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Bud
Joined: 06 May 2010
Posts: 47
Location: Tampa, Florida
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 Posted: Thu Oct 21, 2010 6:50 pm Post subject: Extended M-Ring Example |
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The extended M-Ring in the example has forcing path cells denoted by *. These paths are: (2)r3c7-r9c7=(2)r9c5 and (8)r3c7-r13c9=(8)r7c9-r9c78=(8)r9c5. This proves that r3c7=r9c5 = 28 => r3c7<>1. If these 2 cells=2 or if r9c7=2, then r8c7<>2. If these two cells=8 or if r9c78 & r13c9=8, then r23c8<>8. This M-Ring differs from the examplars in Strmckr's post in that the latter has forcing paths which are only 3 cells long whereas in this example the 8 digit has a path which is 5 cells long (counting grouped cells as one). The fact that the 8 digit has an extended path is why I have called it an extended M-Wing. As long as either or both of these paths have an odd number of cells they will work the same as a normal M-Ring.
Extended M-Ring Pattern Example | Code: |
+--------------------+-------------------+------------------+
| 2 56 569 | 689 5789 1 | 4 3 789* |
| 1389 134 1349 | 2389 23789 29 | 6 17-89 5 |
| 13589 1356 7 | 4 3589 569 | 28* 1-89 1289*|
+--------------------+-------------------+------------------+
| 3579 3457 3459 | 1 6 8 | 3579 2 79 |
| 6 137 13 | 29 259 259 | 378 178 4 |
| 159 8 2 | 7 4 3 | 59 1569 169 |
+--------------------+-------------------+------------------+
| 35 2356 356 | 23689 2389 7 | 1 4 2689*|
| 4 12367 8 | 2369 1239 269 |-2579 5679 2679 |
| 17 9 16 | 5 -128* 4 | 278* 678* 3 |
+--------------------+-------------------+------------------+ |
The original puzzle is yesterdays daily tough at sudoku.com.au. I used an AIC to eliminate 9 from r3c7 and basic moves to reach this point in the puzzle. |
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strmckr
Joined: 18 Aug 2009
Posts: 64
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| Posted: Fri Oct 22, 2010 1:37 am Post subject: |
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nice extension  defiantly fits
also seen as a
Grouped Continuous Nice Loop: 1/2/8 8= r9c5 =2= r9c7 -2- r3c7 -8- r13c9 =8= r7c9 -8- r7c45 =8= r9c5 =2 => r9c5<>1, r8c7<>2, r23c8<>8 |
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