VWXYZ-Wing?

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VWXYZ-Wing?

Postby SpAce » Sun Aug 05, 2018 1:32 am

I was looking at the SudokuWiki APE-examples at http://www.sudokuwiki.org/Aligned_Pair_Exclusion to see what actual patterns were behind them (I consider APE a very awkward t&e method and find no value in it per se -- unless someone can convince me otherwise). All but one of those were basic ALS XZs (including XY-Wings). The very last one ("An Eight-Cell Aligned Pair") was more interesting, however. The simplest pattern Hodoku offered for that elimination was an ALS XY-Wing, which wasn't much prettier than the horrible APE solution.

For a human solver that elimination is much more obvious and far simpler as a five-way Kraken Cell. Is it actually a VWXYZ-Wing, though? I've never seen such a thing before, but this would indeed seem like a logical extension to the WXYZ-Wing. Subset Counting and StrmCkr's Barn-rule seem to work, so I guess it's something.

Code: Select all
+--------------+-----------------+------------------+
| 135  7   2   | 159 8      35   | 6     4     59   |
| 1345 9   6   | 7  *12     2345 | 8     235   25   |
| 345  35  8   | 6  *29     2345 | 23579 23579 1    |
+--------------+-----------------+------------------+
| 579  25  579 | 3  %12679 %26   | 129   8     4    |
| 6    8   1   | 49 x479-2 %27   | 2359  2359  2579 |
| 379  23  4   | 19  5      8    | 129   6     279  |
+--------------+-----------------+------------------+
| 2    1   57  | 8   3     9     | 4     57    6    |
| 8    4   579 | 2   67    567   | 579   1     3    |
| 579  6   3   | 45  47    1     | 2579  2579  8    |
+--------------+-----------------+------------------+

VWXYZ-Wing(?): (2=19)r23c5 - (1|9=672)b5p236 => -2 r5c5

What would you call it?

PS. Seems related to this old discussion: http://forum.enjoysudoku.com/non-als-vwxyz-wing-t30032.html
Last edited by SpAce on Mon Aug 06, 2018 10:37 am, edited 1 time in total.
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: VWXYZ-Wing?

Postby tarek » Sun Aug 05, 2018 11:17 am

This unrelated but here is a puzzle from Mike Barker’s collection

Code: Select all
UVWYXZ-wing
5........3..9.8...8.2..4..2715.................741..872.4.9.........5.79....36..


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Re: VWXYZ-Wing?

Postby SpAce » Sun Aug 05, 2018 12:56 pm

tarek wrote:This unrelated but here is a puzzle from Mike Barker’s collection

Code: Select all
UVWYXZ-wing
5........3..9.8...8.2..4..2715.................741..872.4.9.........5.79....36..

Thanks, tarek -- unfortunately that string only has 80 characters! I'd very much like to see that puzzle so could you find the correct version? I tried adding a dot to the beginning and then to the end, but neither produced anything interesting (the former gave a valid puzzle but it didn't seem very interesting; the latter was invalid).
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: VWXYZ-Wing?

Postby tarek » Sun Aug 05, 2018 2:23 pm

I’ll double check. It must be the empty cell at the start puzzle
I will also if not specified find you the interesting bit

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Re: VWXYZ-Wing?

Postby tarek » Sun Aug 05, 2018 6:16 pm

Code: Select all
.5........3..9.8...8.2..4..2715.................741..872.4.9.........5.79....36..
.------------.-----------.----------------.
| 14  5  279 | 3  8  47  | %179 %127  6   |
| 14  3  27  | 6  9  457 | 8    %1257 %125|
| 6   8  79  | 2  1  57  | 4    %357  359 |
:------------+-----------+----------------:
| 2   7  1   | 5  6  8   | *39  -34   349 |
| 8   6  4   | 9  3  2   | 17   157   15  |
| 5   9  3   | 7  4  1   | 2    6     8   |
:------------+-----------+----------------:
| 7   2  6   | 4  5  9   | 13   8     13  |
| 3   4  8   | 1  2  6   | 5    9     7   |
| 9   1  5   | 8  7  3   | 6    24    24  |
'------------'-----------'----------------'
Almost Locked Set XZ-Rule: *A=r4c7 {39}, %B=r1c78,r2c89,r3c8 {123579}, X=9, Z=3 => r4c8<>3

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Re: VWXYZ-Wing?

Postby tarek » Sun Aug 05, 2018 6:39 pm

This one from the same collection
Complete devastation (beautiful)
Code: Select all
...3.1..7..2...39........5....1...2...3..64..96..2..7.47.....1.6..8.5...2.9......
.---------------.--------------------.---------------.
| 58  4589  458 | 3     %4589  1     | 2     6  7    |
| 7   1458  2   | %456  %4568  %48   | 3     9  148  |
| 3   1489  6   | 2-479 %4789 2-47-89| 18    5  148  |
:---------------+--------------------+---------------:
| 58  458   7   | 1     3458-9 3489  | 569   2  3569 |
| 1   2     3   | 579   5-7-9  6     | 4     8  59   |
| 9   6     458 | 45    2      348   | 15    7  135  |
:---------------+--------------------+---------------:
| 4   7     58  | 269   36-9   239   | 5689  1  5689 |
| 6   3     1   | 8     *79    5     | 79    4  2    |
| 2   58    9   | 467   1      47    | 5678  3  568  |
'---------------'--------------------'---------------'
Almost Locked Set XZ-Rule: *A=r8c5 {79}, %B=r123c5,r2c46 {456789}, X=7,9 => r457c5<>9, r5c5<>7, r3c46<>4, r3c6<>8

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Re: VWXYZ-Wing?

Postby SpAce » Sun Aug 05, 2018 8:14 pm

tarek wrote:
Code: Select all
.5........3..9.8...8.2..4..2715.................741..872.4.9.........5.79....36..
Almost Locked Set XZ-Rule: *A=r4c7 {39}, %B=r1c78,r2c89,r3c8 {123579}, X=9, Z=3 => r4c8<>3

Thanks! Both I and Hodoku were blind to that particular combination. I guess that would indeed count as a UVWXYZ-Wing, at least by StrmCkr's definitions. Jon Welch (Sysudoku) might not agree, if I've understood correctly that he'd like to keep a simpler (or classic) definition for WXYZ-Wings (and probably the more complex ones too), i.e. a fully populated hinge and bivalues only as the wing-parts.

This one from the same collection
Complete devastation (beautiful)
Code: Select all
...3.1..7..2...39........5....1...2...3..64..96..2..7.47.....1.6..8.5...2.9......
Almost Locked Set XZ-Rule: *A=r8c5 {79}, %B=r123c5,r2c46 {456789}, X=7,9 => r457c5<>9, r5c5<>7, r3c46<>4, r3c6<>8

Isn't that a Sue de Coq also? (Core: (45789)r13c5 + (4568)r2c456 + (79)r8c5.) Does it still count as a Wing as well, despite being doubly-linked?
Code: Select all
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: VWXYZ-Wing?

Postby SpAce » Sun Aug 05, 2018 8:27 pm

Btw, what would you call this (from my first post) in ALS-terms:
I wrote:(2=19)r23c5 - (1|9=672)b5p236 => -2 r5c5

The first node is an ALS but the second one is an AALS, and they're doubly-linked (but not looping like a doubly-linked ALS-XZ).
Code: Select all
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: VWXYZ-Wing?

Postby tarek » Sun Aug 05, 2018 9:10 pm

SpAce wrote:Isn't that a Sue de Coq also? (Core: (45789)r13c5 + (4568)r2c456 + (79)r8c5.) Does it still count as a Wing as well, despite being doubly-linked?


In this context it is a doubly linked ALS-XZ. It can obviously work as a wing because the double links could work as XZ and ZX. A special case obviously and that's why I posted it
http://forum.enjoysudoku.com/almost-locked-sets-xz-rule-doubly-linked-t3979.html

I also had a go to show a double linked ALS-XY rule diagram too
http://forum.enjoysudoku.com/almost-locked-sets-als-for-beginners-t3403-15.html#p22822

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Last edited by tarek on Sun Aug 05, 2018 10:00 pm, edited 2 times in total.
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Re: VWXYZ-Wing?

Postby tarek » Sun Aug 05, 2018 9:14 pm

SpAce wrote:Btw, what would you call this (from my first post) in ALS-terms:
I wrote:(2=19)r23c5 - (1|9=672)b5p236 => -2 r5c5

The first node is an ALS but the second one is an AALS, and they're doubly-linked (but not looping like a doubly-linked ALS-XZ).

I can't visualise it now as something that I came across in the past. It looks like something that "Subset counting" would handle?!
If you look at some of the posts in the 2nd linked thread from my post above ... It could be that you have a doubly-weak linked ALS-XZ but my head hurts from attempts to re-construct it now :D

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Re: VWXYZ-Wing?

Postby SpAce » Mon Aug 06, 2018 11:17 am

Thanks for the links, tarek!

tarek wrote:I can't visualise it now as something that I came across in the past. It looks like something that "Subset counting" would handle?!

Subset counting surely handles it, but doesn't it handle pretty much everything? With my limited understanding of it, I don't see it as an actual solving technique for humans any more than APE. To me they both seem suitable for double-checking that a promising pattern works as expected, but not for spotting such patterns.

In this case mapping the counts for the possible digits in the pattern gives [12679] -> [12111] (+1), meaning that the digit 2 can be placed twice within the pattern, i.e. it's the only non-restricted candidate (which makes the pattern a Barn, if I've understood correctly). If 2r5c5 were true, the counts would be [10111] (-1), and the negative result means it has to be false (four digits can't fill five cells). Have I understood this concept correctly? I've only recently looked into subset counting at all.
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: VWXYZ-Wing?

Postby tarek » Mon Aug 06, 2018 7:02 pm

Subset counting was aeb’s baby. it does subsume most techniques as you said, but you’re correct, it is not a visual pattern based technique. It was helpful in confirming some of these fancy doubly linked and ring ALSs. It can show eliminations where no identifiable technique has been developed too. I’m not sure if there is any solver that adopts it fully.

Here is the link to aeb’s thread
http://forum.enjoysudoku.com/subset-counting-t3479.html

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Re: VWXYZ-Wing?

Postby Cenoman » Mon Aug 06, 2018 9:19 pm

I recall the recent discussion we had on the degree of relationship between Sue de Coq and doubly linked ALS-XZ.here

tarek's two examples are doubly linked ALS-XZ, what SpAce APE example is not.

SpAce wrote:...3.1..7..2...39........5....1...2...3..64..96..2..7.47.....1.6..8.5...2.9......
Almost Locked Set XZ-Rule: *A=r8c5 {79}, %B=r123c5,r2c46 {456789}, X=7,9 => r457c5<>9, r5c5<>7, r3c46<>4, r3c6<>8
Isn't that a Sue de Coq also? (Core: (45789)r13c5 + (4568)r2c456 + (79)r8c5.) Does it still count as a Wing as well, despite being doubly-linked?

Note that (45789)r13c5 as a core is an AAALS needing three restricted commons.
I would write it this way: (79)r8c5 -79- (45789)r13c5 -458- (4568)r2c456, spelling out the RCs.
The freedom degree of this chain is 0, same as the doubly linked ALS-XZ, yielding same eliminations.
One could write also this Sue de Coq: (79)r8c5 -79- (456789)r123c5,r2c4 -48- (48)r2c6
Same freedom degree, same eliminations.


Now, as regards the APE example
SpAce wrote:VWXYZ-Wing(?): (2=19)r23c5 - (1|9=672)b5p236 => -2 r5c5
What would you call it?


To me, SpAce writing it into an AIC is correct and very nice.

SpAce's AIC is an ALS doubly linked to an AALS: (129)r23c5 -19- (12679)b5p236. Freedom degree 1
IMHO, no need for any new name or pattern.
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Re: VWXYZ-Wing?

Postby pjb » Tue Aug 07, 2018 1:54 am

Tarek wrote
This one from the same collection
Complete devastation (beautiful)
CODE: SELECT ALL
...3.1..7..2...39........5....1...2...3..64..96..2..7.47.....1.6..8.5...2.9......
Almost Locked Set XZ-Rule: *A=r8c5 {79}, %B=r123c5,r2c46 {456789}, X=7,9 => r457c5<>9, r5c5<>7, r3c46<>4, r3c6<>8


Interestingly, the double ALS at r2c6, r1358c5, X=4, Z=8: [ (4=8)r2c6 - (8=4)r1358c5 - loop ] is similarly devastating

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Re: VWXYZ-Wing?

Postby eleven » Tue Aug 07, 2018 5:31 pm

Some time ago i called this a vwxyz-wing.

Cenoman wrote:SpAce's AIC is an ALS doubly linked to an AALS: (129)r23c5 -19- (12679)b5p236. Freedom degree 1
IMHO, no need for any new name or pattern.

It's neither a new name (just an extension of an old one, which is an extension of a very old one), nor would i prefer "ALS doubly linked to an AALS" to vwxyz-wing.
If there are different methods to arrive at the same pattern/eliminations (and i don't talk about solver programs), different names should be allowed.
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