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M-Ring/APE and extended S-Wing Examples

 
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Bud



Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida

PostPosted: Tue Jul 20, 2010 3:11 pm    Post subject: M-Ring/APE and extended S-Wing Examples Reply with quote

I think the cells labeled ABCD in B14 of this example is an M-Ring, but it does not fit any of the example Types A through D. It can also be considered to be an aligned pair exclusion and maybe it is both. Let me briefly go over the logic in simple terms. The 79 A cell sees an ER iin B4 which forces the candidates in cell D to be either 7 or 9. Any other cnadidates in cell D can be eliminated, in this case 3. This I think could be considered to be an APE or an M-WIng elimination. There is now a grouped continuous 79 loop in B14 and C12, which eliminates the 7 and 9 in R1C1. This I think is an M-Ring elimination. Shouldn't the pattern in this example be added to the list?

The cells in the extended S-Wing are marked with an asterisk in B369. The pivot for the S-Wing is the the 34 cell R8C8. This results in either a 4 in R6C9 or a 3 in R5C9 and a 9 in R1C9. This implies that R6C9<>9. Thus adding a cell to the S-Wing provides a cell elimination whereas the S-Wing by itself does not. I personally have found S-Wings to be about as common and easy to find as W-Wings.

M-Ring/APE Example?
Code:

 |-------------------+--------------------+---------------------|
 | 356-7-9 3679 3568 |  279    69    268  |    4      1     39* |
 |    1    3679  368 |  479   469     68  |  379      5      2  |
 |   79A     2    4  |   5      1      3  |  789    789      6  |
 |-------------------+--------------------+---------------------|
 |  356    346   356 |   8      2      9  |    1    346*     7  |
 |  379B  -379D   1  |   6      5      4  |    2    389*   389* |
 |  269C     8    26 |   3      7      1  |    5    469    4-9* |
 |-------------------+--------------------+---------------------|
 |    4    136    7  |   19   369      5  |  389      2   1389  |
 |   23     13    9  |  124     8      7  |    6     34*     5  |
 |    8      5   236 | 1249  3469     26  |  379   3479   1349* |
 |-------------------+--------------------+---------------------|


The original puzzle is Sudoku 9981 Extreme Book 39 #1.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Tue Jul 20, 2010 3:46 pm    Post subject: Re: M-Ring/APE and extended S-Wing Examples Reply with quote

Bud wrote:
This I think is an M-Ring elimination. Shouldn't the pattern in this example be added to the list?

It is, and yours fits the type D illustration.

Bud wrote:
The cells in the extended S-Wing are marked with an asterisk in B369. The pivot for the S-Wing is the the 34 cell R8C8. This results in either a 4 in R6C9 or a 3 in R5C9 and a 9 in R1C9. This implies that R6C9<>9. Thus adding a cell to the S-Wing provides a cell elimination whereas the S-Wing by itself does not.

Nice extension.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Jul 20, 2010 4:55 pm    Post subject: Re: M-Ring/APE and extended S-Wing Examples Reply with quote

Bud wrote:
I think the cells labeled ABCD in B14 of this example is an M-Ring, but it does not fit any of the example Types A through D.

You labeled the grid improperly for an M-Ring. Here are two M-Rings that use your cells.

Code:
 Loop B (7=9)r3c1 - r56c1 = (9-7)r5c2 = (7)r12c2 - loop  =>  r5c2<>3, r1c1<>79
 +-----------------------------------------------------------------------+
 |  35679 D3679   3568   |  279    69     268    |  4      1      39     |
 |  1     D3679   368    |  479    469    68     |  379    5      2      |
 | A79     2      4      |  5      1      3      |  789    789    6      |
 |-----------------------+-----------------------+-----------------------|
 |  356    4      356    |  8      2      9      |  1      36     7      |
 | B379   C379    1      |  6      5      4      |  2      389    389    |
 | B269    8      26     |  3      7      1      |  5      469    49     |
 |-----------------------+-----------------------+-----------------------|
 |  4      136    7      |  19     369    5      |  389    2      1389   |
 |  23     13     9      |  124    8      7      |  6      34     5      |
 |  8      5      236    |  1249   3469   26     |  379    3479   1349   |
 +-----------------------------------------------------------------------+
 # 84 eliminations remain

Code:
 Loop D (7=9)r3c1 - r56c1 = (9-7)r5c2 = (7)r5c1  - loop  =>  r5c2<>3, r1c1<>79
 +-----------------------------------------------------------------------+
 |  35679  3679   3568   |  279    69     268    |  4      1      39     |
 |  1      3679   368    |  479    469    68     |  379    5      2      |
 | A79     2      4      |  5      1      3      |  789    789    6      |
 |-----------------------+-----------------------+-----------------------|
 |  356    4      356    |  8      2      9      |  1      36     7      |
 | B379D  C379    1      |  6      5      4      |  2      389    389    |
 | B269    8      26     |  3      7      1      |  5      469    49     |
 |-----------------------+-----------------------+-----------------------|
 |  4      136    7      |  19     369    5      |  389    2      1389   |
 |  23     13     9      |  124    8      7      |  6      34     5      |
 |  8      5      236    |  1249   3469   26     |  379    3479   1349   |
 +-----------------------------------------------------------------------+
 # 84 eliminations remain

There are two other M-Rings present as well.

Code:
Loop B (7=9)r3c1 - r12c2 = (9-7)r5c2 = (7)r5c1  - loop  =>  r5c2<>3, r1c1<>79
Loop C (7=9)r3c1 - r12c2 = (9-7)r5c2 = (7)r12c2 - loop  =>  r5c2<>3, r1c1<>79

Personally, I'm impressed by the Type C use of overlapping grouped strong links in [c2] for <7> and <9>.

Hopefully, ronk won't find duplicates in my list this time. _ Smile _
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strmckr



Joined: 18 Aug 2009
Posts: 61

PostPosted: Mon Jul 26, 2010 3:29 am    Post subject: Reply with quote

Quote:
Bud wrote:
The cells in the extended S-Wing are marked with an asterisk in B369. The pivot for the S-Wing is the the 34 cell R8C8. This results in either a 4 in R6C9 or a 3 in R5C9 and a 9 in R1C9. This implies that R6C9<>9. Thus adding a cell to the S-Wing provides a cell elimination whereas the S-Wing by itself does not.

Nice extension.
very nice indeed Smile im glad u found my posts useful.
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