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Extended M-Ring Example

 
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Bud



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

PostPosted: Thu Oct 21, 2010 6:50 pm    Post subject: Extended M-Ring Example Reply with quote

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: 61

PostPosted: Fri Oct 22, 2010 1:37 am    Post subject: Reply with quote

nice extension Smile 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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