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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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 Posted: Sat Dec 10, 2011 9:44 am Post subject: rh121011 |
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| Code: | *-----------*
|...|...|.7.|
|1..|.82|...|
|.68|71.|4..|
|---+---+---|
|.9.|.37|.1.|
|...|...|...|
|.1.|86.|.5.|
|---+---+---|
|..9|.41|63.|
|...|67.|..5|
|.2.|...|...|
*-----------* |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sat Dec 10, 2011 1:15 pm Post subject: |
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Wing : 1C7-8R1-(87)R7C9 => -7r9c7
[edit] :  : typo corrected after Dan's observation in next post ... 
Last edited by JC Van Hay on Sat Dec 10, 2011 3:50 pm; edited 1 time in total |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sat Dec 10, 2011 1:41 pm Post subject: |
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| JC Van Hay wrote: | | Wing : 1C7-8R1-(87)R7C7 => -7r9c7 |
Nicely done 
shouldn't it be
Wing : 1C7-8R1-(87)R7C9 => -7r9c7?
| Code: | *-----------------------------------------------------------------------------*
| 23459 345 2345 | 349 59 6 | 18 7 18 |
| 1 347 347 | 349 8 2 | 5 6 39 |
| 359 6 8 | 7 1 35 | 4 29 239 |
|-------------------------+-------------------------+-------------------------|
| 2468 9 246 | 5 3 7 | 28 1 2468 |
| 345678 34578 34567 | 1 2 49 | 3789 48 46789 |
| 2347 1 2347 | 8 6 49 | 2379 5 2479 |
|-------------------------+-------------------------+-------------------------|
| 578 578 9 | 2 4 1 | 6 3 78 |
| 348 348 1 | 6 7 38 | 29 29 5 |
| 3678 2 367 | 39 59 358 | 178 48 1478 |
*-----------------------------------------------------------------------------*
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Dec 11, 2011 4:46 am Post subject: |
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| I have no idea of what kind of wing was played and how the elimination was made. Regardless, I couldn't make a move and was totally stumped. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Dec 11, 2011 4:50 am Post subject: |
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JC, nice solution!!!
After crippling my solver with some incorrect changes (and wiping out my backups), I finally managed to resurrect it. This was the first puzzle that I tested for a solution. It produced an awkward ALS solution, but it at least produced a solution. _ _
| Code: | after basics and before the <18> UR Type 4 (that's present)
+--------------------------------------------------------------------------------+
| 23459 345 2345 | 349 59 6 | 18 7 18 |
| 1 347 347 | 349 8 2 | 5 6 39 |
| 359 6 8 | 7 1 35 | 4 29 239 |
|--------------------------+--------------------------+--------------------------|
| 2468 9 246 | 5 3 7 | 28 1 2468 |
| 345678 34578 34567 | 1 2 49 | 3789 48 46789 |
| 2347 1 2347 | 8 6 49 | 2379 5 2479 |
|--------------------------+--------------------------+--------------------------|
| 578 578 9 | 2 4 1 | 6 3 78 |
| 348 348 1 | 6 7 38 | 29 29 5 |
| 3678 2 367 | 39 59 358 | 178 48 1478 |
+--------------------------------------------------------------------------------+
# 98 eliminations remain
(7)r79c9 =ALS:r179c9= (4-1)r9c9 = (1)r9c7 => r9c7<>7
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Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Dec 11, 2011 7:23 am Post subject: |
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| Marty R. wrote: | | I have no idea of what kind of wing was played and how the elimination was made. Regardless, I couldn't make a move and was totally stumped. |
Marty,
R7C9 is 7, R9C7<>7
or
R7C9 is 8, R1c7<8>, R9C7<1>78
From JC's position, a less exotic solution is the UR 18 R9C79<>8, and then the XY-wing -178 in C79.
An alternate way to look at JC's elimination is that 8 in R7C9 forces 7 in R9C9 via R9C1<1> and R9C8<4>.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Dec 11, 2011 4:55 pm Post subject: |
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| Thanks Keith. |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sun Dec 11, 2011 10:13 pm Post subject: |
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Marty,
Besides Keith's interpretations, another possible reading of the Wing (1C7-8R1-(87)R7C9 => -7r9c7 or 1r91c7-8r1c79-(87)r7c9 => -7r9c7) is :
Either r1c7=8, r1c7<>1 and r9c7=1; Or r1c9=8, r7c9<>8 and r7c9=7. In both cases, r9c7<>7.
Further comments if needed
Recall
| ronk wrote: | | keith wrote: | | How do you define a "wing"? ... |
Other than the x-wing, a wing is any useful chain of three native strong inferences using two or three digits (candidate values). |
Generalization of Ronk's definition.
WING
- Other than the X-Wing, one could define a Wing as any useful "set" of 3 "sets" A,B,C of native Strong Inference "Sets", 2 by 2 weakly linked :
A-B => -x
\ /
C
- Examples : Naked or Hidden Triple, Swordfish, XY(Z)Wing, (H,L2,L3,M,S,W, ...)Wing, ALS-XY Wing, 3 Almost-Patterns (AFish, ALS, AAIC, AA...) Wing , ...
- Application : See Kobold's step 3. (bivalue-AWRing-AWWing) and Peter's step #1 (ALC-bilocal-AL2Wing) in their solutions of the site puzzle , here
- After basics, XY(Z)Wing, the simplest useful wings (A-B-C => -x) to look for are those where each of the sets A, B and C is either a bivalue, a bilocal or an ALC.
Here : B is the pivot; A and C are the pincers.
- Note : The use of a complex Wing is questionable as it may sometimes be more difficult to understand than the/an ordered list of its native SIS.
Furthermore, it is not always clear how such a pattern explains an elimination without any further comments and, in some cases, catches all the eliminations implied by them.
Best regards,
JC |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Dec 11, 2011 11:06 pm Post subject: |
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JC,
Thank you! I was contemplating the same point, but you have stated it much more elegantly than I could.
Some time ago, Danny and I remarked on "unnamed four-link chains" which, I believe, fit in this discussion.
Best wishes,
Keith |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun Dec 11, 2011 11:16 pm Post subject: |
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| JC Van Hay, it appears you have missed the meaning of "native" in the phrase "native strong inference." For example, the strong inference of an ALS comprised of two or more cells is not a native strong inference. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Dec 12, 2011 12:41 am Post subject: |
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| Thanks JC. I could follow yours and Keith's logic to see that r9c7<>7. It's just that it looked like a Forcing Chain to me; I can't see the wing aspect and how it was recognized. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Dec 12, 2011 1:58 am Post subject: |
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In my notes, I have a number of patterns that people have called "wings". However, none of them have an elimination in a cell that is part of the wing. JC uses r9c7 as part of the wing and for the elimination r9c7<>7.
Note: as a generic chain, I still consider it a nice solution.
| Code: | (1)r9c7 = (1-8)r1c7 = (8)r1c9 - (8=7)r7c9 => r9c7<>7
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Regards, Danny |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Mon Dec 12, 2011 9:05 am Post subject: |
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| ronk wrote: | | JC Van Hay, it appears you have missed the meaning of "native" in the phrase "native strong inference." For example, the strong inference of an ALS comprised of two or more cells is not a native strong inference. |
Ronk, I am using the definitions given by SteveK here.
Therefore, in my mind, a native strong inference set is either all the candidates in one cell or all the candidates for a single digit in a house (row or column or box)
Furthemore, for any partition {A,B} of such a set, the following strong inference may be written : A=B.
Accordingly, a subset of such a set is a native weak inference set, as a weak inference may be written between any two disjoint subsets of a native strong inference set.
In this sense, I agree, I also consider an almost n-tuple ALS or AHS (comprised of n native strong inference sets of the same kind in a single house) to be a derived strong inference set.
May be, to be clearer, A, B and C in my proposed definition of a Wing are made of nA, nB and nC native SIS respectively. In the simplest cases, nA=nB=nC=1.
Best regards,
JC |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Mon Dec 12, 2011 12:39 pm Post subject: |
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| JC Van Hay wrote: | | May be, to be clearer, A, B and C in my proposed definition of a Wing are made of nA, nB and nC native SIS respectively. In the simplest cases, nA=nB=nC=1. |
You are effectively saying a "wing" would be comprised of an unlimited number of native strong inferences. That definition is much too broad IMO. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue Dec 13, 2011 6:36 pm Post subject: |
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Two VH steps..
Type 4 UR(18)r19c79; r9c79<>8
xy-wing(78-1)r71c9+r9c7; r1c7,r9c9<>1
Ted |
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