The XYZ-Wing technique involves three cells. One cell (called the pivot) has three candidate digits. The other two cells each have two candidate digits. The candidate digits in these three cells must fulfill certain relationships. Below, we will use a real Sudoku puzzle to demonstrate the Block-Column pattern of this technique.
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3
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8
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6
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6
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In Figure 1, the pink cell (R8,C1) has three candidate digits 3, 6, and 8. Two yellow cells (R8,C2) and (R3,C1) each have two candidate digits. The yellow cell (R8,C2) shares the same 3x3 block with the pink cell, and they have two candidate digits 3 and 6 in common. The other yellow cell (R3,C1) shares the same column with the pink cell, and they have two candidate digits 6 and 8 in common. Also, all these three cells have a common candidate digit 6. These three cells form an XYZ-Wing (Block-Column) pattern.
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Notice that the orange cells in Figure 2 are those cells falling in the common related area of the pink cell and both yellow cells. That means the orange cells are in the same row, in the same column, or in the same 3x3 block as the pink cell and each of two yellow cells.
There are three possibilities for the pink cell:
So, in any of these three cases, the orange cells cannot be 6. The candidate digit 6's in the orange cells can be removed, as shown in Figure 2.