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m-wings?

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arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Sun Oct 30, 2011 4:00 pm Post subject: m-wings?

Found a good puzzle to try to learn m wings using Keith's tips. Work the puzzle first. It is loaded with one-steppers. Then look at what I found concerning m wings. Any help will be appreciated.

Code:

*-----------*
|641|25.|3..|
|.8.|.63|..4|
|...|...|...|
|---+---+---|
|3.4|...|1..|
|...|9.6|...|
|..6|...|4.2|
|---+---+---|
|...|...|...|
|4..|13.|.5.|
|..9|.27|846|
*-----------*
Choose any cell, a, that has only two candidates, XY. See if you can find another cell, b, such that
1) a = X forces b = X.
2) b contains Y as a candidate.

If you can find a third cell, c, such that bc is a strong link in Y, then ac are the pincers of an M-wing, and eliminate Y.

can "strong link" be a chain?

*-----------------------------------------------------------*
| 6 4 1 | 2 5 89 | 3 79 789 |
| 259 8 25 | 7 6 3 | 59 1 4 |
| 579 579 3 | 4 89 1 | 6 2 589 |
|-------------------+-------------------+-------------------|
| 3 59 4 | 8 7 2 | 1 6 59 |
| 2578 1 2578 | 9 4 6 | 57 78 3 |
| 789 79 6 | 3 1 5 | 4 789 2 |
|-------------------+-------------------+-------------------|
| 578 2 578 | 6 89 4 | 79 3 1 |
| 4 6 78 | 1 3 89 | 2 5 79 |
| 1 3 9 | 5 2 7 | 8 4 6 |
*-----------------------------------------------------------*
(5)r3c2=(5)r4c2-(5=9)r4c9-(9)r8c9=(9)r7c7-(9=5)r2c7 => r2c13,r3c9<>5
x=9, y=5, a=r2c7, b=r4c9, c=r3c2, (y)c=(y)b m wing?

(9=5)r4c2-(5)r4c9=(5)r3c9-(5=9)r2c7-(9)r1c8=(9)r6c8 => r6c12,r4c9<>9
x=5, y=9, a=r4c2, b=r2c7, c=r6c8, (y)c=(y)b m wing?

(8=7)r8c2-(7)r8c9=(7-8)r1c9=(8)r3c9-(8)r3c5=(8)r7c5 => r7c13,r8c6<>8
x=7, y=8, a=r8c2, b=r1c9, c=r7c5, (y)c=(y)b m wing?

(8=9)r1c6-(9)r8c6=(9-7)r8c9=(7-8)r1c9=(8)r3c9 => r1c9,r3c5<>8
x=9, y=8, a=r1c6, b=r8c9 b does not contain candidate -- what is it?

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sun Oct 30, 2011 6:41 pm Post subject: Re: m-wings?

arkietech wrote:

(5)r3c2=(5)r4c2 - (5=9)r4c9-(9)r8c9=(9)r7c7-(9=5)r2c7 => r2c13,r3c9<>5
x=9, y=5, a=r2c7, b=r4c9, c=r3c2, (y)c=(y)b m wing?

(9=5)r4c2-(5)r4c9=(5)r3c9-(5=9)r2c7 - (9)r1c8=(9)r6c8 => r6c12,r4c9<>9
x=5, y=9, a=r4c2, b=r2c7, c=r6c8, (y)c=(y)b m wing?

(8=7)r8c2-(7)r8c9=(7-8)r1c9=(8)r3c9 - (8)r3c5=(8)r7c5 => r7c13,r8c6<>8
x=7, y=8, a=r8c2, b=r1c9, c=r7c5, (y)c=(y)b m wing?

(8=9)r1c6-(9)r8c6=(9-7)r8c9=(7-8)r1c9=(8)r3c9 => r1c9,r3c5<>8
x=9, y=8, a=r1c6, b=r8c9 b does not contain candidate -- what is it?

The first two are extended w-wings and the third is an extended m-wing. I've colored the extensions blue. Other than the x-wing, the term wing is generally applied to chains with three strong links. Such chains, however, are commonly extended with one additional strong link, sometimes more.

If you remove the last strong link from your fourth chain, what remains implies r1c9<>8. This is known as a hybrid wing or h-wing in some circles.

Edit: What I termed "extended" above is normally called "transported" on this site.

Last edited by ronk on Mon Oct 31, 2011 12:07 am; edited 1 time in total

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Oct 30, 2011 8:20 pm Post subject:

Dan, the following descriptions are from my notes, written using Eureka notation, and represent early definitions with common extensions that I'd seen others use. The first thing to note is that they are based on two candidate values!

Code:

===== ===== ===== ===== ===== ===== ===== ===== ===== M/W/S/L2-Wing

gM-Wing: (X=Y)a - (Y)b ... = (Y-X)c = (X)d elims for (X) in peers common to "a","d"
gM-Ring: continuous loop if "a","d" in same unit

gW-Wing: (X=Y)a - (Y)b ... = (Y)c - (Y=X)d elims for (X) in peers common to "a","d"

S-Wing: (X)a = (X)b - (X=Y)c - (Y)d = (Y)e "a" and "e" in same unit; a<>Y, e<>X

L2-Wing: (X)a = (X)b - (X)c = (X-Y)d = (Y)e "a" and "e" in same unit; a<>Y, e<>X
______________________________________________________________________________________

After several recent puzzles included M-Wings and W-Wings using four strong links instead of the tradidional three strong links, I updated my MWSL2_chain() module to (hopefully) identify the most flexible possibilities for extending these wings without destroying their underlying nature.

In the module's internal documentation, I updated the Eureka notation to be based on strong links without the identification of cells. Then, I identified where transitions occur from one value to the other. Finally, I added an asterisk (*) to indicate where SLs could be repeated. The first thing to became obvious was whether a transistion occurred at a strong link or a weak link.

Here's the module's internal documentation for each wing:

Code:

gM-Wing: (A=B) - (B=B)* - (A=A)*
### ######## (two transitions -- 1st must be bivalue)

gW-Wing: (A=B) - (B=B)* - (B=A)
### ### (two transitions -- both must be bivalue)

S-Wing: (A=A)* - (A=B) - (B=B)* {1st A and last B in the same unit}
### (one transition -- must be bivalue)

L2-Wing: (A=A)* - (A=A)* - (B=B)* {1st A and last B in the same unit}
######## (one transition -- bivalue not necessary)

(reverse) (B=B)* - (A=A)* - (A=A)* {1st B and last A in the same unit}
######## (one transition -- bivalue not necessary)
________________________________________________________________________________

The first thing you'll notice is that I only allow the W-Wing to be extended internally. As ronk has already shown, it can also be extended externally. Something I'm considering, but only on the right side of the chain! Also, the "reverse" entry for the L2-Wing is redundant upon close inspection, but I felt the need to include it for the two scenarios when the L2-Wing has only three SLs.

Since ronk was nice enough to specifically identify each of your chains, I won't repeat his effort.

Regards, Danny

arkietech

Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

Posted: Sun Oct 30, 2011 8:38 pm Post subject:

Thanks Ronk and Danny...most helpful.

ronk

Joined: 07 May 2006
Posts: 398

Posted: Sun Oct 30, 2011 8:42 pm Post subject:

daj95376 wrote:

The first thing you'll notice is that I only allow the W-Wing to be extended internally. As ronk has already shown, it can also be extended externally.

I'd like to see a different term for "internally extended", perhaps "stretched" like a stretch limo. Of course, if a wing is then both stretched and extended, "extended stretched" would be a stretch. Laughing

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Oct 30, 2011 10:45 pm Post subject:

ronk wrote:

daj95376 wrote:

The first thing you'll notice is that I only allow the W-Wing to be extended internally. As ronk has already shown, it can also be extended externally.

Ron's terminology reminds me of what I went through when I first joined this site and ran into "extended" and "transported" patterns.

I finally decided that "transported" was a way of describing "- (A=A)" being tacked onto the end of a pattern. As for "extended", it often represented "- (A=A) -" being inserted inside of a pattern.

Today, I try to stay away from "extended" and "transported" whenever possible!!!

Regards, Danny

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