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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Thu Nov 26, 2009 3:27 pm Post subject: Puzzle NR 09/11/26 (A) |
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Fewer advanced steps ... more basic steps.
| Code: | +-----------------------+
| 9 3 . | 7 . . | 4 . . |
| 1 7 . | . . . | . . . |
| . . 8 | 4 . 1 | . . . |
|-------+-------+-------|
| 3 . 1 | 8 . 4 | . . 7 |
| . . . | . 3 . | . . . |
| . . 9 | 2 . 5 | 3 . 8 |
|-------+-------+-------|
| 6 . . | . . 2 | . . . |
| . . . | . . . | . . 3 |
| . . . | 3 . 7 | . 8 . |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Nov 27, 2009 5:58 am Post subject: |
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| A little different, that's for sure. I used a type 1 UR on 25, Remote Pairs four times on 69 and coloring on 6. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Wed Dec 02, 2009 8:00 pm Post subject: |
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I used the Type 1 UR on 25, then a (useless)Type 2 UR on 14.
At that point the only moves I found were the same as Marty.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Dec 02, 2009 9:19 pm Post subject: |
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Too bad the UR Type 2 turned out to be extraneous.
As for the <69> Remote Pair, I guess that I treat Remote Pair differently than everyone else. I treat them as concurrent coloring. This results in my treating the eliminations below as one step using Blue/Green. As it turns out, the eliminations in r4c8 are sufficient to crack the puzzle.
| Code: | +-----------------------------------------------------------------------+
| 9 3 6 | 7 25 8 | 4 25 1 |
| 1 7 4 | B69 25 3 | 8 G69 25 |
| 25 25 8 | 4 G69 1 | 7 3 B69 |
|-----------------------+-----------------------+-----------------------|
| 3 25 1 | 8 B69 4 | 2569 25-69 7 |
| 7 8 25 | 1 3 G69 | 2569 24569 245-69 |
| 4 6 9 | 2 7 5 | 3 1 8 |
|-----------------------+-----------------------+-----------------------|
| 6 149 3 | 59 8 2 | 159 7 459 |
| 8 149 7 | 569 14 B69 | 1259 245-9 3 |
| 25 149 25 | 3 14 7 | 169 8 469 |
+-----------------------------------------------------------------------+
# 59 eliminations remain
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The elimination in r8c8 raises an interesting question. Must a Remote Pair eliminate two values in a cell in order to claim any eliminations in the cell? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Dec 02, 2009 9:48 pm Post subject: |
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| daj95376 wrote: | | Must a Remote Pair eliminate two values in a cell in order to claim any eliminations in the cell? |
No.
But then, in your example, it would be coloring on one digit only.
It is interesting to note that you can establish a remote pair by coloring on one digit only, but the resulting pincers remove both digits.
See Chapter 2 here:
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2143
For example, if I do coloring on 7:
67 = a7 = b7 =67
Where a and b are any candidates, the pincers eliminate both 6 and 7.
(Looks like a bloody W-wing, you say. Yes.)
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Dec 02, 2009 10:58 pm Post subject: |
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Good point, Keith, about the general Remote Pair scenario and coloring on one candidate value and eliminations resulting from the conjugate pair on the endpoints. However, I hope you are mentioning this as a related point and not an interpretation of my intent.
I should have been more specific and said that my coloring is applied to cells present in the classic Remote Pair scenario (Chapter 1). In this context, the eliminations are forced to occur in any cell that sees a Blue cell and a Green cell.
Right now, I don't specifically search for a general Remote Pair. I run across them while examining chains found by my solver. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Dec 02, 2009 11:24 pm Post subject: |
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| daj95376 wrote: | | However, I hope you are mentioning this as a related point ... |
Yes, I am.
I simply saw an opportunity to add my 2 cents.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Dec 03, 2009 9:36 pm Post subject: |
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[Withdrawn: missed an important detail]
Last edited by daj95376 on Fri Dec 04, 2009 12:02 am; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Dec 03, 2009 10:47 pm Post subject: |
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| daj95376 wrote: | | keith wrote: | I simply saw an opportunity to add my 2 cents.
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 ...  ... ...
Dang am I dense 
It just hit me that a generalized W-Wing is a 4-cell general Remote Pair. And what I've been calling an extended W-Wing is a general Remote Pair using more than four cells. Aaaaagh
However, the W-Wing is only credited with performing eliminations for one digit. This seems to be an oversight!
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It's a little early for the hara-kiri!
By my definition, a W-wing only eliminates one digit:
WX-aX=bX-XW
W and X are specific candidates, a and b are any groups of candidates, - is a weak link, = is a strong link. The end cells are pincers on W.
If all the links are strong,
WX=aX=bX=XW
you have a remote pair. The end cells are pincers on both X and W.
You can also make a remote pair if there are two cells with the same two candidates, WX. They are connected as a W-wing by a strong link in X, and by a strong link in W that is not in the same cells as the strong link in X.
I see no value in identifying this last pattern as a remote pair, rather than as two separate W-wings.
Keith
Last edited by keith on Sat Dec 05, 2009 12:58 am; edited 1 time in total |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Dec 04, 2009 12:02 am Post subject: |
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Hello Keith,
I've gotta get more sleep!!!
I missed the strong links requirement on weak inferences in the general Remote Pair. That makes my statement above so much garbage.
Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Dec 04, 2009 6:23 am Post subject: |
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| keith wrote: |
By my definition, a W-wing only eliminates one digit:
WX-aX=bX-XW
W and X are specific candidates, a and b are any groups of candidates, - is a weak link, = is a strong link. The end cells are pincers on W.
If all the links are strong,
WX=aX=bX=XW
you have a remote pair. The end cells are pincers on both X and W.
You can also make a remote pair if there are two cells with the same two candidates, WX. They are connected as a W-wing by a strong link in X, and by a strong link in W that is not in the same cells as the strong link in X.
I see no value in identifying this last pattern as a remote pair, rather than as two separate W-wings.
Keith |
I have made (and withdrawn) the bolded statement once before, and I need to do so again.
In a W-wing,
WX-aX=bX-XW
one or both of the pincers is W.
In a double W-wing we have the same pincer cells, but another strong link:
WX-cW=dW-XW
and one or both of the pincers are X. So far, so good.
But, if you put these statements together, you have a remote pair: One of the pincers is W, and the other is X. Which, I think, is a more powerful statement.
In essence, the pincer cells are a (bidirectional) pseudocell WX, that can be used as a building block in another chain.
(And yes, now I have to define what the hell I mean by "bidirectional pseudocell". Later)
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Dec 04, 2009 8:19 pm Post subject: |
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| keith wrote: | I have made (and withdrawn) the bolded statement once before, and I need to do so again.
In a W-wing,
WX-aX=bX-XW
one or both of the pincers is W.
In a double W-wing we have the same pincer cells, but another strong link:
XW-cW=dW-WX
and one or both of the pincers are X. So far, so good.
But, if you put these statements together, you have a remote pair: One of the pincers is W, and the other is X. Which, I think, is a more powerful statement.
In essence, the pincer cells are a (bidirectional) pseudocell WX, that can be used as a building block in another chain.
(And yes, now I have to define what the hell I mean by "bidirectional pseudocell". Later)
Keith |
Okay, assuming that I've had enough sleep this time, I see Keith's discussion involving two possible scenarios.
| Code: | Scenario #1: strong link on <X> in different unit than strong link on <W>
WX-aX=bX-XW -- W-Wing for elimination on W
WX-cW=dW-XW -- W-Wing for elimination on X
+-----------------------------------+
| . . . | . . . | . / / |
| . WX . | . -WX . | . aX cW |
| . . . | . . . | . / / |
|-----------+-----------+-----------|
| . . . | . . . | . / / |
| . -WX . | . XW . | . bX dW |
| . . . | . . . | . / / |
|-----------+-----------+-----------|
| . . . | . . . | . / / |
| . . . | . . . | . / / |
| . . . | . . . | . / / |
+-----------------------------------+
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I see scenario #1 identified as two concurrent W-wings ... or the continuous chain:
(W=X)r2c2 - r2c8 - r5c8 - (X=W)r5c5 - r5c9 = r2c9 - (W=X)r2c2
| Code: | Scenario #2: strong link on <X> in same unit as strong link on <W>
WX-aX=bX-XW -- W-Wing for elimination on W
WX-cW=dW-XW -- W-Wing for elimination on X
+------------------------------------+
| . . . | . . . | . / / . |
| . WX . | . -WX . | . aXcW . |
| . . . | . . . | . / / . |
|-----------+-----------+------------|
| . . . | . . . | . / / . |
| . -WX . | . XW . | . bXdW . |
| . . . | . . . | . / / . |
|-----------+-----------+------------|
| . . . | . . . | . / / . |
| . . . | . . . | . / / . |
| . . . | . . . | . / / . |
+------------------------------------+
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I see scenario #2 identified as a Remote Pair ... once the <WX> Hidden Pair in [c8] is performed. |
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