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Q: apply two rules at once?

 
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Orkamat



Joined: 20 Dec 2011
Posts: 10
Location: Winnipeg, Canada

PostPosted: Wed Feb 29, 2012 3:00 am    Post subject: Q: apply two rules at once? Reply with quote

Code:

 . 2 . | 8 . 7 | . 3 1
 3 1 . | 9 . 6 | 8 2 7
 7 . 8 | 3 2 1 | 5 . .
-------+-------+------
 2 5 3 | 1 6 8 | 7 4 9
 . 8 . | 7 9 2 | 3 1 5
 9 7 1 | 5 3 4 | 6 8 2
-------+-------+------
 5 . 2 | 4 . 3 | 1 . .
 8 . . | 2 1 5 | . . 3
 1 3 . | 6 . 9 | 2 5 .
 


r1c3 has possibilities 4569

it also forms a corner of two URs: 46 and 45

so ... if you can remove either 45 or 46, your choice, surely you can remove 456, even though resolving one UR removes the other?

it seems obvious, but I wanted to check with those with more experience in case there was some sudoku-specific rule of magical logic that would be violated Very Happy
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keith



Joined: 19 Sep 2005
Posts: 3162
Location: near Detroit, Michigan, USA

PostPosted: Wed Feb 29, 2012 4:16 am    Post subject: Reply with quote

Code:
+----------------+----------------+----------------+
| 46   2    4569 | 8    45   7    | 49   3    1    |
| 3    1    45   | 9    45   6    | 8    2    7    |
| 7    49   8    | 3    2    1    | 5    69   46   |
+----------------+----------------+----------------+
| 2    5    3    | 1    6    8    | 7    4    9    |
| 46   8    46   | 7    9    2    | 3    1    5    |
| 9    7    1    | 5    3    4    | 6    8    2    |
+----------------+----------------+----------------+
| 5    69   2    | 4    78   3    | 1    679  68   |
| 8    469  479  | 2    1    5    | 49   679  3    |
| 1    3    47   | 6    78   9    | 2    5    48   |
+----------------+----------------+----------------+

Orkamat,

Yes. Candidates eliminated by uniqueness arguments remain as "phantom" candidates in other uniqueness patterns. This is a great example!

In R1C3, -456 immediately solves the puzzle. -45 or -46 does not.

Best wishes,

Keith
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