dailysudoku.com

[Earl]

The April 26 DB collapses under a (76) w-wing.


Earl

[storm_norm]

m-wing

{6,7} in r7c7, r8c5

removes 7 in r9c7

[sheryl]

i love the m-wing diagram, but i don't understand the logic. is there anyway you can explain it, please.

[storm_norm]

certainly,

first of all, you need the pair {6,7} to exist.

in this case of the M-wing, we are going to let the 6's be our strong links.

then you might want to read this thread...
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143.

xy=x=xy=y

67=6=67=7

the {6,7} pair is connected through two stong links on 6, you can see the connection via the red lines in the image in my post.

what you need to make the elimination is a strong link on 7 from the second {6,7} pair. in my image its the green line. that is the strong link on 7.

the combination of these strong links eliminate any 7's that the 7 in r7c7 amd r9c5 see.

or,

if r7c7 is not a 7, then r7c7 must be a 6,
which means r7c4 can't be a 6
which means r8c5 must be a 6
which means r8c5 can't be a 7
which means r9c5 has to be a 7
which means r9c7 can't be a 7 .... that is one direction...

then go the other direction...

if r9c5 is not a 7, then r8c5 has to be a 7
which means, r8c5 can't be a 6
which means, r7c4 has to be a 6
which means, r7c6 can't be a 6
which means, r7c6 has to be a 7
which means r9c7 can't be a 7... other direction...

in either direction, r9c7 can't be a 7

[Asellus]

Actually, storm_norm, due to the <7> strong link in r9 that "sees" both of the {67} complementary bivalues, we can go further: those two complementary {67} bivalues must both be <6>. They can't both be <7> else there are no <7>s in r9.

Or, based on that r9 link, the {67} pair is a W-Wing that eliminates <6>(as suggested by Earl), and immediately causes the pair to colapse into <6>s.

Take-home lesson: A W-Wing in a complementary pair immediately collapses into the digit opposite that of the external strong link. The complementary pair means "both are <6> or both are <7>." The W-Wing with external <7> link means "one or both must be <6>." There is only one way out of this: both are <6>.

Or, in keeping with the M-Wing name, we can consult Medusa and she will give us a Wrap:

56  3   15 |#67 


8   67  24 | 367


49  79  12 |#37

We can't have two red <7>s in the same box or column. So, all the reds are false and all the greens are true.
[Edit to clean up line spacing.]

[storm_norm]

thanx Asellus, I was thinking about using medusa to explain it.

this was weird that an m-wing and a w-wing exist on the same pairs.