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Puzzle 11/04/10: ~ Moderate/Difficult++ BBDB

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Apr 10, 2011 5:49 am    Post subject: Puzzle 11/04/10: ~ Moderate/Difficult++ BBDB Reply with quote
There are 2x (essentially equivalent) W-Wings that crack this puzzle. If you miss them and use other traditional techniques, then you could be in for a "world of hurt".

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

Play this puzzle online at the Daily Sudoku site
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Mon Apr 11, 2011 4:45 am    Post subject: Reply with quote
I didn't read your comment beforehand.

W-Wing (45); r6c7, r8c4<>4 +transport; r4c6, r6c8<>4
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK
PostPosted: Mon Apr 11, 2011 9:20 am    Post subject: Reply with quote
Marty, nice! Though it took me five minutes to work out the wing by working back from your eliminations! I assume it is this...
Code:
grouped w-wing(45) ; (4=5)r6c4 - r6c8=r89c8 - (5=4)r8c7 transport - (4)r9c9=r4c9
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Mon Apr 11, 2011 4:31 pm    Post subject: Reply with quote
I want to show an alternate path that uses an ERI on <5>. See the second W-Wing below:

Code:
 +-----------------------------------------------------------------------+
 |  148    49     1489   |  149    7      6      |  2      3      5      |
 |  7      6      3      |  459    45     2      |  8      49     1      |
 |  145    2      1459   |  3      48     18     |  469    469    7      |
 |-----------------------+-----------------------+-----------------------|
 |  145    3      14579  |  8      6      45     | c4579   2      49     |
 |  6      459    459    |  7      2      3      | c459    1      8      |
 |  2      8      457    | a45     1      9      | c4567b b456    3      |
 |-----------------------+-----------------------+-----------------------|
 |  458    1      458    |  6      9      45     |  3      7      2      |
 |  9      7      2      |  145    3      18     | d45     458    6      |
 |  3      45     6      |  2      458    7      |  1      4589   49     |
 +-----------------------------------------------------------------------+
 # 66 eliminations remain

W-Wing:   (4=5)r6c4 - r6c8  = r89c8  - (5=4)r8c7  =>  r6c7,r8c4<>4   -or-
W-Wing:   (4=5)r6c4 - r6c78 = r456c7 - (5=4)r8c7  =>  r6c7,r8c4<>4
                       ^ ^       ^ ^

The ERI cell r6c7 is included twice -- in "b" and in "c" -- in the notation. (I'm probably "preaching to the choir" here.)
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