XY-Wing
Three cells forming a Y-shaped chain — the shared candidate at the wings' intersection can be eliminated.
What is XY-Wing?
XY-Wing (also called Y-Wing) is an elegant expert-level technique that combines multi-cell constraint logic with binary cell analysis. It involves exactly three cells: a pivot and two wings. The pivot cell contains exactly two candidates, labeled [X, Y]. Wing A must be visible from the pivot (same row, column, or box) and contains exactly two candidates [X, Z]. Wing B must also be visible from the pivot and contains exactly two candidates [Y, Z]. Here, Z is the shared candidate that appears in both wings but not in the pivot. The key logic: if the pivot contains X, then Wing A cannot contain X, so Wing A must contain Z. If the pivot contains Y, then Wing B cannot contain Y, so Wing B must contain Z. In either case — regardless of what the pivot holds — at least one of the two wings must contain Z. Therefore, any cell that can simultaneously see both Wing A and Wing B cannot contain Z, because it would be "seen" by whichever wing holds Z. That digit Z can be eliminated from all such cells. XY-Wing is a cornerstone technique of expert-level solving and the conceptual gateway to more powerful patterns like XYZ-Wing, W-Wing, and full Alternating Inference Chains.
When to Use XY-Wing
Use XY-Wing after Coloring and Swordfish when 3-cell, 3-candidate interactions are needed and the board still has locked positions. Find cells with exactly two candidates — these are the building blocks. Look for a 2-candidate cell (the pivot) that can "see" two other 2-candidate cells (the wings), where the wings share one candidate with the pivot each (different candidates) and also share one common candidate Z with each other. The elimination zone is anywhere that sees both wings — often just one or two cells, but occasionally more in favorable board configurations.
How to Apply XY-Wing — Step by Step
- 1
Find a pivot cell
Scan the board for cells with exactly two candidates [X, Y]. Any 2-candidate cell is a potential pivot. There are often several on a hard puzzle — focus on those that are well-connected (have many cells in the same row, column, or box), as they are more likely to have wing candidates nearby.
- 2
Identify potential wings
For each pivot cell with candidates [X, Y], search for two other 2-candidate cells that are visible from the pivot. Wing A should contain [X, Z] (sharing X with the pivot) and Wing B should contain [Y, Z] (sharing Y with the pivot). Z is the new shared candidate — the one that will be eliminated from the board.
- 3
Verify the structure
Confirm that both wings are visible from the pivot (each wing must share a row, column, or box with the pivot). Note that the two wings do not need to see each other — they only need to both see the pivot. Verify the exact candidates of each cell: pivot = [X, Y], Wing A = [X, Z], Wing B = [Y, Z], with no extra candidates in any cell.
- 4
Find the elimination zone
The digit Z can be eliminated from any cell that sees both Wing A and Wing B simultaneously. Identify all cells that share a row, column, or box with Wing A, and also share a row, column, or box with Wing B. Any such cell that contains Z as a candidate can have Z removed. This is the elimination step.
💡 Pro Tip
The elimination zone is the set of cells visible from both wings. In practice, this is often just one or two cells in the intersection of a row/column and box. To systematically find XY-Wings, for each 2-candidate pivot, make a list of all 2-candidate cells visible from it. Then check whether any two of those visible cells share the required candidate relationship (one shares X with pivot, the other shares Y, and both share Z). A useful pattern to remember: the pivot is like a "hinge" and the two wings "point" toward the elimination zone. If the pivot is at the corner of a rectangle and the wings are on two sides, the elimination zone is often cells at the fourth corner of that virtual rectangle.
Practice XY-Wing Now
Put this technique to the test on a live puzzle. The Practice Mode lets you work through real examples with candidate marking.