Y-Wing vs XYZ-Wing: One Extra Candidate Changes Everything
A Y-Wing and an XYZ-Wing are both advanced solving techniques that use three cells to create a chain of logic, but their core structural difference is in the number of candidates in the pivot cell. This single change dictates where you can make eliminations. Understanding this distinction is key to applying these powerful patterns correctly when simpler methods like [Naked Pairs](/techniques/naked-pairs) are exhausted. This guide breaks down the anatomy of each wing, shows how to spot them, and explains their distinct elimination rules.
What is the Basic Structure of a Y-Wing?
A Y-Wing, sometimes called a Bent Triple, is a pattern formed by three cells. The structure consists of a pivot cell and two wing cells. The pivot cell contains two candidates, which we can label as AB. One wing cell shares one candidate with the pivot (e.g., AC) and the other wing shares the other candidate (e.g., BC). Critically, the two wing cells must see each other, meaning they are in the same row, column, or 3x3 box. This interconnected triad creates a powerful logical fork. If the pivot is not A, then it must be B, forcing a chain of decisions that eliminates a specific candidate from any cell that sees both wings.
What is the Basic Structure of an XYZ-Wing?
An XYZ-Wing also uses three cells, but its pivot cell contains three candidates, labeled XYZ. The two wing cells are bivalue cells (cells with only two candidates) that share a different pair of these candidates with the pivot. One wing will be XZ, and the other will be YZ. Like the Y-Wing, the two wing cells must see each other. The presence of the extra candidate Z in the pivot is the defining structural difference from a Y-Wing. This configuration allows for eliminations based on the common candidate Z. A deep understanding of candidate notation is essential for spotting this; our guide on Sudoku Notation can help.
Where Can a Y-Wing Make Eliminations?
The Y-Wing's logic eliminates one specific candidate from any cell that is seen by both wing cells. The eliminated candidate is the one that is not shared with the pivot. In our AB/AC/BC example, the eliminated candidate is C. The reasoning is this: if the pivot is A, then the AC wing must be C, eliminating C from common peers. If the pivot is B, then the BC wing must be C, also eliminating C from common peers. Therefore, C can never appear in any cell that is a peer of both wing cells. This elimination can occur in a row, column, or box, potentially far from the wing cells themselves. Mastering the Y-Wing technique involves scanning for these bivalue cell connections.
Where Can an XYZ-Wing Make Eliminations?
The XYZ-Wing's elimination focuses on the common candidate Z. It can eliminate Z from any cell that is seen by all three cells in the wing: the pivot and both wings. The logic is similar but hinges on the pivot's third candidate. If the pivot is Z, then Z is immediately placed there. If the pivot is not Z, then it becomes a standard Y-Wing on candidates X and Y, which forces one of the wings to be Z. In both scenarios, any cell that sees all three cells cannot contain Z. This is a more restrictive elimination zone than the Y-Wing, as the target cell must be a peer of the pivot as well. For a full walkthrough of this pattern, see our article on the XYZ-Wing.
What is the Key Difference in Elimination Power?
The fundamental difference lies in the "visibility" required for an elimination. A Y-Wing requires the target cell to see both wing cells. The pivot cell's visibility is irrelevant for the elimination. An XYZ-Wing requires the target cell to see all three cells: the pivot and both wings. This makes the XYZ-Wing's elimination zone often smaller and more specific. Consequently, a Y-Wing can sometimes make an elimination in a different box from the pivot, while an XYZ-Wing's elimination is always confined to the intersection of the three cells' influence. Choosing the right Y-Wing strategy involves recognizing which pattern's elimination zone contains your target candidates.
How Do I Practice Finding These Patterns?
Start by looking for bivalue cells (cells with only two pencil marks). For a potential Y-Wing, look for two bivalue cells that share a common peer and have one candidate in common (like AC and BC). Then check if their common peer is a bivalue cell with the other two candidates (AB). For an XYZ-Wing, look for a cell with three candidates (the pivot). Then search for two bivalue cells that are peers of the pivot and of each other, each sharing two candidates with the pivot (XZ and YZ). The puzzle provided with this article is an excellent training ground. After filling in basic candidates, search the grid for these triangular relationships. Our hint engine is designed to point out these advanced patterns when you get stuck.
Key Facts
- ▪A Y-Wing uses three bivalue cells (two candidates each) in a specific AB, AC, BC configuration.
- ▪An XYZ-Wing uses one trivalue pivot cell (XYZ) and two bivalue wing cells (XZ and YZ).
- ▪In both patterns, the two wing cells must be peers (share a row, column, or box).
- ▪A Y-Wing eliminates a candidate from any cell that sees both wing cells.
- ▪An XYZ-Wing eliminates candidate Z from any cell that sees all three cells in the pattern.
- ▪The Y-Wing's elimination zone is defined by the wings; the pivot's visibility doesn't matter for the elimination.
- ▪The XYZ-Wing's elimination zone is the intersection of influence from the pivot and both wings.
- ▪The XYZ-Wing is essentially a Y-Wing with an extra candidate Z in the pivot cell.
- ▪Both techniques are used after simpler methods like singles and pairs are exhausted.
Frequently Asked Questions
Are Y-Wing and XYZ-Wing considered advanced techniques?
Yes. They are advanced intermediate techniques, typically used after solving all Naked and Hidden Singles. They rely on strong chain logic rather than direct placement.
Can the pivot cell in a Y-Wing have three candidates?
No. By definition, the pivot in a Y-Wing is a bivalue cell with exactly two candidates. A three-candidate pivot creates an XYZ-Wing.
Do the three cells in a wing pattern have to be in different boxes?
No. They can be arranged anywhere on the grid. The only requirement is that the two wing cells see each other (are peers).
What happens if I find an XYZ-Wing but the wings don't see each other?
It is not a valid wing pattern. The direct peer relationship between the two wing cells is essential for the logical chain to work.
Which technique is more powerful, Y-Wing or XYZ-Wing?
Neither is universally more powerful. A Y-Wing can eliminate over a broader area, while an XYZ-Wing can eliminate in a specific, often crucial, intersection. Their utility depends on the puzzle.
How is an XY-Wing different from a Y-Wing?
They are the same technique. XY-Wing is another common name for the Y-Wing pattern. The structure (AB, AC, BC) is identical.