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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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 Posted: Thu Feb 09, 2012 10:49 pm Post subject: patterns game by joel64 Dec 06, 2010 |
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| Code: | *-----------*
|1..|...|2..|
|...|3..|.4.|
|...|.5.|6.7|
|---+---+---|
|.3.|7..|...|
|5..|.1.|8..|
|..4|..3|.9.|
|---+---+---|
|..2|4..|...|
|.7.|..9|...|
|8..|.6.|..1|
*-----------* |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 10, 2012 5:56 am Post subject: |
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I hope my understanding of an X-Chain is correct. If it is, it's my first.
Multi-coloring; r4c7<>1
X-Chain; r9c8<>7 proves r6c7=7; r5c8, r7c7<>7 |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Fri Feb 10, 2012 11:48 am Post subject: |
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| Marty R. wrote: | I hope my understanding of an X-Chain is correct. If it is, it's my first.
Multi-coloring; r4c7<>1
X-Chain; r9c8<>7 proves r6c7=7; r5c8, r7c7<>7 |
I don't see or understand x-chain 
| Code: | *-----------------------------------------------------------------------------*
| 1 45689 356789 | 689 479 4678 | 2 358 3589 |
| 279 25689 56789 | 3 279 12678 | 159 4 589 |
| 34 2489 389 | 1289 5 1248 | 6 138 7 |
|-------------------------+-------------------------+-------------------------|
| 29 3 18 | 7 2489 56 | 145 1256 2456 |
| 5 269 679 | 29 1 24 | 8 237 234 |
|a27 18 4 | 56 8-2 3 |x157 9 256 |
|-------------------------+-------------------------+-------------------------|
| 36 15 2 | 4 b37 18 |x3579 5678 5689 |
| 346 7 15 | 18 c23 9 | 345 2568 24568 |
| 8 49 39 | 25 6 257 | 34 27 1 |
*-----------------------------------------------------------------------------*
an 273 xy-wing with extension cord.
(2=7)r6c1-(7)r6c7=(7)r7c7-(7=3)r7c5-(3=2) => r6c5<>2 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 10, 2012 1:49 pm Post subject: |
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Dan,
I don't understand the extension cord thing.
Multi-coloring sets r4c7<>1, exposing a 345 triple in c7. I had a third number in r9c8 so I used the X-Chain. Using your grid, it would have been an AIC. The 2 in r9c8 proves 7 in r6c7; r7c7<>7. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Feb 10, 2012 3:30 pm Post subject: |
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Flightless w-wing 27 SL (7)r5c38: (2=7)r6c1-r5c3=r5c8-(7=2)r9c8-r9c46=r8c5; r6c5<>2
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 10, 2012 4:39 pm Post subject: |
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Nice find Ted.  |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Fri Feb 10, 2012 4:57 pm Post subject: |
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| Marty R. wrote: | | Multi-coloring sets r4c7<>1, exposing a 345 triple in c7. I had a third number in r9c8 so I used the X-Chain. Using your grid, it would have been an AIC. The 2 in r9c8 proves 7 in r6c7; r7c7<>7. |
Marty, after your step one I have your position as below:
| Code: | *-----------------------------------------------------------------------------*
| 1 45689 356789 | 689 479 4678 | 2 358 3589 |
| 279 25689 56789 | 3 279 12678 | 19 4 589 |
| 34 2489 389 | 1289 5 1248 | 6 138 7 |
|-------------------------+-------------------------+-------------------------|
| 29 3 18 | 7 2489 56 | 45 1256 2456 |
| 5 269 679 | 29 1 24 | 8 237 234 |
| 27 18 4 | 56 28 3 | 17 9 56 |
|-------------------------+-------------------------+-------------------------|
| 36 15 2 | 4 37 18 | 79 5678 5689 |
| 346 7 15 | 18 23 9 | 345 2568 24568 |
| 8 49 39 | 25 6 257 | 34 27 1 |
*-----------------------------------------------------------------------------* |
I can't find an x-chain/x-cycle at this point. With the x-chain being a single digit
technique, it's not clear how (2)r9c8 gets into the picture. |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Fri Feb 10, 2012 6:07 pm Post subject: |
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1. Dan's move may be interpreted as a pseudo W Wing : pseudo-cell(2=7)r78c5-7r7c7=7r6c7-(7=2)r6c1 => -2r6c5.
2. Even if they aren't usefull in this puzzle, there are 3 easily detected swordfishes : 1C248, 7C157, 9R359.
3. The complementary fishes are respectively 2 swordfishes on the rows (1R267 and 7R159) and 1 jellyfish on the columns (9C1579).
JC |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 10, 2012 6:32 pm Post subject: |
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Luke, I'm having a technical problem trying to quote your post, so here's my response without it.
I had a third number in r9c8 so I used the X-Chain. Using your grid, it would be an AIC. R9c8=2-->r8c5=2-->r6c5=8-->r6c2=1-->r6c7=7. Now we have pincers on 7 at r9c8 and r6c7. I call it an AIC because the trivalue cell at r9c6, by definition, precludes it from being an XY-Chain. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Fri Feb 10, 2012 9:06 pm Post subject: |
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| Marty R. wrote: | I hope my understanding of an X-Chain is correct. If it is, it's my first.
...
X-Chain; r9c8<>7 proves r6c7=7; r5c8, r7c7<>7 |
I was also unable to find an x-chain for these eliminations. Please post your pencilmarks at this point. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Feb 10, 2012 10:40 pm Post subject: |
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| ronk wrote: | | Marty R. wrote: | I hope my understanding of an X-Chain is correct. If it is, it's my first.
...
X-Chain; r9c8<>7 proves r6c7=7; r5c8, r7c7<>7 |
I was also unable to find an x-chain for these eliminations. Please post your pencilmarks at this point. |
Could you tell me if my understanding of an X-Chain is anywhere near correct? I have inferred from reading previous threads that it's a negative proving a positive, e.g., if cell A is not "X", then cell "B" must "X." |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sat Feb 11, 2012 12:10 am Post subject: |
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| Marty R. wrote: | | Could you tell me if my understanding of an X-Chain is anywhere near correct? I have inferred from reading previous threads that it's a negative proving a positive, e.g., if cell A is not "X", then cell "B" must "X." |
So far so good. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Feb 11, 2012 1:10 am Post subject: |
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Thank you. Below is the solution I used, which I think is an AIC, whereby the 2 in A proves a 7 in F. When I first posted about using an X-Chain I had 257 in A, so I used the logic that A<>7 proved 7 in F.
| Code: | +-------------------+--------------------+-------------------+
| 1 45689 356789 | 689 479 4678 | 2 358 3589 |
| 279 25689 56789 | 3 279 12678 | 19 4 589 |
| 34 2489 389 | 1289 5 1248 | 6 138 7 |
+-------------------+--------------------+-------------------+
| 29 3 18 | 7 2489 56 | 45 1256 2456 |
| 5 269 679 | 29 1 24 | 8 23-7 234 |
| 27 E18 4 | 56 D28 3 | F17 9 256 |
+-------------------+--------------------+-------------------+
| 36 15 2 | 4 37 18 | -79 5678 5689 |
| 346 7 15 | 18 C23 9 | 345 2568 24568 |
| 8 49 39 | B25 6 B257 | 34 A27 1 |
+-------------------+--------------------+-------------------+ |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sat Feb 11, 2012 3:39 am Post subject: |
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Marty R, it never occurred to me that you might be trying to use more than one digit in your "x-chain." An x-chain on digit 7, if there were one, would be based on only the pencilmarks for digit 7. IOW you'd be considering only this:
| Code: |
. . 7 | . 7 7 | . . .
7 . 7 | . 7 7 | . . .
. . . | . . . | . . 7
---------+----------+----------
. . . | 7 . . | . . .
. . 7 | . . . | 7 .
7 . . | . . . | 7 . .
---------+----------+----------
. . . | . 7 . | 7 7 .
. 7 . | . . . | . . .
. . . | . . 7 | . 7 . |
[edit: correct illustration]
Last edited by ronk on Sat Feb 11, 2012 5:42 am; edited 1 time in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Feb 11, 2012 4:46 am Post subject: |
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OK, so if the X-Chain only considers PMs with the particular number that's involved, wouldn't that be some sort of coloring?
Also, what would you call what I thought was an X-Chain, where you start with the negative to prove the positive? |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sat Feb 11, 2012 4:20 pm Post subject: |
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| Marty R. wrote: | | OK, so if the X-Chain only considers PMs with the particular number that's involved, wouldn't that be some sort of coloring? |
Of course, it's either the results of simple-coloring or multi-coloring expressed as a chain. Here "multi-" refers to the use of two or more conjugate chains.
| Marty R. wrote: | | Also, what would you call what I thought was an X-Chain, where you start with the negative to prove the positive? |
Every useful chain has your "negative-to-positive" property, and it doesn't have to start and end with the same candidate value. These chains may all be expressed as AICs. |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Sat Feb 11, 2012 8:37 pm Post subject: |
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| JC Van Hay wrote: | | 1. Dan's move may be interpreted as a pseudo W Wing : pseudo-cell(2=7)r78c5-7r7c7=7r6c7-(7=2)r6c1 => -2r6c5. |
| Code: | *-----------------------------------------------------------------------------*
| 1 45689 356789 | 689 479 4678 | 2 358 3589 |
| 279 25689 56789 | 3 279 12678 | 159 4 589 |
| 34 2489 389 | 1289 5 1248 | 6 138 7 |
|-------------------------+-------------------------+-------------------------|
| 29 3 18 | 7 2489 56 | 145 1256 2456 |
| 5 269 679 | 29 1 24 | 8 237 234 |
| 27 18 4 | 56 28 3 | 157 9 256 |
|-------------------------+-------------------------+-------------------------|
| 36 15 2 | 4 37 18 | 3579 5678 5689 |
| 346 7 15 | 18 23 9 | 345 2568 24568 |
| 8 49 39 | 25 6 257 | 34 27 1 |
*-----------------------------------------------------------------------------* |
Thanks for pointing that out, it made me wonder about something that could be exploited.
Could any (2=7) can act as a w-wing pseudo-cell as long as it meets the necessary endpoint
criteria? The two values don't need to be in the same box as above, or even the same house for that matter.
Just as an example, it seems (2)r8c5 and (7)r9c8 could also be considered a pseudo-cell, as the values are strongly linked. |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sat Feb 11, 2012 9:36 pm Post subject: |
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| JC Van Hay wrote: | | 1. Dan's move may be interpreted as a pseudo W Wing : pseudo-cell(2=7)r78c5-7r7c7=7r6c7-(7=2)r6c1 => -2r6c5. |
First what I see as the extension cord.
Then a corresponding view of the w-wing.
(Did I get the Eureka right?)
Why are not both correct?
| Code: | *-----------------------------------------------------------------------------*
| 1 45689 356789 | 689 479 4678 | 2 358 3589 |
| 279 25689 56789 | 3 279 12678 | 159 4 589 |
| 34 2489 389 | 1289 5 1248 | 6 138 7 |
|-------------------------+-------------------------+-------------------------|
| 29 3 18 | 7 2489 56 | 145 1256 2456 |
| 5 269 679 | 29 1 24 | 8 237 234 |
|a27 18 4 | 56 8-2 3 |x157 9 256 |
|-------------------------+-------------------------+-------------------------|
| 36 15 2 | 4 b37 18 |x3579 5678 5689 |
| 346 7 15 | 18 c23 9 | 345 2568 24568 |
| 8 49 39 | 25 6 257 | 34 27 1 |
*-----------------------------------------------------------------------------*
A xy-wing is defined as 3-SIS using bivalue(XY), bivalue(YZ), and bivalue(ZX).
an 273 xy-wing with extension cord.
(2=7)r6c1- (7)r6c7=(7)r7c7- (7=3)r7c5-(3=2)r8c5 => r6c5<>2
x y extension cord y z z x
A w-wing is defined as 3-SIS using bivalue(XY), bilocation(Y), and bivalue(YX).
(2=7)r6c1-(7)r6c7=(7)r7c7- (7=3-3=2)r78c5 => r6c5<>2
x y y bilocation y x pseudo cell |
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