non-ALS vwxyz-wing

Advanced methods and approaches for solving Sudoku puzzles

non-ALS vwxyz-wing

Postby surbier » Wed May 26, 2010 6:20 pm

Hi,

I was thinking about the vwxyz-wing and the uvwxyz-wing.

I thought the vwxyz wing has a very restricted definition: A pilot cell
of five candidates vwxyz and four bi-value wings with xz, yz, wz and
vz. In this case two constellations can be distinguished. One with one
wing in a house and three wings in the other house.

Code: Select all
  -z  vwxyz -z |  xz . wz  |  .  yz .
   .     .   . |  .  .  .  |  .  .  .
   vz    .   . |  .  .  .  |  .  .  .


which can be extended via ALS-XZ logic, and another constellation with two
wings in one house and two wings in the other house:

Code: Select all
  -z  vwxyz -z |  xz .   . |  .  wz .
   .     .   . |  .  .  .  |  .  .  .
   vz   yz   . |  .  .  .  |  .  .  .


The elimination of the latter constellation cannot be replicated by any
ALS-XZ (using the same cells !). For this reasons, there doesn't exist
any extended version of this vwxyz constellation.

The same arguments can be applied to the uvwxyz-wing:
A sixpack pilot cell and five bi-value cells wings
One constellation with one wing in
one house and four wings in the other house can be considered as an ALS-XZ.

Code: Select all
  -z  uvwxyz -z |  xz . wz  |  .  yz vz
   .     .   uz |  .  .  .  |  .  .  .
   .     .    . |  .  .  .  |  .  .  .



The other uvwxyz-wing constellation with 2 wings in one house and three
wings in the other house is again a logical pattern on its own. It
cannot be replicated by an ALS-XZ using the same cells. There is also
no extended version for this uvwxyz-wing constellation.

Code: Select all
  -z  uvwxyz -z |  xz .  .  |  .  yz .
   .     .   uz |  .  .  .  |  .  .  .
  wz    vz    . |  .  .  .  |  .  .  .



Here is an example of a non-ALS vwxyz-wing:

hinge=r6c4(14789) wings: r5c4(18) r6c3(17) r6c7(14) r4c6(19) : r6c6<>1

Code: Select all
+----------------------+------------------------+-------------------------+
|  8      9      3     | 14       45      125   | 12         7       6    |
|  7      5      6     | 19        8      129   |   3      12        4    |
|  1      4      2     |  6        7        3   |   8        5       9    |
+----------------------+------------------------+-------------------------+
|  5      8     17     | 1479       2      (19) | 146      169       3    |
|  4      2      9     |(18)        3        6  |   7      18        5    |
|  6      3    (17)    |(14789)   45      -159  |(14)      189       2    |
+----------------------+------------------------+-------------------------+
|  2      1      4     |   5        6        8  |   9        3       7    |
|  3      6      8     |   2        9        7  |   5        4       1    |
|  9      7      5     |   3        1        4  | 26       26        8    |
+----------------------+------------------------+-------------------------+


890000070000000304100603000080020003029036700600000000000068000000207500905004008 # s tf(1) s (from hodoku benchmark list)



I just read the wxyz-wing thread extension-of-xyz-wing-t1169.html
and as far as I understand the generalisation of the [[[u]v]w]xyz-wing is an ALS-XZ.

How does the non-ALS vwxyz-wing example (if it is a vwxyz-wing) fit into this ?

Thanks, surbier
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Re: non-ALS vwxyz-wing

Postby ronk » Wed May 26, 2010 7:31 pm

surbier wrote:I just read the wxyz-wing thread extension-of-xyz-wing-t1169.html
and as far as I understand the generalisation of the [[[u]v]w]xyz-wing is an ALS-XZ.

How does the non-ALS vwxyz-wing example (if it is a vwxyz-wing) fit into this ?

At the time of that thread, the concept of an ALS doubly-linked to an AALS didn't yet exist AFAIK. For your vwxyz-wing ...

r6c6 -1- als:r4c6,r5c4 -89- aals:r6c457 -147- r6c6 --> r6c6<>1

Don't let the notation put you off. If digit <1> is removed from the ALS it becomes naked pair <89> ... removing both digits <8> and <9> from the AALS ... which then becomes naked triple <147>. Perhaps it should be called an AALS-xz. :)

In the absence of other constraints, note that r4c6, r5c4 and r6c47 could all be trivalued cells.
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Re: non-ALS vwxyz-wing

Postby StrmCkr » Thu May 27, 2010 3:32 am

was thinking about the vwxyz-wing and the uvwxyz-wing.

I thought the vwxyz wing has a very restricted definition:
same with the uvwxyz wings:

my current view is that not all uvwxyz digits need be present with in the "hinge" for these to function correctly nor do all the digits need to be bivalves.

i have taken the time to translate them into the same format as my wxyz wing thread and have programed them both as separate steps and concur with previous definitions lacking the doubly linked function via same houses that allows the extra elimination that are not normally seen via als-xz function.

how ever the oddity cases that are a bit more complex in formalizing are the the ability for 4+ cells/digits to utilize box-box relations, forming an eliminations like the following. which is also not covered under any als-xz rule. i have also tested this theory out in hodoku and xsuodo and neither list this as an als-xz elimination. {also to note that this is an example of doubly linked }

Code: Select all
| .   1234  . | . . . | 145  .  145 |
| 23  -23  -23| . . . | .   253   . |
| .     .   . | . . . | .    .    . |


Code: Select all
 *-----------*
 |.7.|1..|34.|
 |.9.|.8.|..2|
 |4..|...|...|
 |---+---+---|
 |8.6|..9|...|
 |...|.1.|6.7|
 |..5|...|..9|
 |---+---+---|
 |9..|..3|..8|
 |...|87.|2..|
 |6..|...|.7.|
 *-----------*


Code: Select all
 *-----------------------------------------------------------*
 | 25    7     8     | 1     9     256   | 3     4     56    |
 | 135   9     13    | 3456  8     45    | 7     156   2     |
 | 4     6     123   | 235   235   7     | 9     8     15    |
 |-------------------+-------------------+-------------------|
 | 8     123@  6     | 7     35    9     | 145@  1235  145@  |
 | 23@   4-23  9     | 345   1     8     | 6     235@  7     |
 | 7     134   5     | 2346  346   24    | 8     13    9     |
 |-------------------+-------------------+-------------------|
 | 9     25    7     | 2456  2456  3     | 145   156   8     |
 | 13    35    134   | 8     7     1456  | 2     9     3456  |
 | 6     8     1234  | 9     245   145   | 45    7     345   |
 *-----------------------------------------------------------*
here is the chain
(23)R5C3 - (2=3)R5C1 - (23=1)R4C2 - (1=45)R4C79 - (5=23)R5C8 - (23)R5C3 =>> R5C3 <>23
Last edited by StrmCkr on Thu May 27, 2010 7:35 am, edited 3 times in total.
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Re: non-ALS vwxyz-wing

Postby David P Bird » Thu May 27, 2010 6:27 am

StrmCkr, I'm trying to notate these new wing eliminations using Eureka conventions, and a quick look at your tagged cells suggests this chain:

(23)r4c2,r5c1 = (1)r4c2 - (1=45)r4c79 - (5)r5c8 = (23)r5c18

which eliminates both 2 and 3 from r5c2.

Does this reflect the way you recognise your elimination pattern?
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Re: non-ALS vwxyz-wing

Postby StrmCkr » Thu May 27, 2010 7:05 am

interesting i seem to have overlooked a type in wxyz wings as ... examining the above post i realized that it can be reduced as follows and it still functions thus becomes a wxyz wing.

Code: Select all
| .   123   . | . . . | 15   .    . |
| 23  -23  -23| . . . | .   253   . |
| .     .   . | . . . | .    .    . |
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Re: non-ALS vwxyz-wing

Postby David P Bird » Thu May 27, 2010 7:12 am

StrmCkr,
Thanks for your PM but I'm afraid I'm not yet allowed to PM back to you, as I only have one post to my new name.

My view of things is that we have two problems:

a) Proving that our eliminations are sound to our readers as simply as possible.
b) Explaining how we made that discovery, namely what pattern elements we looked for.

As there are often several ways to prove the same elimination, these two things don't necessarily coincide. The best proof should be the one that uses the elements used to find the pattern as nodes in the inference stream. Hence my question.

I've found that playing around like this can sometimes suggest better discovery methods.
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Re: non-ALS vwxyz-wing

Postby surbier » Wed Jun 23, 2010 11:40 am

Thanks all for your comments.

@ Ronk , thanks for this:

If digit <1> is removed from the ALS ...

explanation.
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