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Sudoku Algorithms

XYZ Wing
The XYZ-Wing is an advanced Sudoku-solving technique, extending the Y-Wing technique. It involves three cells that contain only three possible values. Below is an example of the XYZ-Wing pattern.
XYZ-Wing Example Three cells, D4, F5, and F8, have possible values of '1', '3', and '7' marked in yellow. Cell F5 acts as a hinge, containing all three numbers and linking to both D4 and F8. This is because F5 shares the same row with F8 and the same square with D4. Cell F6 is connected to all three of these cells; it is in the same row as F7 and in the same square as F5 and D4. In any scenario, at least one of the cells D4, F5, or F8 must have a value of 7. Therefore, any cell linked to all three of these cells should not have a value of 7. Consequently, we can remove the hint of '7' (marked in red) from cell F6.
XYZ-Wing Example The picture on the left illustrates another example of the XYZ-Wing pattern. Three cells, E1, D3, and D9, have hints of '6', '8', and '9' marked in yellow. Cell D3 acts as a hinge, containing all three hints and connecting to E1 (in the same square) and D9 (in the same row). In any scenario, at least one of these three cells must have a value of 6. Since cell D2 is connected to all three XYZ-Wing cells, we can remove the hint of '6' (marked in red) from D2.