z.

If both branches protect the elimination, the move is proved.

A valid XY-Wing can be unproductive

Finding the three pattern cells does not guarantee progress.

The Wing may exist while no other candidate Z sees both pincers.

In that situation:

• the logical structure is real;
• there is simply no current elimination.

This is an important general lesson for advanced Sudoku. A named structure becomes a useful solving move only when its conclusion changes the candidate state.

XY-Wing as a short XY-Chain

XY-Wing is not an isolated trick. It can be represented as a short XY-Chain.

The pivot connects two bivalue implications so that one of the two endpoint pincers must contain Z.

That makes XY-Wing a useful introduction to chain reasoning:

• each bivalue cell creates an either/or relationship;
• a candidate becoming false forces the other candidate in that cell true;
• the implications connect through peer relationships;
• the two endpoints support a common elimination.

Longer XY-Chains extend the same idea through more than three cells.

XY-Wing vs Naked Triple

Both patterns can involve:

• three cells;
• three total candidate digits.

But their proofs are different.

Naked Triple

Three cells share one house, and the union of their candidates contains exactly three digits.

Those three digits are reserved for those three cells, so they can be removed from other cells in the shared house.

XY-Wing

The three cells do not need to share one house.

The proof comes from the pivot seeing both pincers and from the two pivot states forcing Z into one pincer or the other.

If {XY}, {XZ}, and {YZ} all share one unit, test the simpler Naked Triple explanation first.

XY-Wing vs XYZ-Wing

The names are similar, but one extra candidate in the pivot changes the elimination rule.

XY-Wing

• pivot {X,Y};
• pincers {X,Z} and {Y,Z};
• Z is absent from the pivot;
• Z must occur in one of the pincers;
• target needs to see both pincers.

XYZ-Wing

• pivot {X,Y,Z};
• pincers {X,Z} and {Y,Z};
• Z may occur in the pivot itself;
• target must see pivot + both pincers.

This visibility difference is one of the most useful ways to keep the two techniques separate.

XY-Wing vs W-Wing

Both techniques often begin with bivalue cells, but they use different structures.

XY-Wing

A bivalue pivot directly sees two different pincers.

W-Wing

Two matching bivalue wing cells are connected indirectly through a Strong Link on one of their candidates.

So XY-Wing is primarily a pivot-and-pincers pattern, while W-Wing is a compact link/chain pattern.

Common XY-Wing mistakes

Using a pivot with three candidates

A standard XY-Wing pivot is bivalue {X,Y}.

A trivalue {X,Y,Z} pivot belongs to XYZ-Wing logic.

Using different Z candidates

The two pincers must share the same third candidate.

{X,4} and {Y,8} do not create an XY-Wing because there is no common endpoint candidate to eliminate.

Forgetting that both pincers must see the pivot

Sharing the correct candidate symbols is not enough. The peer relationships are part of the proof.

Requiring the pincers to see each other

That is not a requirement.

Eliminating Z from a cell that sees only one pincer

That cell is not protected against the branch where the other pincer becomes Z.

Treating any three bivalue cells using three digits as a Wing

The exact role structure must be:

{X,Y} → {X,Z} and {Y,Z}.

Forcing an elimination when there is no target

A structurally valid Wing can be unproductive.

A practical XY-Wing recognition drill

Pick a bivalue cell and call 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?

If yes, ask:

Which cells see both Z pincers?

This two-question process is more reliable than searching visually for a Y-shaped diagram.

FAQ

Is XY-Wing the same as Y-Wing?

Yes. Y-Wing is a common alternative name for the standard XY-Wing pattern.

What is the pivot in an XY-Wing?

The pivot is the bivalue {X,Y} cell that sees both pincers.

What are the pincers?

The pincers are {X,Z} and {Y,Z}. Each sees the pivot, and they share the elimination candidate Z.

Which candidate is eliminated?

Z, the candidate shared by the two pincers.

Do the pincers have to see each other?

No. The elimination target must see both pincers, but the pincers themselves do not need to be peers.

Can an XY-Wing produce more than one elimination?

Yes. Every candidate Z that sees both pincers can be eliminated.

Is XY-Wing a chain?

It can be represented as a short XY-Chain, which is why it is a useful bridge into longer bivalue chains.

What to learn next

Learn XYZ-Wing to see how adding Z to the pivot changes the proof and forces a stricter target-visibility rule.

Later, XY-Chain generalizes the same bivalue implication language beyond three cells.