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[nataraj]

[cgordon]

[Steve R]

In Marty’s original grid you could try:

r4c7 = 9 => r9c7 = 7 => r9c1 = 8 => r2c1 = 3 => r4c1 =9 => r4c7 ≠ 9

Steve

[Marty R.]

[cgordon]

I must be a purist because I once wrote down a posted explanation of extended xy wings (from Keith I think). It went: xy - xy = xy = xy - yz. Nothing like the above. Very confusing to a young lad trying to find his way in the big league !

[Asellus]

nataraj's "M-Wing" is only a very slight variant of an M-Wing, and one which has been discussed before on this board. As Marty notes, the basic M-Wing involves a pair of matching bivalues in remote cells. Plus, the links involved are all conjugate. That allows the M-Wing to be colored with basic Medusa.

We could notate the M-Wing as:
YX=X=XY=Y
Or, showing all of the links:
(Y=X)=X=(X=Y)=Y
While all of these links are conjugate in the basic M-Wing, the inferences are strong (in red) and weak (in green).

ravel introduced a "half M-Wing" with an actual weak (only) link in the second position:
YX-X=XY=Y

nataraj's elimination is similar except that the actual weak (only) link is now in the fourth position inside what would otherwise be the second bivalue cell:
YX=X=(X-Y)=Y

If r6c1 were a 79 bivalue instead of a 789 triple, the M-Wing would be just fine and easily recognized. But, that non-pincer bivalue doesn't actually need to be a bivalue and the wing still works.

The "classic" all-conjugate M-Wing is a simple case of basic Medusa. These two forms of "half M-Wings" are simple cases of Medusa multi-coloring. In ravel's case, with the Aa and Bb coloring indicated below the XY notation:
YX-X=XY=Y
Aa-b=Bb=B
The weak link bridges the two clusters with "ab" making "AB" the strong color pair. In nataraj's case:
YX=X=(X-Y)=Y
Aa=A=(a-b)=B

So Medusa coloring IS involved, just multi-coloring instead of basic coloring. For the record, we could have a "half half M-wing" with both weak (only) links present. But, this requires 3-cluster Medusa multi-coloring:
YX-X=(X-Y)=Y
Aa-b=(B-C)=c
The "AB" strong pair and "bc" strong pair induce the "Ac" strong pair of the pincers. But, this getting a bit far afield from that all conjugate M-Wing. Still, it is all related to Medusa and there is a common structure. That common structure is just the underlying AIC:
(Y=X)-(X)=(X-Y)=(Y)

[nataraj]

[keith]