Saturday 8-May-2010
... by: Nassir M
RemovedAndrew Stuart writes:
Comments removed as the pertained to previous examples
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| This is an extension of Y-Wing or (XY-Wing). John MacLeod defines one as "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 Extended Trio cannot have that number as its true value. |
| 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. |
 XYZ-Wing eg 1 |
In this example the candidate number is 1 and F9 is the Hinge. It can see a 1/2 in D9 and a 1/4 in F1. We can reason this way: If D9 contains a 2 then F1 and F9 become a naked pair of 1/4 - and the naked pair rule applies. Same with F1. If that's a 4 then D9 and F9 become a naked pair of 1/2 each. If any of the three are 1 then 1 is still part of the formation. Any 1 visible to all three cells must be removed, in this case in F7. |
 XYZ-Wing example 1: Load Example or : From the Start |
The second example shows an XYZ-Wings based on a row and a box. The hinge cell is on E8 and the common candidate is 6. The 6 in E9 can see all the 6s in the whole XYZ formation. Aligned Pair Exclusion The logic on an XYZ-Wing is completely different and lot simpler than the Aligned Pair Exclusion described below but the funny thing is that XYZ-Wing is a total sub-set of APE. Every XYZ-Wing can be solved by APE (but not vis versa). |
 XYZ-Wing eg 2: Load Example or : From the Start |
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