The New Sudoku Players' Forum

[tarek]

I see it as a special form of ALS XY with the center ALS Doubly linked to each of the other 2 ALSs

Which center ALS ? Wouldn't you see the strong links first ?

Also if you can identify it as a special case of a more general doubly linked construct, it is an own pattern for me. For a manual solver it can be spotted almost as easy as a single ERI or kite (grouped or not), but probably the additional eliminations would not be found.

I can see the strong links and it looks now to me like a w-wing. 2 w-wings that share the same bivalue cells. That is how the loop is achieved. is a doubly-linked w-wing a better way to see it?

tarek

[eleven]

Yes, i just wanted to write the same double w-wing.
However harder to spot in the first sample ...

[tarek]

Yes, i just wanted to write the same double w-wing.
However harder to spot in the first sample ...

Just had a look at the 1st sample … The strong links are both grouped (both are empty rectangles). I'm not going into a naming contest but would simply describe it as a "grouped doubly-linked w-wing" and the r4c1 eliminations are cannibalistic

I'm waiting for a fancy AIC to descend from space any moment

[eleven]

SpAce had found a double w-wing here.

Code: Select all

+-------------------+-------------------+-------------------+
| 6     2     7     | 5     89    3     | 489   1     489   |
|#49    5     48-9  | 6     7     1     | 2     89    3     |
| 3     1    @89    | 4     2    @89    | 6     7     5     |
+-------------------+-------------------+-------------------+
| 1     7     3     | 8     49    5     | 49    6     2     |
| 58-49 489   459   | 2     6    #49    | 7     3     1     |
| 2     49    6     | 3     1     7     | 489   5     489   |
+-------------------+-------------------+-------------------+
| 7     489   459   | 1     458   2     | 3     489   6     |
|*48    6     1     | 9     3    *48    | 5     2     7     |
| 589-4 3     2     | 7     458   6     | 1     489   89    |
+-------------------+-------------------+-------------------+

There are 2 additional eliminatons -9r2c3 and -4r9c1.

[rjamil]

SpAce had found a double w-wing here.

Or, is the pattern simply called Grouped W-Ring?

R. Jamil

[yzfwsf]

SpAce had found a double w-wing here.

Code: Select all

+-------------------+-------------------+-------------------+
| 6     2     7     | 5     89    3     | 489   1     489   |
|#49    5     48-9  | 6     7     1     | 2     89    3     |
| 3     1    @89    | 4     2    @89    | 6     7     5     |
+-------------------+-------------------+-------------------+
| 1     7     3     | 8     49    5     | 49    6     2     |
| 58-49 489   459   | 2     6    #49    | 7     3     1     |
| 2     49    6     | 3     1     7     | 489   5     489   |
+-------------------+-------------------+-------------------+
| 7     489   459   | 1     458   2     | 3     489   6     |
|*48    6     1     | 9     3    *48    | 5     2     7     |
| 589-4 3     2     | 7     458   6     | 1     489   89    |
+-------------------+-------------------+-------------------+

There are 2 additional eliminatons -9r2c3 and -4r9c1.

My solver can not catch this case, i think they are not same pattern.

[champagne]

Hi Cenoman & Leren
I mean the following structure, Only two bivalue cells with the same two candidates + ER of these two candidates are considered.

ERI_Pairs.png

Hi yzfwsf,

Nice example of a rank0 logic with a triple point 2 links. (in fact 2 triple points one for digit 2, one for digit 6)

As it is globally a rank 0 logic, it can be applied ignoring that we have a triple point (this would not be true with a triple point 2 truths)
and we know that more can happen when the triple point is assigned.

I have no general rule, but here, it is clear that r4c1=2 and r4c1=6 are not valid within the rank 0 logic. This is why XSUDO find these eliminations

[eleven]

There are 2 additional eliminatons -9r2c3 and -4r9c1.

My solver can not catch this case, i think they are not same pattern.

Your pattern is an interesting special case of a "grouped w-ring", as rjamil calls it (with the strong links in the same house), which is a special case of what champagne describes above.

[tarek]

and here is another link to a thread where the w-wing/w-ring has been extended to any ALS not just bivalue:
http://forum.enjoysudoku.com/als-w-wings-rings-t36860.html

The 1st sample was (as eleven mentioned) a special example because:

1. both strong links are grouped strong links in a box sharing the same cells.
2. The eliminations of r4c1 were cannibalistic

I used the cannibalistic term as the Rank-0 logic allows me to visualize it as a fish with candidates in the "Heart cell" being covered twice by 2 weak links (actually each candidate is covered twice by 2 weak links)

My attempt at connecting the correct way of naming grouped strong links with historical terms:
http://forum.enjoysudoku.com/empty-mini-area-ema-emr-and-eml-t36953.html#p285515

This is how I programmed it in Sukaku explainer:

From a programming point of view:
There are 9 configurations of ER per box (based on the intersection cell). I refer to that cell as the "Heart cell". The remaining candidates in location occupy "Cross" cells and there is 1 set of "Cross" cells configuration per "Heart Cell". The empty cells occupy a "Rectangle" and there is 1 set of "Rectangle" cells per "Heart cell". The "Cross" is further divided into 2 "Blades" (Basically one is the mini-column and the other the mini-row). You need the "Rectangle" cells to be empty & each blade of the Cross cells to have at least 1 candidate to qualify as an "ER".

tarek

[Cenoman]

I'm waiting for a fancy AIC to descend from space any moment

Sorry tarek, to disappoint you. It's only me, Cenoman, trying to write an AIC (without fancy)
SpAce, you have a right to treat me "Usurper !"

In the 8th post of this thread, I wrote the two W-wings eliminating ab from r4c1 and r7c5 (in this pattern diagram, Leren's way)

Code: Select all

-ab       .       .      |  .   .   .   | .   .   .
-ab       .       .      |  .   .   .   | .   .   .
-ab       .       .      |  .   .   .   | .   .   .
-------------------------+--------------+-------------
+,-ab    *ab+    *ab+    | -ab *ab -ab  |-ab -ab -ab
#ab+      /       /      |  .   .   .   | .   .   .     / cells without a or b
#ab+      /       /      |  .   .   .   | .   .   .     + extra candidates <> a OR b
-------------------------+--------------+-------------
#ab       .       .      |  .  -ab  .   | .   .   .
-ab       .       .      |  .   .   .   | .   .   .
-ab       .       .      |  .   .   .   | .   .   .

(a=b)r4c5 - r4c123 = r56c1 - (b=a)r7c1 => r4c1<>a
(b=a)r4c5 - r4c123 = r56c1 - (a=b)r7c1 => r4c1<>b

forgetting r7c5<>a, r7c5<>b

Now, writing an AIC, from this starting point is easy:
^(a=b)r4c5 - r4c123 = r56c1 - #(b=a)r7c1^ - r56c1 = (a)r4c123 - (a=b)r4c5# loop

=> -b r4c46789, -b r123489c1, -a r23489c1, -a r4c46789, -a r7c5^, -b r7c5#

Note that most eliminations (including cannibalistic r4c1 <> a,b at the ER Intersection) result from the loop elimination rules, loop which could omit the last term, but the eliminations in r7c5 are demonstrated by the W-wing subchains (hence the last term...)

Note also that (a)r4c1 and (b)r4c1 are included in nodes (a)r4c123 and (b)r4c123. They could be included in nodes (a)r456c1 and (b)r456c1 as well:
alternative AIC ^(a=b)r4c5 - r4c23 = r456c1 - #(b=a)r7c1^ - r456c1 = (a)r4c23 - (a=b)r4c5# loop => same eliminations.

[rjamil]

Hi all,

2. The eliminations of r4c1 were cannibalistic

I don't think that the eliminations of r4c1 were cannibalistic, due the ER Intersection cell won't check/include in Empty Rectangle pattern.

See "1. Empty mini-Rectangle (EmR):" pattern here and Tarek confirmed here.

R. Jamil

[yzfwsf]

Another example：

Code: Select all

.---------------------------------.---------------------------------.---------------------------------.
|  6          1          39       |  348        7          89       |  2          345        45       |
|  5          7          39       |  2          14         19       |  134        8          6        |
|  8          2          4        |  5          13         6        |  139        139        7        |
:---------------------------------+---------------------------------+---------------------------------:
|  7          45         156      |  9          14568      2        |  1458       145        3        |
|  2          3459       56       |  346        134568     15       |  14589      7          4589     |
|  1349       3459       8        |  34         1345       7        |  6          1459       2        |
:---------------------------------+---------------------------------+---------------------------------:
|  149        4589       15       |  168        56         3        |  7          2          4589     |
|  139        3589       7        |  18         2          4        |  3589       6          589      |
|  34         6          2        |  7          9          58       |  3458       345        1        |
'---------------------------------'---------------------------------'---------------------------------'

ERI_Pairs.png (27.75 KiB) Viewed 892 times

[tarek]

Another nice example yzfwsf,

2. The eliminations of r4c1 were cannibalistic

I don't think that the eliminations of r4c1 were cannibalistic, due the ER Intersection cell won't check/include in Empty Rectangle pattern.

See "1. Empty mini-Rectangle (EmR):" pattern here and Tarek confirmed here.

Thanks for pointing this out. When using Fish logic … The heart cell is always at the intersection of 2 sectors …
If the empty rectangle is used as a grouped strong link then the heart cell is always a potential cannibalistic elimination. On the other hand if you chose to use the Empty rectangle pattern as a weak link then the heart cell would always be an endofin.
If my diagrams gave the impression that it is not part of the pattern then I may need to amend that. The heart cell would have an parenthesized X to indicate that it can be omitted. I'm not too fussed about missing a cannibalistic elimination but I would be disappointed if it we missed an endofin and assumed we have rank 0 logic or a ring/loop. That is why IMO it needs to be part of the pattern.

[tarek]

(a=b)r4c5 - r4c123 = r56c1 - (b=a)r7c1 => r4c1<>a
(b=a)r4c5 - r4c123 = r56c1 - (a=b)r7c1 => r4c1<>b

forgetting r7c5<>a, r7c5<>b

Now, writing an AIC, from this starting point is easy:
^(a=b)r4c5 - r4c123 = r56c1 - #(b=a)r7c1^ - r56c1 = (a)r4c123 - (a=b)r4c5# loop

=> -b r4c46789, -b r123489c1, -a r23489c1, -a r4c46789, -a r7c5^, -b r7c5#

Note that most eliminations (including cannibalistic r4c1 <> a,b at the ER Intersection) result from the loop elimination rules, loop which could omit the last term, but the eliminations in r7c5 are demonstrated by the W-wing subchains (hence the last term...)

Note also that (a)r4c1 and (b)r4c1 are included in nodes (a)r4c123 and (b)r4c123. They could be included in nodes (a)r456c1 and (b)r456c1 as well:
alternative AIC ^(a=b)r4c5 - r4c23 = r456c1 - #(b=a)r7c1^ - r456c1 = (a)r4c23 - (a=b)r4c5# loop => same eliminations.

Nice!!!

[rjamil]

Hi all,

Found another very nice example of W-Ring, detected by SpAce for September 18, 2018 OTP puzzle, as follows:

Code: Select all

 +---------------------+----------------------+---------------------+
 | 23467  12346  1367  | 1457   13457  134578 | 9      12356  13568 |
 | 2349   8      139   | 1459   1345   6      | 25-3   7      135   |
 | 3679   1369   5     | 179    2      1378   | (38)   136    4     |
 +---------------------+----------------------+---------------------+
 | 4679   1469   1679  | 3      14567  12457  | 2457   8      5679  |
 | 34679  3469   2     | 4567   8      457    | 1      3569   35679 |
 | 34678  5      13678 | 12467  1467   9      | 247-3  236    367   |
 +---------------------+----------------------+---------------------+
 | 1      2-3    (38)  | 2457   9      2457-3 | (6)    [3]5   7[8]  |
 | 23569  7      369   | 8      1356   1235   | [3]5   4      19    |
 | 35689  369    4     | 1567   13567  1357   | 7[8]   19     2     |
 +---------------------+----------------------+---------------------+

W-Ring: 38 @ r3c7 r7c3 ERI 38 @ b9r7c7 => -3 @ r26c7 r7c26; stte

R. Jamil