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Dec 5 DB

 
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
PostPosted: Sat Dec 05, 2009 3:30 pm    Post subject: Dec 5 DB Reply with quote
The Dec 5 DB can be dispatched with a single blow.

Solutions: A w-wing (17) or coloring in (1)


Earl


Code:

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

Play this puzzle online at the Daily Sudoku site
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Sat Dec 05, 2009 4:31 pm    Post subject: Reply with quote
Some linkage was needed:
Quote:
(9=1)r7c2-(1)r8c2=(1)r8c6-(1)r6c6=(1)r6c9-(1)r9c9=(1)r7c8 => r7c2<>1, r7c8<>9
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Dec 05, 2009 7:35 pm    Post subject: Reply with quote
After basics:
Code:
+-------------+-------------+-------------+
| 1   4   7   | 6   89  89  | 3   5   2   |
| 9   5   2   | 17  4   3   | 6   17  8   |
| 6   8   3   | 5   17  2   | 14  179 149 |
+-------------+-------------+-------------+
| 8   6   1   | 2   579 49  | 45  3   47  |
| 7   3   9   | 18  158 48  | 145 2   6   |
| 4   2   5   | 3   6   17  | 9   8   17  |
+-------------+-------------+-------------+
| 2   19  8   | 4   3   6   | 7   19  5   |
| 5   17  6   | 9   2   17  | 8   4   3   |
| 3   179 4   | 178 178 5   | 2   6   19  |
+-------------+-------------+-------------+

I don't know what to call this, but R9C9 [cell reference corrected] cannot be 1, for it forces 1 in both R68C6.

Also, R7C2 and R9C9 are a W-wing, connected by a chain of four cells 17; R7C8 and R9C2 are not 9.

Keith

Last edited by keith on Sat Dec 05, 2009 8:20 pm; edited 2 times in total
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sat Dec 05, 2009 7:58 pm    Post subject: Reply with quote
keith wrote:
After basics:
Code:
+-------------+-------------+-------------+
| 1   4   7   | 6   89  89  | 3   5   2   |
| 9   5   2   | 17  4   3   | 6   17  8   |
| 6   8   3   | 5   17  2   | 14  179 149 |
+-------------+-------------+-------------+
| 8   6   1   | 2   579 49  | 45  3   47  |
| 7   3   9   | 18  158 48  | 145 2   6   |
| 4   2   5   | 3   6   17  | 9   8   17  |
+-------------+-------------+-------------+
| 2   19  8   | 4   3   6   | 7   19  5   |
| 5   17  6   | 9   2   17  | 8   4   3   |
| 3   179 4   | 178 178 5   | 2   6   19  |
+-------------+-------------+-------------+

I don't know what to call this, but R9C9 cannot be 1, for it forces 1 in both R68C6.

Also, R7C2 and R9C9 are a W-wing, connected by a chain of four cells 17; R7C8 and R9C2 are not 9.

Empty Rectangle r7b8: (1) r6c9 = r6c6 - r8c6 = r9c45 => r9c9<>1

Code:
 as Blue/Green coloring
 +-----------------------------------------------------+
 |  1    4    7    |  6    89   89   |  3    5    2    |
 |  9    5    2    |  17   4    3    |  6    17   8    |
 |  6    8    3    |  5    17   2    |  14   179  149  |
 |-----------------+-----------------+-----------------|
 |  8    6    1    |  2    579  49   |  45   3    47   |
 |  7    3    9    |  18   158  48   |  145  2    6    |
 |  4    2    5    |  3    6   B17   |  9    8   G17   |
 |-----------------+-----------------+-----------------|
 |  2    19   8    |  4    3    6    |  7    19   5    |
 |  5    17   6    |  9    2   G17   |  8    4    3    |
 |  3    179  4    | B178 B178  5    |  2    6    9-1  |
 +-----------------------------------------------------+
 # 34 eliminations remain
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Dec 05, 2009 8:25 pm    Post subject: Reply with quote
Danny,

Interesting perspectives! I have corrected the cell reference in my original post.

Thank you,

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sat Dec 05, 2009 9:05 pm    Post subject: Reply with quote
keith wrote:
Danny,

Interesting perspectives! I have corrected the cell reference in my original post.

Thank you,

Keith

You're very welcome!!! However, I should be thanking you for a trip down memory lane.

Before I studied fish patterns in detail (and added the technique to my solver), I use to encounter single-digit patterns like the one you mentioned. After awhile, it occurred to me that I could use Blue/Green coloring on the two cells that were forced true -- r68c6 in your example. Then, I backtracked using coloring through the cells originally used to get to the contradiction. It always made the elimination stand out ... and it sometimes pointed out secondary eliminations. I included the Blue/Green coloring as an example of this approach!

Regards, Danny
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