XY-Wing
XY-Wing uses the chain relationship between three cells’ candidate numbers. From a central cell and its two related cells, you can eliminate a specific number from cells that both of those cells can see.
Overview of XY-Wing
XY-Wing consists of three cells, each with exactly two candidates. The central cell has candidates ‘X, Y,’ and two cells in the same row/column/block as the central cell have candidates ‘X, Z’ and ‘Y, Z’ respectively. Regardless of which number the central cell takes, one of those two cells will always contain ‘Z.’ Therefore, ‘Z’ can be eliminated from any cell that shares a row, column, or block with both of those cells.
How to Use XY-Wing
Find a cell with exactly two candidates. Call them ‘X, Y.’
Find a cell in the same row/column/block with candidates ‘X, Z.’
Find a different cell in the same row/column/block with candidates ‘Y, Z.’
Eliminate ‘Z’ from any cell that can see both cells found in steps 2 and 3 (shares a row, column, or block with each).
Example
Suppose a cell has candidates ‘3, 7,’ a cell in the same row has candidates ‘3, 9,’ and a cell in the same block has candidates ‘7, 9.’ If the ‘3, 7’ cell takes ‘3,’ the ‘3, 9’ cell in the same row can no longer be ‘3,’ so ‘9’ is confirmed there. If the ‘3, 7’ cell takes ‘7,’ the ‘7, 9’ cell in the same block can no longer be ‘7,’ so ‘9’ is confirmed there. Since the ‘3, 7’ cell must contain either ‘3’ or ‘7,’ one of those two cells will always end up with ‘9.’ Any cell that can see both the ‘3, 9’ cell and the ‘7, 9’ cell is always in the same row, column, or block as whichever one ends up containing ‘9,’ so ‘9’ can be removed from its candidates.
Tips for Finding XY-Wing
Finding many cells with exactly two candidates is the prerequisite. When you find a cell with candidates ‘A, B,’ look for ‘A, C’ and ‘B, C’ in cells that share its row, column, or block. XY-Wing takes practice to spot, but careful candidate notation makes it much easier to find.