W-Wing ?

Everything about Sudoku that doesn't fit in one of the other sections

Postby daj95376 » Thu Jun 12, 2008 2:31 pm

hobiwan wrote:Do we really need a name for this? Why not stick with XY-Chain?

Because the strong links are not always between bivalue cells and, besides, XY-Chains don't describe what's happening.

It is an AIC, so we could just drop giving it a name and use the generic AIC designation. (ala the forcing chain variety.)
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Postby ronk » Thu Jun 12, 2008 3:39 pm

Many people are already familiar with the terms xy-wing and xy-chain. An xy-wing has three bivalues (strong inferences) and an xy-chain is a chain with more than three bivalues.

A w-wing also has three strong inferences. However, it is comprised of two identical bivalues and one (simple or grouped) conjugate link. With two or more conjugate links (in the chain between the two bivalues), using the term w-chain seems the most approprate to me.

Code: Select all
--- strong inferences ---
  =3               >3
xy-wing          xy-chain
 w-wing           w-chain
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Postby hobiwan » Thu Jun 12, 2008 5:44 pm

daj95376 wrote:...besides, XY-Chains don't describe what's happening.

Me and my big mouth:(
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Postby daj95376 » Thu Jun 12, 2008 6:11 pm

ronk wrote:using the term w-chain seems the most approprate to me.

I'm game! It sure sounds better than my idea of calling it:

X-Chain linking two identical bivalue cells ___:D:D:D:D:D

Say, does this open up the possibility of a W-Network where multiple identical bivalue cells are linked by a Colors network:?:

hobiwan would like this because it's similar to how he's handling Remote Pairs.
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Postby ronk » Thu Jun 12, 2008 6:49 pm

daj95376 wrote:Say, does this open up the possibility of a W-Network where multiple identical bivalue cells are linked by a Colors network:?:

If we start giving different names to different networks -- true networks, that is, and not those special cases we call chains -- I may have to start some serious drinking.:(
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Postby daj95376 » Tue Jun 17, 2008 7:54 pm

Okay, W-Network is out. How about Siamese W-Wings or Siamese W-Chains:?::D

Code: Select all
 +--------------------------------------------------------------+
 |  8     1     9     |  4     36    36    |  7     2     5     |
 |  6     357   37    |  2     1     58    |  348   348   9     |
 |  235   235   4     |  7     58    9     |  6     38    1     |
 |--------------------+--------------------+--------------------|
 |  24    6     8     |  35    35    1     |  24    9     7     |
 |  345   9     13    |  8     2     7     |  345   134   6     |
 |  235   257-3 1237  |  6     9     4     |  2358  138  *23    |
 |--------------------+--------------------+--------------------|
 |  1     4    ~235   |  35    68    68    |  9     7    ~23    |
 |  9     8     25-3  |  1     7     235   | *23    6     4     |
 |  7    *23    6     |  9     4     23    |  1     5     8     |
 +--------------------------------------------------------------+

 3- r9c2 -2- r7c3 =2= r7c9 -2- ( r6c9,r8c7 ) -3  =>  [r6c2],[r8c3]<>3
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Postby ronk » Tue Jun 17, 2008 8:26 pm

It's two different sets of three strong inferences to yield two different eliminations so, for me, it's two w-wings.

Since two of the strong inferences are the same, however, I certainly don't have a problem with someone else calling them Siamese w-wings.
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Postby coloin » Wed Jun 18, 2008 4:02 pm

People from Siam might not like it !
But there are "Siamese fighting fish".....so perhaps its OK
Conjoined twins is the more correct medical term.

C
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Postby daj95376 » Wed Jun 18, 2008 5:16 pm

coloin wrote:People from Siam might not like it !

According to Wikipedia, it's been Thailand since 1949. I don't think there are many people from Siam left to complain!
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Postby coloin » Wed Jun 18, 2008 5:33 pm

Calling "Thailand"........

Are you offended:?:

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Postby daj95376 » Mon Jun 23, 2008 2:00 am

Code: Select all
keith:  Generalized Remote Pair
ronk:   W-Chain
me:     a fun way to crack a PM

Code: Select all
 +-----------------------------------------------------------------------+
 |  5      4      9      |  1      8      3      |  2      6      7      |
 |  3      2      8      |  6      5      7      |  9      1      4      |
 |  7      1      6      |  49     49     2      |  58     3      58     |
 |-----------------------+-----------------------+-----------------------|
 |  16     8      2      |  7      169    1569   |  3      4      569    |
 |  9      5      4      |  28     3     *16     |  7      28    *16     |
 |  16     7      3      |  2589   129    4      |  158    258    5689   |
 |-----------------------+-----------------------+-----------------------|
 |  48     3      157    |  245    12479  189    |  6      58    *158    |
 |  48     6      17-5   |  3      147   #15     |  458    9      2      |
 |  2      9     #15     |  4-5    16     68-5   | *1458   7      3      |
 +-----------------------------------------------------------------------+ # P_Set_A: 27

 5- r8c6 -1- r5c6 =1= r5c9 -1- r7c9 =1= r9c7 -1- r9c3 -5  =>  [r8c3],[r9c46]<>5
_______________________________________________________________________________
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Postby storm_norm » Tue Jun 24, 2008 6:57 am

this is what happens when you have sooooo many names that stick for each pattern. the fact that the sudoku community still seems to separate the xy-wing and xy-chain is a case and point. WHY ??? an xy-wing is a xy-chain !! why have two names for the exact same thing? why isn't there more effort from all the geniuses to streamline all the jumble of names??

kind of like this puzzle...

Code: Select all
.------------------.------------------.------------------.
| 6     17    9    | 278   25    578  | 123   37    4    |
| 257   3     257  | 27    1     4    | 9     6     8    |
| 1247  8     247  | 6     9     3    | 125   57    27   |
:------------------+------------------+------------------:
| 45    9     3    | 128   26    68   | 7    #45    16   |
| 127   17    267  | 5     4     679  | 36    8     369  |
| 8    #45    67   | 17    3     679  |#45    2     169  |
:------------------+------------------+------------------:
| 3     6     48   | 9     7     2    | 48    1     5    |
| 579   2     578  | 4     56    1    | 368   379   367  |
| 4579 #45    1    | 3     8     56   | 246  -479   267  |
'------------------'------------------'------------------'


notice the {4,5} cells... they absolutely fit the definitions of w-wing/classic remote naked pair/xy-chain and an M-wing:!::!::!: don't know what it is, I will gladly fill anyone in on it.

IMO... the w-wing is best served when connecting four cells. after you go beyond four cells in order to connect a remote pair, then you have left behind the true spirit of the w-wing... one of the best weapons you can have for sudoku.

not only is it a great weapon, but also easy to spot, not unlike the Type 1 UR, and the naked pair.
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Postby 999_Springs » Thu Jul 03, 2008 7:55 pm

daj95376 wrote:
Code: Select all
+-----------------------------------------------------------------------+
 |  5      4      9      |  1      8      3      |  2      6      7      |
 |  3      2      8      |  6      5      7      |  9      1      4      |
 |  7      1      6      |  49     49     2      |  58     3      58     |
 |-----------------------+-----------------------+-----------------------|
 |  16     8      2      |  7      169    1569   |  3      4      569    |
 |  9      5      4      |  28     3     *16     |  7      28    *16     |
 |  16     7      3      |  2589   129    4      |  158    258    5689   |
 |-----------------------+-----------------------+-----------------------|
 |  48     3      157    |  245    12479  189    |  6      58    *158    |
 |  48     6      17-5   |  3      147   #15     |  458    9      2      |
 |  2      9     #15     |  4-5    16     68-5   | *1458   7      3      |
 +-----------------------------------------------------------------------+


This looks like a Y-wing with two strong links instead of one. Here is another example of these, which I found last Tuesday, and I considered calling it a "y-turbot".

Code: Select all

     8 |     1 |     4 ||     9 |     2 |    36 ||    36 |     5 |     7
-------+-------+-------||-------+-------+-------||-------+-------+-------
    27 |   236 |  3567 ||    58 |     4 | 35678 ||     9 |   236 |     1
-------+-------+-------||-------+-------+-------||-------+-------+-------
     9 |   236 |  3567 ||     1 |   367 |  3567 ||     8 |     4 |   236
=======================||=======================||=======================
     3 |     4 |     1 ||    58 |    67 |    58 ||   267 |  2679 |   269
-------+-------+-------||-------+-------+-------||-------+-------+-------
     6 |     5 |    79 ||     2 |   379 |     4 ||    37 |     1 |     8
-------+-------+-------||-------+-------+-------||-------+-------+-------
    27 |    29 |     8 ||   367 |     1 |  3679 ||     5 |   367 |     4
=======================||=======================||=======================
     4 |     8 |   369 ||   367 |  3679 |     1 ||  2367 | 23679 |     5
-------+-------+-------||-------+-------+-------||-------+-------+-------
     5 |   369 |     2 ||     4 |     8 |  3679 ||     1 |   367 |    36
-------+-------+-------||-------+-------+-------||-------+-------+-------
     1 |     7 |   369 ||    36 |     5 |     2 ||     4 |     8 |   369

turbot: r1c67 and r5c57 => r3c5<>3
locked candidate: r68c6<>3
naked pair: r57c5<>67


     8 |     1 |     4 ||     9 |     2 |    36 ||    36 |     5 |     7
-------+-------+-------||-------+-------+-------||-------+-------+-------
    27 |   236 |  3567 ||    58 |     4 | 35678 ||     9 |   236 |     1
-------+-------+-------||-------+-------+-------||-------+-------+-------
     9 |   236 |  3567 ||     1 |    67 |  3567 ||     8 |     4 |   236
=======================||=======================||=======================
     3 |     4 |     1 ||    58 |    67 |    58 ||   267 |  2679 |   269
-------+-------+-------||-------+-------+-------||-------+-------+-------
     6 |     5 |    79 ||     2 |    39 |     4 ||    37 |     1 |     8
-------+-------+-------||-------+-------+-------||-------+-------+-------
    27 |    29 |     8 ||   367 |     1 |   679 ||     5 |   367 |     4
=======================||=======================||=======================
     4 |     8 |   369 ||   367 |    39 |     1 ||  2367 | 23679 |     5
-------+-------+-------||-------+-------+-------||-------+-------+-------
     5 |   369 |     2 ||     4 |     8 |   679 ||     1 |   367 |    36
-------+-------+-------||-------+-------+-------||-------+-------+-------
     1 |     7 |   369 ||    36 |     5 |     2 ||     4 |     8 |   369

y-turbot: strong links r6c48 and r15c7, bivalue cells r9c4 and r1c6 => r8c6<>6


My notes from last Tuesday say r6c4<>7 at this point but now I don't quite see that...
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Postby daj95376 » Thu Jul 03, 2008 8:38 pm

Withdrawn:
Last edited by daj95376 on Sat Jul 05, 2008 12:05 am, edited 1 time in total.
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Postby 999_Springs » Fri Jul 04, 2008 6:17 pm

The y-turbot is still valid:
Code: Select all
y-turbot: strong links r6c48 and r157c7, bivalue cells r9c4 and r1c6 and r8c9 => r8c6<>6
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