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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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 Posted: Sat Jul 12, 2008 6:34 pm Post subject: M-wing. |
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Here is an interesting puzzle, Jsudoku generated.
(JSudoku does not support M-wings at this time. July 12th 2008)
One M-wing or:
1 X-Wing
1 Finned X-Wing
1 XY-Wing
1 XYZ-Wing
1 Uniqueness Test 3
1 Y-Wing.
| Code: | . 5 .|. 6 .|. 8 .
. . .|. . 4|. . 7
. 1 3|. 8 .|. . .
-----+-----+-----
. . .|5 . 6|. 7 .
. . .|. . .|4 . 9
6 4 .|. . 2|. . .
-----+-----+-----
. . .|. . .|9 . .
2 . .|4 . .|1 . 6
5 8 .|3 . .|. . . |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jul 12, 2008 9:00 pm Post subject: |
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Wapati, I fouund: | Code: | +-------------+-------------+-------------+
| 479 5 247 | 279 6 379d| 23a 8 1 |
| 89 6 28 | 1 -35 4 | 35 29 7 |
| 79 1 3 | 279 8 579 | 6 249 245 |
+-------------+-------------+-------------+
| 138 9 18 | 5 4 6 | 28b 7 23c |
| 378 2 5 | 78 137 137 | 4 6 9 |
| 6 4 78 | 789 379f 2 | 58 1 35e |
+-------------+-------------+-------------+
| 14 37 14 | 6 2 57 | 9 35 8 |
| 2 37 9 | 4 57 8 | 1 35 6 |
| 5 8 6 | 3 19 19 | 7 24 24 |
+-------------+-------------+-------------+ |
a and c are a complementary pair, connected abc by strong links on <2>. The M-wing is dabc; any cell that sees both ends cannot be <3>. We can color on <3>, cef, eliminating <3> in R2C5, solving the puzzle.
Is this what you had in mind?
Keith
(It's been a good few days for M-wings  ) |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Jul 12, 2008 9:21 pm Post subject: |
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| Code: | .---------------.---------------.---------------.
| 479 5 247 | 279 6 379 | 23 8 1 |
| 89 6 28 | 1 -35 4 |A35 29 7 |
| 79 1 3 | 279 8 579 | 6 249 *245 |
:---------------+---------------+---------------:
| 138 9 18 | 5 4 6 | 28 7 23 |
| 378 2 5 | 78 137 137 | 4 6 9 |
| 6 4 78 | 789 C379 2 | 58 1 B35 |
:---------------+---------------+---------------:
| 14 37 14 | 6 2 57 | 9 35 8 |
| 2 37 9 | 4 57 8 | 1 35 6 |
| 5 8 6 | 3 19 19 | 7 24 24 |
'---------------'---------------'---------------' |
here is another one A and B complimentary pairs on strong links on 5
3 then is strong linked over to C r6c5, removes 3 in r2c5.
(3=5)r2c7-(5)r3c9=(5-3)r6c9=(3)r6c5; r2c5<>3 |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Sat Jul 12, 2008 9:51 pm Post subject: |
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Here’s another variant:
| Code: | +--------------+--------------+-------------+
| 479 5 247 | 279 6 *379 | 23a 8 1 |
| 89 6 28 | 1 35 4 | 35 29 7 |
| 79 1 3 | 279 8 579 | 6 249 245 |
+--------------+--------------+-------------+
| =138 9 18 | 5 4 6 | 28 7 23c |
| =378 2 5 | 78 137 *137 | 4 6 9 |
| 6 4 78 | 789 379 2 | 58 1 35 |
+--------------+--------------+-------------+
| 14 37 14 | 6 2 57 | 9 35 8 |
| 2 37 9 | 4 57 8 | 1 35 6 |
| 5 8 6 | 3 19 19 | 7 24 24 |
+--------------+--------------+-------------+ |
The (23)s in the cells a and c used by Keith could be the pincers of a W-Wing. The conjugates for 3 marked * in column 6 do not quite link them but add the conjugates marked = in column 1 and the link is complete.
So 2 can be eliminated from r4c7.
Steve |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Sat Jul 12, 2008 9:55 pm Post subject: |
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Hi keith,
| keith wrote: | Wapati, I fouund: | Code: | +-------------+-------------+-------------+
| 479 5 247 | 279 6 379d| 23a 8 1 |
| 89 6 28 | 1 -35 4 | 35 29 7 |
| 79 1 3 | 279 8 579 | 6 249 245 |
+-------------+-------------+-------------+
| 138 9 18 | 5 4 6 | 28b 7 23c |
| 378 2 5 | 78 137 137 | 4 6 9 |
| 6 4 78 | 789 379f 2 | 58 1 35e |
+-------------+-------------+-------------+
| 14 37 14 | 6 2 57 | 9 35 8 |
| 2 37 9 | 4 57 8 | 1 35 6 |
| 5 8 6 | 3 19 19 | 7 24 24 |
+-------------+-------------+-------------+ |
a and c are a complementary pair, connected abc by strong links on <2>. The M-wing is dabc; any cell that sees both ends cannot be <3>. We can color on <3>, cef, eliminating <3> in R2C5, solving the puzzle.
Is this what you had in mind?
Keith
(It's been a good few days for M-wings ) |
Well, it is a horse of a different color. 
I don't do colors but the elimination is valid so you know what you are doing. The one I had in mind is shown by storm_norm.
Your pattern, to me, is an M-wing chain. You can add an even number of strong links to the ends of an M-wing and have a valid pattern. If we use all the cells that you have lettered, your colorful elimination is duplicated. Good fun!
Edited to add: Cool post Steve.
A swordfishy W-wing, gotta like it  |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Jul 13, 2008 9:40 pm Post subject: |
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As Keith pointed out on a neighboring thread, whenever you have a remote pair that is both complementary and a W-Wing, you can set both bivalues to the pincer digit of the W-Wing.
So, those 23's (ac in the prior post) both become <2>. At least one of them must be <2> (W-Wing) and they must be the same (complementary pair). So, they must both be <2>.
It can be seen as a Medusa multi-coloring trap that collapses one of the two clusters:
| Code: | +--------------+---------------+---------------+
| 479 5 247 | 279 6 3X79 | 2X3x 8 1 |
| 89 6 28 | 1 35 4 | 35 29 7 |
| 79 1 3 | 279 8 579 | 6 249 245 |
+--------------+---------------+---------------+
| 13Y8 9 18 | 5 4 6 | 2x8 7 2X3x |
| 3y78 2 5 | 78 137 13x7 | 4 6 9 |
| 6 4 78 | 789 379 2 | 58 1 35 |
+--------------+---------------+---------------+
| 14 37 14 | 6 2 57 | 9 35 8 |
| 2 37 9 | 4 57 8 | 1 35 6 |
| 5 8 6 | 3 19 19 | 7 24 24 |
+--------------+---------------+---------------+ |
The Xx and Yy clusters are weak-link bridged on xy in r5, making XY the strong pair. This traps the 3x in r4c9 and collapses the Xx cluster (making all x values false and all X values true).
The W-Wing is activated by the (otherwise useless) Skyscraper (aka Turbot Fish or Color Wing or Multi-Coloring on 3) in c16. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jul 14, 2008 2:26 am Post subject: |
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So, why is it, this weekend, that M-wings seem to be able to solve all puzzles?  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jul 14, 2008 2:49 am Post subject: |
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| Asellus wrote: | As Keith pointed out on a neighboring thread, whenever you have a remote pair that is both complementary [pair] and a W-Wing, you can set both bivalues to the pincer digit of the W-Wing.
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No, Keith would say, "a pair (that is not in the same house)".
Not: "a remote pair".
(A remote pair is, by definition, not a complementary pair.)
Keith |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon Jul 14, 2008 7:02 pm Post subject: |
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There is a w-wing (35) with strong link on 5 either in box 3 or row 3 or col 7
It, too, solves the puzzle in one move
| Code: |
+--------------------------+--------------------------+--------------------------+
| 479 5 247 | 279 6 379 | 23 8 1 |
| 89 6 28 | 1 35* 4 | 35 29 7 |
| 79 1 3 | 279 8 579 | 6 249 245 |
+--------------------------+--------------------------+--------------------------+
| 138 9 18 | 5 4 6 | 28 7 23 |
| 378 2 5 | 78 137 137 | 4 6 9 |
| 6 4 78 | 789 -379 2 | 58 1 35* |
+--------------------------+--------------------------+--------------------------+
| 14 37 14 | 6 2 57 | 9 35 8 |
| 2 37 9 | 4 57 8 | 1 35 6 |
| 5 8 6 | 3 19 19 | 7 24 24 |
+--------------------------+--------------------------+--------------------------+
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Jul 14, 2008 10:53 pm Post subject: |
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| Keith wrote: | No, Keith would say, "a pair (that is not in the same house)".
Not: "a remote pair".
(A remote pair is, by definition, not a complementary pair.) |
I have always said "Remote Naked Pair" in such cases to be clear about what I mean. For me, "remote pair" just means any pair of matching bivalues in cells that are not peers, i.e. they are "remote." It's what you look for when scanning for possible M-Wings or W-Wings. However, I just checked and see that Sudopedia uses "Remote Pair" to mean what I and others refer to as "Remote Naked Pair." So, I'll avoid using the term "remote pair" for any purpose because I now find it to be confusing. |
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