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[Victor]

M3782391 (41)

[nataraj]

no x-(xy-, xyz-) wing, indeed

After basics,

[nataraj]

[Victor]

Nataraj queried:

[nataraj]

bummer.
And just when I thought I had it all figured out ...

Let me take it one step at a time.

I start at r8c9. 14. OK
Go left, go up: 14 at r5c5.

So far, I think I follow the M-wing logic: the two cells r8c9 and r5c5 must always have the same solution.

Now I go one cell further, but not r5c7 but r4c6 ("46")
r5c5 and r4c6 have a strong link in 4.

The whole chain reads: If r8c9<>4 then r5c5<>4 (same solution) then (strong link) r4c6=4. Which I thought was the essence of an M-wing: two conjugates and a strong link. Where did I go wrong?

[Victor]

Well . . . , the chain in 4s from r8c9 to r4c6 is just a 3-step colouring chain: one end is definitely 4, the other end definitely not-4. So yes, you can eliminate any 4 they both see.

If it were a true M-wing you'd get from r8c9 to r5c5 in 1s only, and then swap to 4s, i.e. if r8c5 were 1x (where x <> 4). I.e. 2 conjugate steps in 1s from one 14 to the other 14 and then, as you say, one more conjugate step, now in 4s.

[tlanglet]

Hi nataraj and Victor,

I am very much still in the learning mode and reviewed this discussion with great interest. I believe that you are both correct. (If not, then I am more confused that I had hoped.)

I think we have both a classic "remote pair" and an M-wing condition sharing the first two links in the sequence; the <14> in r8c9, r8c5, and r5c5. If the <14> sequence is continued to the <14> in r5c7, we have a "remote pair" which will eliminate all <1> and <4> values seen by both r8c9 and r5c7. If the sequence is continued to the <46> in r4c6, we have an M-wing which will only eliminate any <4> seen by r8c9 and r4c6.

If I am correct, the "remote pair" is a specialized case of an M-wing that eliminates both bivalue candidates. Previously, it was my understanding that all cells involved in a remote pair must contain the same two candidate values but I now believe that only the beginning and ending cells must be the same.

In any case, the logic offered by both of you seems correct to me regardless of what it is called.

Hopefully this will be clarified by those that really know.

Ted

Edit by Ted: Victor, you submitted your last response while I was preparing my comments.

[tlanglet]

[storm_norm]

remember, the classic remote pair is both the m-wing and the w-wing. the classic remote pair is the most specific form of both of these named techniques simply because you have to have the same pair after each conjugate link. then you can expand this relationship of conjugacies to incorporate the w-wing and the M-wing.

if the classic remote pair is not conjugate on each link then its called a xy-chain.

[tlanglet]

Hi Norm,

Thanks for the detailed response. It helped clear up the specifics for me, especially the M-wing. Previously, I understood the M-wing to include the condition of the first three cells all being conjugate as in nataraj's M-wing.

So, it is now my understanding that W-wings and M-wings are a special, specific sequence of linked cells that provide eliminations, and that the sequence noted by nataraj simply does not have a "name".

Do we need N-wings?

Ted

Another day, a little bit smarter about Sudoku (I hope) !

[storm_norm]

HI Ted.

firstly, I have to give a lot of the credit for my sudoku addiction and learning process to the very wings we are discussing and ERs and medusa coloring. if I didn't see Ravel's m-wing here, I would still be somewhat in the dark with some puzzles. and I believe Ravel is the progenitor of the M-wing here on this forum.

nataraj's cells (14)=(14)=(14)=(46) is an m-wing.

but you are right. it just so happens that in this example the first three cells have the same pair.

[Victor]

Ravel is one of my gurus, but I think it was Keith who publicised M-wings (tho' maybe that was after Ravel had mentioned the idea - I don't know):
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2143&sid=4d54d74a9af22f7d18e6d0d37a82ecd4

I guess we all see things in different ways, & so here is the way I look at it, neither better not worse than Norm's, just different. Here's the grid again:

[nataraj]

I think I know much more about these wings now that so many helpful explanations have been given. Now that Victor's mentioned Medusa, I remember the reason keith (or was it ravel?) called it an M-wing is that it is a form of mini-Medusa, so to speak. That helps me along, I can relate to that.

And thanks Victor, for pointing out that my 14-14-14-46 chain is in fact a coloring chain (when one looks at the "4"s only). Funny I never looked at it this way...

Indeed the workings of the M-wing are much better explained (like you did with your 1y (B) cell) when the M-wing is not another wing at the same time.

I will try to summarize what - after this thread's crash course - I understand as the essence of an M-wing:

a) like every good Medusa coloring, it starts with a bi-value cell. One of the two candidates will be the pincer, the other will be used for the M-wing, in my mind I call it the "helper".
b) next we need two links for the helper candidate, preferably both strong links (not sure, but I think the elimination will still work if the first link is weak and the second link is strong).
c) the end cell after these two links must be bi-value again, and have the same two candidates as the original cell. Since we were using a weak link-strong link combination, we know that

if original cell = helper, then end cell = helper

(again, I think the elimination will still work if the end cell is not bi-value but at least contains the original two candidates, plus possibly some others. But ... since for me, both w-wing and M-wing are really mostly a pattern based method to spot useful chains, I would rather stick to the original definition, which says that original cell and end cell must be conjugate pairs)

d) from the end cell, there must be a strong link in the pincer candidate to one more cell, the pincer cell.

Since we are using a weak link (within the end cell) and a strong link, we know that:

if end cell = helper then pincer cell = pincer.

putting the parts together, we get:

if original cell is not pincer then pincer cell is pincer.

Written as an AIC, and using Victor's A,B,C...
-A(4=1)-B(1)=C(1-4)=D(4)-

In a nutshell (basically, I like simple patterns! )
The pattern to look for: two identical bi-value cells
If they are linked in a way that they always have the same solution, look for strong link -> M-wing
If they have complementary solutions, they form a W-wing (or remote pair) already

[Victor]

Yep, Nataraj, sounds good, except perhaps for:

[nataraj]

Victor, I really appreciate your patience in trying to get the subtleties through my head! It is almost midnight here and I am afraid that my mind is not working at full capacity any more.

I'll be abroad for a few days and not be able to access the forum, so there won't be a reaction from me for some time. I'll take it up again when I come back. For the moment, I am happy to have learned a new method, the M-wing (even if I am still slightly off the mark).

There'll be so many "other" puzzles to solve when I come back! Practice makes perfect...

[keith]

[storm_norm]

thanks Keith.

[Victor]

[keith]

If you look at the end of this thread:

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2143

You will find an "Appendix" on half-M-wings.

Maybe if you think that the M-wing starts with a complementary pair, where you can add a link on either end, the half-wing allows you to add the link on only one end

Also, look at this:

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2298

Keith

.

[Asellus]