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
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.
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