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Bud
Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida
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 Posted: Tue Jul 20, 2010 3:11 pm Post subject: M-Ring/APE and extended S-Wing Examples |
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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: 398
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| Posted: Tue Jul 20, 2010 3:46 pm Post subject: Re: M-Ring/APE and extended S-Wing Examples |
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| 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: 3854
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| Posted: Tue Jul 20, 2010 4:55 pm Post subject: Re: M-Ring/APE and extended S-Wing Examples |
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| 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
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| 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
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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
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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. _  _ |
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strmckr
Joined: 18 Aug 2009
Posts: 64
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| Posted: Mon Jul 26, 2010 3:29 am Post subject: |
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| 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 im glad u found my posts useful. |
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