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 XYZ-Wing Strategy
XYZ-Wing Strategy

This extends Y-Wings which have three bi-value cells to bi-tri-bi, in other words the hinge contains three candidates, not two.

 Fig. 20.1 It gets its name from the three numbers X, Y and Z that are required in the hinge. The outer cells in the formation will be XZ and YZ, Z being the common number.  (Perhaps it would have been better to call it the ABC-Wing strategy but we’d be swimming against the tide)

But we have to be careful about the way the three cells are aligned.  All on one row or column will not do.

More precisely an XYZ-Wing has three cells that contain only 3 different numbers between them, but which fall outside the confines of one row/column/box, with one of the cells (the 'apex' or 'hinge') being able to see the other two; those other two having only one number in common; and the apex having all three numbers as candidates.”

It follows therefore that one or other of the three cells must contain the common number; and hence any extraneous cell (there can only be two of them!) that "sees" all three cells of the XYZ-Wing cannot have that number as its true value.

Fig. 20.2

In this example the candidate number is 5 and B3 is the Hinge. It can see a 5/7 in B6 and a 4/5 in A1. We can reason this way: If B6 contains a 7 then B3 and A1 become a naked pair of 4/5 - and the naked pair rule applies.

A similar logic allies to A1. If that's a 4 then B3 and B6 become a naked pair of 5/7 each. Any 5 visible to all three cells must be removed, in this case in B1.

XYZ-Wings are not uncommon.  Here the target number is 8.

Fig. 20.3

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