A WXYZ-Wing is an expert Sudoku pattern built from four cells containing four digits in total. It extends the recognizable Wing family beyond XY-Wing and XYZ-Wing, but the useful modern definition is broader than a single fixed hinge shape.
The key idea is that the four-cell structure has one candidate that is non-restricted inside the pattern. That candidate must occur somewhere in the Wing. Any outside cell that sees every possible occurrence can eliminate it.
WXYZ-Wing is also closely related to ALS-XZ, so learning it is a useful bridge from named patterns into Almost Locked Set logic.
Quick recognition rule
For the common Type 1 interpretation:
- find four cells containing exactly four distinct digits in total;
- the cells must form a tightly restricted structure, commonly across two intersecting houses;
- among the four digits, identify one non-restricted common candidate Z;
- the other candidates are restricted inside the pattern;
- Z is guaranteed to be true in at least one of its Wing occurrences;
- eliminate Z from any outside cell that sees all those occurrences.
What does “restricted” mean here?
A candidate is restricted in the Wing when its occurrences inside the four pattern cells all see one another through a shared house.
If candidate 4 appears in two Wing cells and those cells share a row, the two 4s cannot both be true. The candidate behaves as a restricted relationship within the pattern.
The elimination digit Z is different. At least two of its occurrences do not see each other, so Z is the non-restricted common candidate.
This asymmetry is what creates the Wing deduction.
Why four cells and four digits matter
The WXYZ structure is an almost-locked counting situation.
If an outside assumption removed all possible Zs from the pattern, the four cells would be left trying to hold only the other three digits. Four cells cannot be filled with three Sudoku digits without repeating one in a restricted house.
Therefore Z cannot disappear from the whole pattern.
At least one Wing occurrence of Z must be true.
That is why a target seeing every possible Z in the Wing cannot itself be Z.
The narrow hinge-and-pincers picture
A traditional teaching shape uses:
- one hinge with
{W,X,Y,Z}; - three wing cells such as
{W,Z},{X,Z},{Y,Z}.
Whichever value the hinge takes, a Z is forced either in the hinge or one of the wing cells.
This picture is useful for learning, but it is not the full definition. Modern implementations allow candidate distributions where the hinge does not contain all four digits and where the non-restricted candidate is present in only part of the four-cell set.
Worked WXYZ-Wing
How to find WXYZ-Wings efficiently
A blind search through every four-cell combination is expensive for a human.
Use anchors:
1. Start with a constrained house intersection
Look for cells concentrated in a row+box, column+box, or sometimes row+column relationship.
2. Count the union
Four selected cells should contain exactly four distinct candidates.
3. Check restriction candidate by candidate
Do the occurrences of W all see one another? What about X and Y?
You are looking for one candidate whose occurrences are not fully mutually visible.
4. Search targets only after the Wing is proven
The target must see every occurrence of the non-restricted candidate that could be true.
If it misses even one, the elimination is unsupported.
WXYZ-Wing vs XYZ-Wing
XYZ-Wing normally has three cells and three digits, with a trivalue pivot and two bivalue pincers.
WXYZ-Wing uses four cells and four digits and admits much more varied candidate distributions.
Both prove that a shared elimination candidate must appear somewhere in a restricted pattern, but WXYZ-Wing is less visually rigid.
WXYZ-Wing vs Naked Quad
Both can involve four cells and four digits.
A Naked Quad is contained inside one house and reserves four digits for four cells, eliminating those digits from other cells in that same house.
A WXYZ-Wing uses restriction relationships across houses and normally eliminates one non-restricted common candidate from cells that see its possible Wing locations.
The count may look similar; the proof and target rule are different.
WXYZ-Wing vs ALS-XZ
This is the most important expert connection.
A WXYZ-Wing can often be represented as an ALS-XZ relationship between two Almost Locked Sets. In that framework:
- the Wing cells are partitioned into ALS structures;
- a Restricted Common Candidate links the ALS;
- another shared digit becomes the elimination candidate.
ALS-XZ is more general. WXYZ-Wing remains useful because a recognizable four-cell pattern is faster to spot and communicate.
Common mistakes
Requiring the old four-candidate hinge
The narrow teaching pattern is sufficient, not necessary.
Treating any four cells/four digits as a Wing
The restriction structure must be validated.
Eliminating the wrong candidate
The ordinary Type 1 elimination is on the non-restricted common candidate.
Using a target that misses one Wing occurrence
The target must see all possible true occurrences of the elimination digit.
Confusing the pattern with a Naked Quad
A Quad is a one-house reservation. A WXYZ-Wing is a cross-house implication structure.
Recognition checklist
Before making an elimination, confirm:
- four cells;
- exactly four candidate values across them;
- valid restricted geometry;
- one identifiable non-restricted common candidate;
- at least one occurrence of that candidate must be true;
- target is outside the Wing;
- target sees every possible true occurrence.
FAQ
Is WXYZ-Wing just a larger XYZ-Wing?
It is historically taught that way, but the general modern definition is broader than simply adding one cell to the classic XYZ shape.
Is WXYZ-Wing the same as a Bent Quad?
Bent Quad is a common alternative name for related four-cell/four-digit Wing structures.
Does the hinge need four candidates?
No. That is a useful narrow teaching form, not a requirement of the broader pattern.
Is WXYZ-Wing an ALS technique?
It can be expressed through ALS-XZ logic. The named Wing remains useful as a recognizable special case.
Is WXYZ-Wing common?
It is much less basic than XY-Wing, but broad definitions find substantially more instances than the old narrow hinge form.
What to learn next
After WXYZ-Wing, study Almost Locked Sets and ALS-XZ. That turns the pattern from a special shape into an example of a much wider expert solving language.