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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Mon Dec 08, 2008 6:05 am Post subject: Paul's Pages, random Outlaw |
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I couldn't find anything here but Medusa, although it looked like something should've been there. I'm interested in what others find.
| Code: |
+-------+-------+-------+
| . . . | 6 . . | 9 . . |
| . . . | . 7 4 | 8 . . |
| 2 9 3 | . . . | . 7 . |
+-------+-------+-------+
| 1 . . | . . 6 | 7 . . |
| . 3 . | . 5 . | . . . |
| . 8 . | 2 . 1 | . 9 6 |
+-------+-------+-------+
| . 5 . | 8 . . | . . 9 |
| . . 7 | 4 6 . | 5 . 1 |
| 3 . . | . . . | . . . |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Mon Dec 08, 2008 1:10 pm Post subject: |
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This worked for me:
| Code: | *--------------------------------------------------*
| 48 7 48 | 6 23 23 | 9 1 5 |
| 5 16 16 | 9 7 4 | 8 2 3 |
| 2 9 3 | 15 18 58 | 6 7 4 |
|----------------+----------------+----------------|
| 1 4 29 | 3 89 6 | 7 5 28 |
| 69 3 269 | 7 5 89 | 1 4 28 |
| 7 8 5 | 2 4 1 | 3 9 6 |
|----------------+----------------+----------------|
| 46 5 146 | 8 13 7 | 2 36 9 |
| 89 2 7 | 4 6 39 | 5 38 1 |
| 3 16 89 | 15 129 259 | 4 68 7 |
*--------------------------------------------------*
8=r1c1=4=r7c1=6=r7c8=3=r8c8=8=>r8c1<>8 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Dec 08, 2008 10:03 pm Post subject: |
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| Dan, I tried some XY-Chains but missed that one. There seems to be considerable overlap between them and Medusa. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Dec 09, 2008 4:35 am Post subject: |
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While not a suggested alternate solution, this is an interesting example of a BUG+4 that can be done without forcing. The extra digits are <6> in r7c3, <1> in r9c5 and <9>s in r5c3|r9c6. This provides a grouped strong inference:
BUG[(9)r5c3|r9c6=(61)r7c3|r9c5]
This 61 "pseudocell" also provides what is essentially an XY-Wing with <6> pincers in r7c38:
(6=1)r7c3|r9c5 - (1=3)r7c5 - (3=6)r7c8
Note that (61)r7c3|r9c5 and (6=1)r7c3|r9c5 are logically identical. The group (61) is true if either or both of 6 and 1 are true. This is the same as a strong inference. And note that this XY-Wing-like thing, which I put in brackets below, can be thought of as "(6)r7c38". So, we can write:
(9)r9c3 - BUG:(9)r5c3|r9c6=[(6=1)r7c3|r9c5:endBUG - (1=3)r7c5 - (3=6)r7c8] - (6=4)r7c1 - (4=8)r1c1 - (8=9)r8c1 - (9)r9c3; r9c3<>9
The notation isn't quite up to the concept. I suppose some sort of branching structure might be an option. Perhaps better is a telescoping sequence of non-branching AICs. How's this?
| Code: | (9)r9c3 - BUG[(9)r5c3|r9c6=(61)r7c3|r9c5]
(6=1)r7c3|r9c5 - (1=3)r7c5 - (3=6)r7c8
(6)r7c38 - (6=4)r7c1 - (4=8)r1c1 - (8=9)r8c1 - (9)r9c3;
r9c3<>9 |
PS @ arkietech:
I believe your NL notation should be something like
[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8] => r8c1<>8
The links between the cells are weak, not strong. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Dec 09, 2008 5:26 am Post subject: |
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| Asellus wrote: | PS @ arkietech:
I believe your NL notation should be something like
[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8] => r8c1<>8
The links between the cells are weak, not strong. |
The XY-Chain as an AIC in NL notation.
| Code: | 8-[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8]-8 => [r8c1]<>8
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For those more comfortable with Eureka notation.
| Code: | (8=4)r1c1 - (4=6)r7c1 - (6=3)r7c8 - (3=8)r8c8 => r8c1<>8
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Dec 09, 2008 5:30 am Post subject: |
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Shouldn't it be
8=[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8]=8 => r8c1<>8
if you're going to include dangling pincer <8>s? Or perhaps...
[r8c1]-8-[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8]-8-[r8c1] => r8c1<>8 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Dec 09, 2008 5:45 am Post subject: |
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| Asellus wrote: | Shouldn't it be
8=[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8]=8 => r8c1<>8
if you're going to include dangling pincer <8>s? Or perhaps...
[r8c1]-8-[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8]-8-[r8c1] => r8c1<>8 |
No dangling pincers. The 8s are part of the chain -- just like they are part of the Eureka chain I included above.
| Code: | Strong inference within a bivalue cell is denoted by: n-[cell]-m
Weak inference between cells is denoted by: [cell]-z-[cell]
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Here's arkietech's (AIC) XY-Chain disected in NL notation:
| Code: | 8-[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8]-8 => [r8c1]<>8
8-[r1c1]-4 strong inference
[r1c1]-4-[r7c1] weak inference
4-[r7c1]-6 strong inference
[r7c1]-6-[r7c8] weak inference
6-[r7c8]-3 strong inference
[r7c8]-3-[r8c8] weak inference
3-[r8c8]-8 strong inference
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The problem with NL notation is that a connector symbol reverses its meaning depending upon which side of the cell it resides.
When reading the AIC from left-to-right:
| Code: | 8-[r1c1] means: [r1c1]<>8
[r1c2]-4 means: [r1c1]=4
8=[r1c1] means: [r1c1]=8
[r1c2]=4 means: [r1c1]<>4
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When reading the AIC from right-to-left:
| Code: |
[r1c2]-4 means: [r1c1]<>4
8-[r1c1] means: [r1c1]=8
[r1c2]=4 means: [r1c1]=4
8=[r1c1] means: [r1c1]<>8
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Last edited by daj95376 on Tue Dec 09, 2008 5:51 pm; edited 3 times in total |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Dec 09, 2008 2:06 pm Post subject: |
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Thanks
The links look strong to me. Should xy-chain always be weak? I will learn notation some day. 
dan |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Dec 10, 2008 7:49 am Post subject: |
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| dan wrote: | | Should xy-chain always be weak? I will learn notation some day. |
In an XY-Chain, the inferences within bivalue cells are strong and those between bivalue cells are weak. This should be evident because, when we jump from one cell to the next, we only care that they share a digit and we don't care how many other instances of that digit there are in their mutual houses.
Only the inferences between cells are shown in Nice Loops (NL) notation, where as in Eureka notation all of the inferences are shown explicitly. This is why I prefer Eureka: all the cards are on the table.
I rechecked Sudopedia (something I should have done originally) and, per them, the correct NL notation is as I wrote it the second time:
[r8c1]-8-[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8]-8-[r8c1] => r8c1<>8
This makes sense to me because there are no "dangling" inferences on the ends (and no need to interpret them in terms of true/false assumptions).
The correct (i.e. "full") Eureka notation of the same thing is:
(8)r8c1 - (8=4)r1c1 - (4=6)r7c1 - (6=3)r7c8 - (3=8)r8c8 - (8)r8c1; r8c1<>8
You can see that the strong inferences within the bivalue cells are explicit in Eureka, plus one can see readily that the inferences alternate as required. (I believe that that is a bit harder to do using NL notation, particularly in more complex chains.)
Anyway, don't get discouraged regarding notation. There aren't hard and fast rules and people have their own variations. What is important is to get the inferences down correctly. If one does that, then the notation will be understood. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Dec 10, 2008 4:28 pm Post subject: |
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| Asellus wrote: | rechecked Sudopedia (something I should have done originally) and, per them, the correct NL notation is as I wrote it the second time:
[r8c1]-8-[r1c1]-4-[r7c1]-6-[r7c8]-3-[r8c8]-8-[r8c1] => r8c1<>8
This makes sense to me because there are no "dangling" inferences on the ends (and no need to interpret them in terms of true/false assumptions).
The correct (i.e. "full") Eureka notation of the same thing is:
(8)r8c1 - (8=4)r1c1 - (4=6)r7c1 - (6=3)r7c8 - (3=8)r8c8 - (8)r8c1; r8c1<>8
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Strange, we must be reading different Sudopedia sites. Here's the Eureka notation they show for their example here.
| Code: | (5=1)r3c3-(1=6)r7c3-(6=1)r8c1-(1=5)r8c5
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It clearly matches the Eureka notation that I listed above. This notation translates into the NL notation that I use.
For reference
| Myth Jellies wrote: | It turns out that all chains found so far which qualify as theoretical can be described as Alternating Inference Chains. XY-Wings, X-Cycles, Bivalue XY-Chains, Bilocation XY-Chains, Mixed XY-Chains, Continuous and Discontinuous Nice Loops, Dual Implication Chains, chains employing Unique Rectangles, XYZ-Wings, even the ALS XZ-Rule deductions are all Alternating Inference Chains (AICs). Furthermore, AIC's are all guaranteed to be pattern-based, theoretical, and not brute force.
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| Quote: | Deductions
Quite simply, at least one or the other (possibly both) of the two endpoint candidates (or candidate premises) of an AIC is true. Any deductions that you can make based on that are valid. This tends to produce the best results if the endpoints either share a group, or if the endpoints involve the same candidate. When your chain endpoints satisfy one of those conditions, it is time to check for any deductions.
If the two endpoints candidates are weakly linked, then you have an AIC loop. In this case, you could cut the loop at any weak link and end up with a valid AIC. Thus, for every weak link in the loop, either one or the other of the candidates joined by that weak inference are true, and you can make all appropriate deductions based on that.
That is pretty much all you need.
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| Code: | pure bivalue loop:
*-----------------------------------------------------------*
| 5 6 29 | 7 3 1 |G29 4 8 |
| 247 248 17 | 5 9 48 | 6 3 12 |
| 349 348 A13 | 48 6 2 | 5 7 H19 |
|-------------------+-------------------+-------------------|
| 367 9 B37 | 2 C47 5 | 1 8 467 |
| 27 25 4 | 68 1 68 | 3 59 579 |
| 16 15 8 | 3 D47 9 |E47 2 56 |
|-------------------+-------------------+-------------------|
| 1234 7 6 | 9 8 34 |F24 15 245 |
| 1349 134 5 | 46 2 3467 | 8 19 479 |
| 8 24 29 | 1 5 47 | 2479 6 3 |
*-----------------------------------------------------------*
A1=A3-B3=B7-C7=C4-D4=D7-E7=E4-F4=F2-G2=G9-H9=H1 (-A1)
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| Myth Jellies wrote: | Eureka notation
(1=3)r3c3 - (3=7)r4c3 - (7=4)r4c5 - (4=7)r6c5 - (7=4)r6c7 - (4=2)r7c7 - (2=9)r1c7 - (9=1)r3c9...
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For further support of my position see here
Last edited by daj95376 on Wed Dec 10, 2008 5:05 pm; edited 4 times in total |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Dec 10, 2008 4:46 pm Post subject: |
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| Marty: My apologies for helping to hijack your thread. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Dec 21, 2008 12:38 am Post subject: |
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| Code: | +-------------+-------------+-------------+
| 48a 7 48 | 6 23 23 | 9 1 5 |
| 5 16 16 | 9 7 4 | 8 2 3 |
| 2 9 3 | 15 18 58 | 6 7 4 |
+-------------+-------------+-------------+
| 1 4 29 | 3 89 6 | 7 5 28 |
| 69 3 269 | 7 5 89 | 1 4 28 |
| 7 8 5 | 2 4 1 | 3 9 6 |
+-------------+-------------+-------------+
| 46b 5 146 | 8 13 7 | 2 36c 9 |
|-89 2 7 | 4 6 39 | 5 38d 1 |
| 3 16 89 | 15 129 259 | 4 68 7 |
+-------------+-------------+-------------+ |
Continuing my extended XY-wing campaign. (I don't like the name, I like the way to find them.)
In C1, <48> and <46> are a pseudocell <68>. They make a wing with <36> and <38> in B9 to eilimnate <8> in R8C1.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Dec 21, 2008 6:02 pm Post subject: |
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Keith, I respect your extended XY-Wing campaign, but your interpretation bothers me. Here is a contrived XY-Chain.
| Code: | ** ** ** ** ** ** ** a pseudocell for <18> using your method
12-23-34-45-56-67-78-89-91 an extended XY-Wing using your method
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Now, an XY-Wing of three cells with extensions on one or both ends, that's what I'd call an extended XY-Wing.
| Code: | ** ** ** an XY-Wing
12-23-37-75-56-67-78-89-91 an extended (in both directions) XY-Wing
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Dec 21, 2008 11:00 pm Post subject: |
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Danny,
I'm going to stop using the name.
I think I first used the term "extended XY-wing" to mean an extension such as:
XZ-XY-YZ-YZ-YZ
Nataraj and I had a brief campaign to call this a flightless wing, but most now call it a wing with transport. The transport can, of course be via coloring, as in
XZ-XY-YZ=aZ=bZ
where = is a strong link, and a and b are any candidates.
====
What I mean here is a 4-cell chain:
XZ-XY-WY-WZ
which has Z as the pincer value. My point is, if you have two cells
XZ-XY
and are looking for a third cell to YZ make an XY-wing, you may as well look for the "pseudocell" combination WY-WZ, which acts like YZ.
Of course, any two adjacent cells in any XY-chain can be regarded as a pseudocell. I am just trying to explain a systematic method for finding longer chains.
Keith
===
Marty,
How about them Lions? Not only a record for losing, but the press is finding all kinds of other records:
First game ever where a team did not have to punt.
NFL record for losing margin in home games. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Dec 21, 2008 11:58 pm Post subject: |
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| keith wrote: | Danny,
I'm going to stop using the name.
I think I first used the term "extended XY-wing" to mean an extension such as:
XZ-XY-YZ-YZ-YZ
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| Code: | ** ** ** XY-Wing
ZX-XY-YZ-ZW-WZ XY-Wing (extension #2 that I listed awhile back)
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| Quote: | Nataraj and I had a brief campaign to call this a flightless wing, but most now call it a wing with transport. The transport can, of course be via coloring, as in
XZ-XY-YZ=aZ=bZ
where = is a strong link, and a and b are any candidates.
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| Code: | ** ** ** XY-Wing
** ** strong link on Z
ZX-XY-YZ - Za = Zb XY-Wing w/transport (extension #4 that I listed awhile back)
_________________________________________________________________________________
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| Quote: | I am just trying to explain a systematic method for finding longer chains.
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If it works for you and others, great! I can't find an XY-Chain if it fell on me 
Bottom Line: I don't have a problem with you or others using an extended/transported XY-Wing. I never heard of them until I joined this forum. I think they are a great idea -- especially for manual solvers to describe what they found. All I ask is that some part of the chain actually contain an XY-Wing.
As for your pseudocell example. I think that it's covered by:
| Code: | ** * * **
ZX-XV-VY-YZ XY-Wing (extension #1 that I listed awhile back)
84-46-63-38 <348> XY-Wing with extended/pseudo pivot cell
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But, I never (truthfully) accepted this as an XY-Wing extension. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Dec 22, 2008 1:26 am Post subject: |
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| Quote: | How about them Lions? Not only a record for losing, but the press is finding all kinds of other records:
First game ever where a team did not have to punt.
NFL record for losing margin in home games. |
The Matt Millen legacy. When he's back in the broadcast booth, how much credibility will he have when critiquing GMs?
I didn't know about those two records. wait til next year!! |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Dec 22, 2008 2:44 am Post subject: |
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The only 4th down for New Orleans was when they put the knee down to run out the clock on the last play of the game.
Mercifully, the local TV broadcast was blacked out.
Keith |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Mon Dec 22, 2008 5:02 pm Post subject: |
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I may be responsible for the “extended XY- wing” description but it seems that I saw the pattern from a totally different perspective. What I had in mind was that the pivot was extended (to two cells).
The grid below is Keith’s, adjusted to identify the twin pivots with asterisks and the pincers with “pin:”
| Code: | +----------------+-------------+---------------+
| pin48 7 48 | 6 23 23 | 9 1 5 |
| 5 16 16 | 9 7 4 | 8 2 3 |
| 2 9 3 | 15 18 58 | 6 7 4 |
+----------------+-------------+---------------+
| 1 4 29 | 3 89 6 | 7 5 28 |
| 69 3 269 | 7 5 89 | 1 4 28 |
| 7 8 5 | 2 4 1 | 3 9 6 |
+----------------+-------------+---------------+
| *46 5 146 | 8 13 7 | 2 *36 9 |
| -89 2 7 | 4 6 39 | 5 pin38 1 |
| 3 16 89 | 15 129 259 | 4 68 7 |
+----------------+-------------+---------------+ |
Perhaps this makes the connexion with the XY-wing clearer but it doesn’t help you much if your search for the pattern has a different starting point.
There is only one way for the Lion's to go. But then, I thought that last season too....
Steve |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Dec 22, 2008 8:00 pm Post subject: |
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Steve,
Thanks. The way I described it, I would find the chain by starting with the two cells at either end.
Using these things on the Brain Bashers (super hard) puzzles is almost like having an unfair advantage.
Keith |
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