XY-Wing Sudoku Technique Explained

What Is an XY-Wing?

The XY-Wing (also called Y-Wing) is an advanced Sudoku solving technique that uses three cells, each containing exactly two candidates. The three cells together use exactly three different digits — traditionally labeled X, Y, and Z. One cell (the "pivot") can see both of the other two cells (the "pincers"), but the two pincers do not need to see each other.

The technique eliminates the digit Z — the candidate shared by both pincers — from any cell that can see both pincer cells simultaneously. This works because the logic of the pivot guarantees that at least one pincer must always contain Z.

XY-Wings appear in hard, expert, and evil Sudoku puzzles. They are independent of the fish family (X-Wing, Swordfish, Skyscraper) and rely on a completely different type of logic — candidate pairs in bivalue cells rather than single-digit strong links in rows and columns.

How the XY-Wing Works

The XY-Wing involves three cells with these candidate pairs:

Pivot cell: contains candidates X and Y.

Pincer 1: contains candidates X and Z. Must see the pivot (share a row, column, or box).

Pincer 2: contains candidates Y and Z. Must see the pivot (share a row, column, or box).

Notice that both pincers contain Z, and the pivot does not. The pivot contains X and Y — one digit shared with each pincer.

Here is why the elimination works. The pivot must eventually contain either X or Y. If the pivot contains X, then Pincer 1 cannot contain X, so Pincer 1 must contain Z. If the pivot contains Y, then Pincer 2 cannot contain Y, so Pincer 2 must contain Z. Either way, at least one pincer ends up with Z.

Therefore, any cell that can see both Pincer 1 and Pincer 2 cannot contain Z — because one of those pincers will always claim Z first. You can safely eliminate Z from all such cells.

Prerequisites

XY-Wings require solid pencil mark skills and familiarity with these prior techniques:

Naked singles and hidden singles — foundational placements.

Naked pairs and hidden pairs — candidate elimination within groups.

Pointing pairs and box-line reduction — box-line interactions.

You do not need to know X-Wing or Swordfish before learning XY-Wing — they use different logic. However, most solvers learn the fish patterns first because they are slightly more common in practice.

Step-by-Step: Finding an XY-Wing

Step 1: Make sure all pencil marks are fully updated. The XY-Wing pattern is invisible without complete candidate tracking.

Step 2: Scan for bivalue cells — cells with exactly two candidates. These are your building blocks. Mark them mentally or highlight them.

Step 3: Pick a bivalue cell as a potential pivot. Call its candidates X and Y.

Step 4: Look at all bivalue cells that the pivot can see (same row, column, or box). Does any contain X and some other digit Z? That is a potential Pincer 1 with candidates XZ.

Step 5: Now look for a second bivalue cell that the pivot can see, containing Y and that same digit Z. That is Pincer 2 with candidates YZ.

Step 6: If you found both pincers: eliminate Z from any cell that can see both Pincer 1 and Pincer 2. The two pincers do not need to see each other — only the pivot needs to see both.

Worked Example

Suppose you spot three bivalue cells in your puzzle:

Row 1, Column 1 has candidates 3 and 5. This will be the pivot.

Row 1, Column 6 has candidates 3 and 8. This sees the pivot (same row). Pincer 1: candidates 3 and 8, so X = 3, Z = 8.

Row 3, Column 2 has candidates 5 and 8. This sees the pivot (same box — both are in Box 1). Pincer 2: candidates 5 and 8, so Y = 5, Z = 8.

The digit Z is 8 — the candidate shared by both pincers but absent from the pivot. The pivot has 3 and 5 (X and Y).

Check the logic: if the pivot is 3, then Pincer 1 loses 3 and becomes 8. If the pivot is 5, then Pincer 2 loses 5 and becomes 8. Either way, 8 appears in at least one pincer.

Now find cells that can see both pincers. Pincer 1 is at R1C6. Pincer 2 is at R3C2. If any cell shares a row, column, or box with both of them and contains 8 as a candidate, eliminate 8 from that cell.

For instance, R3C6 shares Row 3 with Pincer 2 and Column 6 with Pincer 1 — it sees both. If R3C6 has 8 as a candidate, remove it. That elimination may reveal a naked single or unlock further progress.

The Pivot Identification Shortcut

Finding the pivot is often the hardest part. Here is a practical shortcut:

Instead of starting from a random bivalue cell, start from a digit that appears frequently as a candidate. Say the digit 8 shows up in many bivalue cells. Look for two bivalue cells that both contain 8 — those are your candidate pincers. Then check whether a third bivalue cell exists that sees both pincers, does not contain 8, and shares one candidate with each pincer. If so, that third cell is the pivot and you have an XY-Wing eliminating 8.

This "Z-first" approach is often faster because you start from the elimination target rather than the pivot.

XY-Wing vs. XYZ-Wing

The XYZ-Wing is a closely related pattern where the pivot has three candidates (X, Y, and Z) instead of two. The two pincers still have XZ and YZ. The logic is similar but the elimination zone is smaller — only cells that can see all three cells (pivot plus both pincers) can have Z removed.

XYZ-Wings are rarer and harder to spot, but they use the same fundamental reasoning. If you master XY-Wings, XYZ-Wings are a natural extension.

Common Mistakes

The pivot must see both pincers. This is the most common error. The pivot must share a row, column, or box with each pincer individually. If the pivot sees only one pincer, the pattern is not valid.

All three cells must be bivalue. Each cell in the XY-Wing must have exactly two candidates. If any cell has three or more candidates, it is not part of a standard XY-Wing (though it might form an XYZ-Wing if the pivot has three).

The three cells use exactly three digits. The pivot has XY, one pincer has XZ, the other has YZ. If the three cells together involve four or more different digits, it is not an XY-Wing.

Eliminating from the wrong cells. You eliminate Z only from cells that see both pincers — not from cells that see the pivot. The pivot is irrelevant for the elimination step; only the pincers matter.

The pincers do not need to see each other. This is a common source of confusion. The pivot sees both pincers, but the pincers can be completely unrelated in terms of rows, columns, and boxes. The pattern still works.

Frequently Asked Questions