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nataraj
Joined: 03 Aug 2007 Posts: 1048 Location: near Vienna, Austria

Posted: Wed Apr 23, 2008 8:22 pm Post subject: 


DannyOR, I really like your chain. It starts with a simple pattern search (for xywing), but goes beyond the simple pattern while still keeping the essence of all the wing methods (look for usable pincers and try to connect them).
The way this chain might have developped:
lets look for xywings, ok...
here's a possible one: 5778 hm, where's the missing 58?
we do have a 48, but that's no xywing, mmmhhh what now?
ah, there is a 45, too. So we found an (generalizeded) xywing after all:
57(7884)45, which means either r1c2 or r3c8 (or both) must be "5"
but, alas, it is "useless".
so try transporting ...
if r1c2=5 then (by way of a weak and a strong link) r7c3=5
heureka, now the chain is useful, it solves r7c8!
congratulations.
the whole chain with alternating strong and weak links:
(5=4)r3c8(4=8)r3c7(8=7)r1c9(7=5)r1c2(5)r1c3=(5)r7c3;r7c8<>5
looks forbidding, doesn't it? And still, it developped so naturally.... 

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nataraj
Joined: 03 Aug 2007 Posts: 1048 Location: near Vienna, Austria

Posted: Wed Apr 23, 2008 8:33 pm Post subject: 


stevieboy wrote:  I was "reaching" wrongly, no doubt about it! 
Isn't that what learning / progress is all about?
experience > mental picture (=theory) > apply theory > be wrong > refine theory > apply > ... and so on
no other way to make progress, really, but to "reach" and be wrong sometimes. 

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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA

Posted: Wed Apr 23, 2008 8:43 pm Post subject: 


DennyOR wrote:  Since I like to look for xy chains, from nataraj's position I solved the puzzle with what I would notate as (r3c8) 54488775=458=58 (r7c3), or what maybe would be called an xy chain with a coloring extension. Somebody a while back suggested looking for a coloring extension (my words) on an otherwise useless xywing (or chain), and that's turned out to be pretty useful. 
That somebody might have been me.
What you have used is an AIC (Alternate Implication Chain). Thinking of it as a coloring extension of an XY Chain pincer is fine. However, it is even better (and consistent with AIC thinking) to consider it as adding the strongly linked pair of <5>s in c3 to the end of your XY Chain. The reason is that the <5>s in r1 do not need to be strongly linked (as they would be in basic coloring). If the XY Chain "pincer" <5> in r1c2 is true, then r1c3 must be false no matter how many <5>s are in r1 (and r7c3 must then be true).
We can use your notation to show how this AIC approach works, using the Eureka convention that "" means a weak inference link and "=" means a strong inference link. You wrote:
54488775=458=58
But, I will rewrite it as:
54488775458=58
The sequential bivalues in the XY Chain are all weakly linked by their shared digits, as marked. Next, keep in mind that a conjugate ("either/or") link can be considered as either strong or weak. (Conjugate links are called "strong links" in common parlance, so this confuses some folks. The "one or both must be true" strong links of wing pincers or extra DP cells, as earlier in this thread, are examples of "strong only" links.) That's why I am able to write "75458" in r1 as a weak link.
We've almost got the complete picture. The digits within bivalue cells are also conjugate. So, we'll consider them as strong links in this case and modify your chain notation so:
(5=4)(4=8)(8=7)(7=5)(458)=(58)
I have put cell contents in parentheses for clarity. Note that as you read from left to right (or right to left), the link signs alternate strongweakstrongweaketc. (These are the "alternating implications.") The strongly linked <5>s on the two ends are the pincers of this chain.
Since the {48} in the penultimate cell and the <8> in the last cell don't really matter, I can leave them out and, instead, add cell references after each set of parentheses to make the cells clear:
(5=4)r3c8(4=8)r3c7(8=7)r1c9(7=5)r1c2(5)r1c3=(5)r7c3
Starting to look suspiciously like that Eureka stuff, isn't it? In fact, it is. The only thing needed to make it kosher Eureka is to add the victim(s) to both ends, connected by weak links, and add a note that the victim is eliminated:
(5)r7c8(5=4)r3c8(4=8)r3c7(8=7)r1c9(7=5)r1c2(5)r1c3=(5)r7c3(5)r7c8; r7c8<>5
If this all makes sense, then you can see that one or more conjugate links can be exploited in the middle of an XY Chain as well, not just at the end(s). Or, you could call it extending the ends of basic coloring by using XYChains, to turn the whole thing on its head! 

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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA

Posted: Wed Apr 23, 2008 8:45 pm Post subject: 


Synchronicity! 

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storm_norm
Joined: 18 Oct 2007 Posts: 1741

Posted: Wed Apr 23, 2008 9:43 pm Post subject: 


this is a record for the number of replies for a daily sudoku thread topic. 

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DennyOR
Joined: 12 Sep 2007 Posts: 33 Location: Portland, Oregon

Posted: Thu Apr 24, 2008 6:39 pm Post subject: 


nataraj and Asellus, thanks for your responses to my post. Asellus, you are exactly right, in looking at my notation, that I didn't realize that a mushy weak link was an acceptable connection at the end of my xy chain.
All the techniques I use to solve Sudokus are things I found somewhere on the internet, which is embarrassing for someone who usually likes to figure things out for himself. As a result, even though I can solve all the very hards, I really don't understand Sudokus. I'm going to study your posts and try to get a little smarter.
Denny 

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cgordon
Joined: 04 May 2007 Posts: 769 Location: ontario, canada

Posted: Thu Apr 24, 2008 9:01 pm Post subject: 


Quote:  As an extra comment: any of the other cells in box 1 can contain an <8> candidate except the cell at the intersection of our row and column, in this case r1c2, marked "#" 
Asellus: Surely for the two perpendicular skyscrapers to exist, there should also be a # sign in R1C1 and R2C2.
Code: 
++++
 . . 8  8 8 .  . . 8 
 # . 8c . 8p.  . . . 
 8c. .  . . .  8 . 8 
++++
 . . .  . . .  . . . 
 . . .  8 . 8  . . 8 
 . . .  . . 8  8 . 8 
++++
 . . 8  8 . .  . . . 
 . . .  . . .  . . . 
 8p. .  .8v8  . . . 
++++

I had similar comment with you diagonal Turbot examples. I won't try copying them but looking at "c to c" in both grids, shouldn't the ~ signs "completely" fill up spaces beyond and between the two c's. (pls see R2 in first example and C6 in righthand example).
Otherwise it seems there are no skyscrapers. 

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Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA

Posted: Fri Apr 25, 2008 8:11 pm Post subject: 


cgordon wrote:  Asellus: Surely for the two perpendicular skyscrapers to exist, there should also be a # sign in R1C1 and R2C2. 
You are asking good questions!
Any cell in box 1 can be <8> except for r2c1 and the Kite/Turbot Fish/Skyscraper is still valid. There are a couple of different ways of looking at this.
First, if any of the 4 cells r13c23 is <8>, then both of the pincer cells must be <8> and we eliminate our victim. If either of r13c1 is <8>, then pincer r2c5 must be <8>. And, if either of r2c23 is <8>, then pincer r9c1 must be <8>. The only cell in box 1 that can eliminate <8> from both pincers is r2c1. So, it is verboten!
A more sophisticated way of seeing the same thing is to note that the grouped cells r2c23 are weakly linked with the grouped cells r13c1. (A weak link exists when two things can't both be true.) AND, each of these cell groups is strongly linked with a pincer. I.e., the r2c23 group is strongly linked with r2c5 and the r13c1 group is strongly linked with r9c1. Since one or both of the cell groups must be false, one of both of the pincers must be true. (This means that the pincers have a strong inference link, to complete the technical picture.) This is what I meant when I referred to grouped links.
As for the "diagonal Turbot," there is similar reasoning but without need of grouped links. The two c's only need to be weakly linked. It is okay if both of them are false because this makes both pincers true. 

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