XY-Wing vs Y-Wing: Two Names for the Same Sudoku Pattern?
XY-Wing and Y-Wing are two names for the exact same Sudoku solving technique. Both terms describe a powerful, three-cell pattern that allows you to eliminate candidates logically. This advanced strategy is a cornerstone for moving beyond basic strategies like [Naked Pairs](/techniques/naked-pairs) and is a simpler precursor to more complex patterns like [XY-Chains](/blog/xy-chains). While the names are interchangeable, understanding the mechanism is key to applying it effectively in tougher puzzles.
What is an XY-Wing (or Y-Wing)?
An XY-Wing is an advanced Sudoku technique that uses three cells to make a logical deduction about candidate elimination. It is sometimes called a 'bent triple' because the three cells form an L or T shape, connected by rows, columns, and boxes. The pattern consists of a 'pivot' cell and two 'wing' cells. The pivot shares a unit (row, column, or box) with each wing, but the two wings do not share a unit with each other. Understanding this foundational pattern is the first step to mastering the Y-Wing technique in your solves.
How does the XY-Wing pattern work?
The pattern works because of a forced logical relationship between three candidates. The pivot cell contains exactly two candidates, which we label 'X' and 'Y'. One wing cell shares a unit with the pivot and contains candidates 'X' and 'Z'. The other wing cell shares a different unit with the pivot and contains candidates 'Y' and 'Z'. The key insight is that one of the two wing cells must contain digit 'Z'. Therefore, any cell that is a common peer of both wing cells cannot contain the digit 'Z', as it would be eliminated no matter which wing cell ends up being correct. This logic is identical whether you call it an XY-Wing or a Y-Wing.
Why are there two different names for it?
The technique is known by two names due to different naming conventions that emerged in the Sudoku community. 'XY-Wing' describes the candidate composition of the cells: the pivot has candidates XY, one wing has XZ, and the other has YZ. 'Y-Wing' describes the visual shape of the pattern, where the three cells form a 'Y' shape on the grid when connected by their shared units. Both names are correct and refer to the same logical construct. For a deeper exploration of the pattern's mechanics, our guide on Y-Wing Sudoku breaks it down in detail.
How do I identify an XY-Wing in a puzzle?
To spot an XY-Wing, you must first be looking at a puzzle's candidate notes (pencil marks). Scan for a bi-value cell (the pivot) with exactly two candidates. Then, look for two other bi-value cells that each share a row, column, or box with the pivot. One wing must contain one of the pivot's candidates plus a third digit, and the other wing must contain the pivot's other candidate plus that same third digit. The two wings must not see each other. The puzzle provided in this article is solved entirely by singles, so no XY-Wing is required in this specific grid. However, in harder puzzles where singles are exhausted, this pattern becomes a common next step.
- Focus your search on bi-value cells first, as they are the only ones that can serve as the pivot or wings.
- The third digit 'Z' is the key to the elimination. Always check which cells see both wings where 'Z' could be removed.
Can you show a hypothetical example?
Let's construct a clear example. Suppose a pivot cell (r5c5) has candidates 3 and 7 (X=3, Y=7). One wing cell (r5c8) shares the same row and has candidates 3 and 9 (X=3, Z=9). The other wing cell (r9c5) shares the same column and has candidates 7 and 9 (Y=7, Z=9). The digit 9 is the common 'Z' candidate. The logic dictates that either r5c8 or r9c5 must be a 9. Therefore, any cell that sees both r5c8 and r9c5 cannot be a 9. The only cells seen by both r5c8 and r9c5 are r5c5 (the pivot itself) and r9c8, so candidate 9 could be removed from r9c8.
How is an XY-Wing different from an XY-Chain?
An XY-Wing is a specific, three-cell pattern, while an XY-Chain is a more generalized extension of the same logic. An XY-Chain can involve four or more bi-value cells linked in a chain, where the start and end cells share a common candidate for elimination. You can think of the XY-Wing as the shortest possible XY-Chain. Mastering the XY-Wing is an excellent foundation for learning longer XY-Chains, which are needed for the most extreme puzzles.
When should I look for an XY-Wing?
You should search for XY-Wings after you have exhausted all basic strategies like Naked and Hidden Singles, Pairs, and Triples. Our hint engine finds that this technique most commonly appears in Hard and Expert-level puzzles. If you are stuck and many cells still have several pencil marks, an XY-Wing might be the key to revealing the next placement. For more practice in recognizing this pattern, our dedicated article on Y-Wing Explained provides additional examples and puzzles.
Key Facts
- ▪XY-Wing and Y-Wing are two names for the identical three-cell Sudoku solving technique.
- ▪The pattern requires one pivot cell with two candidates (XY) and two wing cells with candidates (XZ) and (YZ).
- ▪The two wing cells must each share a row, column, or box with the pivot, but they cannot share a unit with each other.
- ▪The logical conclusion is that the common candidate 'Z' must appear in one of the two wing cells.
- ▪This allows you to eliminate candidate 'Z' from any cell that is a common peer of both wing cells.
- ▪An XY-Wing is the shortest possible form of a more complex strategy called an XY-Chain.
- ▪The technique is considered advanced and is typically used in Hard or Expert level puzzles.
- ▪It is visually identified by an L or Y-shaped connection between three bi-value cells on the grid.
Frequently Asked Questions
Are XY-Wing and Y-Wing the same thing?
Yes, XY-Wing and Y-Wing are completely interchangeable terms for the same three-cell, candidate-elimination pattern in Sudoku.
What is the pivot cell in an XY-Wing?
The pivot is the central bi-value cell with candidates labeled XY. It shares a unit with each of the two wing cells.
Which candidate gets eliminated in an XY-Wing?
The common candidate 'Z', which appears in both wing cells, is eliminated from any cell that sees both of those wings.
Do the wing cells see each other?
No. For the logic to work, the two wing cells must not share a row, column, or box. They only connect via the pivot.
Is an XY-Wing harder than an X-Wing?
They are different techniques. An X-Wing uses two rows and columns. An XY-Wing uses three bi-value cells. Many find the XY-Wing's logic more intuitive.
Can I solve Sudoku without learning XY-Wing?
Yes, for easier puzzles. For harder ones, techniques like XY-Wing are essential logical tools to progress without guessing.