Not every hard sudoku puzzle yields to row-and-column patterns like the X-Wing. Sometimes the key elimination comes from three specific cells scattered around the grid, connected only by the candidates they share. That is the Y-Wing sudoku technique, also written as XY-Wing, and it is one of the more approachable "three cell" strategies once you understand the logic behind it.
This guide breaks down what a y-wing is, how to locate the pivot and pincer cells that make it work, and how it differs from the X-Wing pattern. If you have not yet worked through the basics, start with our sudoku tips and strategies guide first, then come back once scanning and elimination feel automatic.
What Is the Y-Wing Sudoku Technique
A y wing sudoku pattern involves exactly three cells, each of which has only two remaining candidates. One cell is called the pivot, and the other two are called pincers.
The pivot has two candidates, which we can label X and Y. Each pincer shares exactly one of those candidates with the pivot, plus a third candidate, Z, that both pincers have in common:
- Pivot: candidates X and Y
- Pincer 1: candidates X and Z
- Pincer 2: candidates Y and Z
The pivot must "see" both pincers, meaning it shares a row, column, or box with each of them. The two pincers do not need to see each other.
Here is why this eliminates Z from other cells. If the pivot turns out to be X, then Pincer 1 (which sees the pivot and also contains X) cannot also be X, so it must be Z. If the pivot turns out to be Y instead, then by the same logic Pincer 2 cannot be Y, so it must be Z. Either way — regardless of which value the pivot actually takes — at least one of the two pincers is guaranteed to be Z. That means any cell that sees both pincers at once cannot be Z, since one of the pincers is definitely going to occupy that value.
Finding the Pivot and Pincers
Locating a y-wing by hand takes a bit of pattern recognition, but the search process is straightforward once you know what to look for:
- List every cell on the grid with exactly two candidates. These are your only pivot and pincer candidates; cells with three or more candidates cannot participate in a Y-Wing.
- Pick one of those two-candidate cells as a potential pivot, and note its two candidates, X and Y.
- Look for two other two-candidate cells that each share exactly one candidate with the pivot. One should share X (and have some third candidate Z), and the other should share Y (and have that same Z).
- Check that the pivot sees both of these cells — meaning each pincer is in the same row, column, or 3x3 box as the pivot. The two pincers themselves do not need any relationship to each other.
- Find the overlap. Look for any cell that is seen by both pincers at once (shares a row, column, or box with each). If that overlap cell currently lists Z as a candidate, it can be eliminated.
It helps to work through the grid methodically rather than hunting at random. Many solvers scan box by box for cells with exactly two candidates first, since a pivot is most useful when it sits near several other restricted cells.
A Worked Y-Wing Example
Here is a full pass through the logic using grid coordinates. Suppose R4C4 has exactly two candidates remaining, 3 and 7, making it a potential pivot.
Now look for pincers. R4C8, in the same row as the pivot, has candidates 3 and 9 — it shares the 3 with the pivot, and adds a new candidate, 9. R2C4, in the same column as the pivot, has candidates 7 and 9 — it shares the 7 with the pivot, and also carries that same 9. Both pincers see the pivot (one shares its row, the other shares its column), so the Y-Wing shape is complete: pivot X/Y = 3/7, Pincer 1 = 3/9, Pincer 2 = 7/9, with Z = 9 as the shared outside candidate.
Walk through the logic: if the pivot is 3, Pincer 1 cannot also be 3 (same row), so it becomes 9. If the pivot is 7, Pincer 2 cannot also be 7 (same column), so it becomes 9. Either way, one of the two pincers ends up as 9.
Now find a cell that sees both pincers. R2C8 shares column 8 with Pincer 1 (R4C8) and shares row 2 with Pincer 2 (R2C4), so it sees both. If R2C8 currently lists 9 as a candidate, it can be removed, since one of the two pincers is guaranteed to hold that 9 no matter how the pivot resolves.
Common Y-Wing Mistakes to Avoid
- Using a pivot or pincer with more than two candidates. The Y-Wing pattern only works with cells that have exactly two candidates. A cell with three or more candidates cannot serve as a pivot or a pincer.
- Forgetting to check that the pivot sees both pincers. If the pivot does not share a row, column, or box with one of the two supposed pincers, the pattern is invalid and no elimination follows.
- Eliminating Z from the pincers themselves. The elimination only applies to cells that see both pincers, never to the pincers or the pivot.
- Mixing up which candidate is Z. Z is always the candidate the two pincers share with each other, not the one either pincer shares with the pivot. Double-check this before eliminating anything.
Y-Wing vs X-Wing: The Difference
Both the Y-Wing and X-Wing sudoku techniques eliminate candidates based on patterns rather than direct placement, but the shape of the pattern and the logic behind it are different.
An X-Wing works with a single candidate digit across exactly two rows and two columns, forming a rectangle of four cells. The elimination follows from the fact that the digit must occupy one of two positions in each row, and those positions always line up in the same two columns.
A Y-Wing works with three different cells and involves three different candidate digits (X, Y, and Z), connected through a pivot cell rather than aligned rows and columns. There is no rectangle shape to look for; instead, you are tracing a chain of shared candidates between cells that see each other.
In practice, this means the two techniques are useful in different situations. If you notice a digit that is unusually restricted across two rows or columns, look for an X-Wing. If instead you are staring at a handful of cells with only two candidates each, scattered around the grid without any obvious row or column alignment, a y wing sudoku pattern is more likely to be hiding there. Strong solvers eventually check for both, since expert puzzles often need more than one technique layered together.
Once Y-Wing feels comfortable, revisit the fundamentals in our sudoku tips and strategies guide, and put the pattern into practice on a fresh puzzle from the sudoku generator.