Sudoku Solving Techniques

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WXYZ-Wing Strategy

WXYZ-Wing Strategy

This is an extension of XYZ-Wing that uses four cells instead of three. Each possible value of the hinge cell results in a Z value in one of the cells in the WXYZ-Wing pattern, thus leaving no room for a Z on any cell all four can 'see'.

Fig. 21.1

Its name derives from the four numbers W, X, Y and Z that are required in the hinge. The outer cells in the formation will be Wz, XZ and YZ, Z being the common number.

In this example our four-value hinge is C3 (darkest shade). The three outlier cells, B3, C5 and C8 each contain a 9 (our Z) plus one other number unique to themselves and the hinge. It’s important that these extra numbers really are common only to the hinge and there are no pairs like 5/9 and 5/9 in two of the outlier cells.

Naked Pairs
Fig. 21.2

There is only one cell that all four of the WXYZ can see - R3C1, marked with a cross. It has a 9 which can be removed. No matter what number is the final solution in the hinge, one of the WXYZ must be a 9.

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