A pivot cell with two candidates connects to two wing cells. The digit shared by both wings is eliminated from cells seeing both.
Also known as: Y-Wing
Find a pivot cell with two candidates {X, Y} that shares a unit with one wing holding {X, Z} and another wing holding {Y, Z}. However the pivot resolves, one of the wings is forced to Z. Remove Z from every cell that sees both wings; the pivot plays no part in the elimination.
An XY-Wing (also called Y-Wing) uses three bivalue cells, cells with exactly two candidates each. One cell is the "pivot" and the other two are "wings." The pivot shares one candidate with each wing, and the two wings share a candidate with each other (but not with the pivot).
The key insight: whatever digit the pivot turns out to be, one of the wings will always contain the shared wing digit. If the pivot is X, wing A must be Z. If the pivot is Y, wing B must be Z. Either way, Z appears in one of the two wings. So any cell that sees both wings cannot contain Z.
XY-Wing is one of the most elegant techniques in Sudoku. It appears regularly in Hard and Extreme puzzles and often breaks open positions that resist simpler methods.
Find a pivot cell with candidates {X, Y}. Find a wing cell in the same unit (row, column, or box) as the pivot with candidates {X, Z}. Find a second wing cell in the same unit as the pivot with candidates {Y, Z}. The digit Z is the elimination target.
Note that each wing must share a unit with the pivot, but the two wings do not need to share a unit with each other. However, the elimination happens from cells that can see both wings.
Apply the elimination: remove digit Z from every cell that shares a unit with both wing cells. The pivot doesn't matter for the elimination, only the wings' positions determine what gets eliminated.
Step 1: We find pivot R4C4 with candidates {3, 8}. Wing R5C6 has {3, 5} (shares box 5 with the pivot). Wing R8C4 has {5, 8} (shares column 4 with the pivot). The shared wing digit is 5.
Step 2: If the pivot is 3, then R5C6 cannot be 3, so R5C6 = 5. If the pivot is 8, then R8C4 cannot be 8, so R8C4 = 5. Either way, digit 5 appears in one of the two wings.
Step 3: Cells seeing both wings: R6C4 sees R8C4 (column 4) and R5C6 (box 5). R8C6 sees R8C4 (row 8) and R5C6 (column 6). Eliminate 5 from R6C4 and R8C6.
Start from cells with exactly two candidates. Pick one as the pivot, then list the other two-candidate cells it sees. You need two of them that each borrow a different digit from the pivot and share a third digit with each other. That third digit, Z, is the one you get to eliminate.
No. Only cells that see both wings lose the digit Z. The pivot's job is finished once it has forced the wings — its own position is irrelevant to the elimination, and Z is not even a candidate in the pivot. A cell that sees the pivot and one wing is not enough.
All three guarantee one digit somewhere in a small group of cells, but the machinery differs. An XY-Wing uses three two-candidate cells: a pivot plus two wings. An XYZ-Wing has a three-candidate pivot, so eliminations apply only to cells seeing all three. A W-Wing joins two cells with identical candidates by a strong link instead of a pivot.
They are the same technique under two names. Y-Wing is the alternative label you will meet in books and solvers; XY-Wing describes the shape more literally, naming the pivot's two candidates X and Y and the digit Z that both wings share. If a solver reports a Y-Wing, look for the same three two-candidate cells.
No. Each wing must share a row, column or box with the pivot, but the wings need not share a unit with each other. What matters is that some other cell can see both wings, because that is where digit Z is eliminated. Wings sitting in different boxes are normal.
Yes. If any of the three carries a third candidate, the pattern is not an XY-Wing. The deduction depends on a wing being forced to Z the moment it loses the digit it shares with the pivot. Where the pivot has a third candidate you may instead have an XYZ-Wing, whose elimination zone is much smaller.
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