Lesson:XY-Wing
An XY-Wing involves three cells forming a Y-shape: a pivot (XY) and two wings (XZ and YZ).
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XY-Wing (also written as Y-Wing) is a powerful multi-digit elimination technique that uses three cells arranged in a Y-shape — or "pivot and two wings" — to prove that a specific digit can be eliminated from cells that can see both wings simultaneously. It is one of the most elegant techniques in Sudoku, combining the simplicity of bi-value cells with long-range elimination power.
The three cells involved are: the pivot (XY), which contains exactly two candidates {X, Y}; Wing 1 (XZ), which contains exactly two candidates {X, Z}; and Wing 2 (YZ), which contains exactly two candidates {Y, Z}. The pivot shares a unit with each wing, but the two wings do not need to share a unit with each other. The shared candidate Z appears in both wings but not in the pivot.
The logic: if the pivot is X, then Wing 1 must be Z (since Wing 1 is {X, Z} and X is taken by the pivot). If the pivot is Y, then Wing 2 must be Z (since Wing 2 is {Y, Z} and Y is taken). Either way, at least one of the two wings must be Z. Therefore, any cell that can see both Wing 1 and Wing 2 cannot be Z — regardless of which configuration holds.
How It Works — Step by Step
Step 1 — Find a pivot cell
Look for a bi-value cell (exactly two candidates). This is your pivot, containing candidates {X, Y}.
Step 2 — Find Wing 1
In the same unit as the pivot (same row, column, or box), find another bi-value cell containing {X, Z} — one of the pivot's digits and one new digit Z.
Step 3 — Find Wing 2
In another unit of the pivot (it must see the pivot but not necessarily Wing 1), find a bi-value cell containing {Y, Z} — the other pivot digit and the same new digit Z.
Step 4 — Eliminate Z from cells seeing both wings
Find any empty cells that can see both Wing 1 and Wing 2 (share a unit with each). Remove Z from their candidate lists.
When to Use This Technique
After X-Wing, Swordfish, and Coloring. XY-Wing is particularly effective when many bi-value cells exist on the board — they serve as both pivot and wing candidates. It is a hallmark technique of Hard and Expert puzzle solving.
Worked Examples
Pivot R4C2 = {3, 7}. Wing 1 R4C8 = {3, 5} (shares Row 4 with pivot). Wing 2 R1C2 = {7, 5} (shares Column 2 with pivot). Z = 5. Any cell that can see both R4C8 and R1C2 cannot be 5. R1C8 shares Row 1 with Wing 2 and Column 8 with Wing 1 — eliminate 5 from R1C8.
Frequently Asked Questions
Does the pivot need to share a unit with both wings?
Yes. Each wing must be in a unit that includes the pivot. Wing 1 and Wing 2 do not need to share a unit with each other — only with the pivot.
Can the pivot be in the same box as a wing?
Yes. The pivot can share any unit type (row, column, or box) with each wing. All three combinations are valid.
How does XY-Wing relate to AICs?
XY-Wing is a three-node multi-digit AIC: pivot→wing1 is a strong link on X within the bi-value cell; wing1→wing2 is a weak link on Z; the elimination is the AIC conclusion. Understanding XY-Wing as an AIC helps you extend the pattern to XY-Chains (longer chains of bi-value cells).
Related Lessons
Ready to test your knowledge? Try applying this technique in our Hard Sudoku puzzles, Expert level course or explore Coloring technique guide. Keep training to improve your solve times and master the grid!
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