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Puzzle 10/10/06: C XY

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Wed Oct 06, 2010 12:35 am    Post subject: Puzzle 10/10/06: C XY Reply with quote

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

Play this puzzle online at the Daily Sudoku site
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JC Van Hay



Joined: 13 Jun 2010
Posts: 373
Location: Charleroi, Belgium

PostPosted: Wed Oct 06, 2010 1:42 pm    Post subject: Reply with quote

Quote:
XY Wing (46-8), vertex at R3C2 : => r2c89<>8
To prevent DP(67)R29C89 : => r2c35<>49
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Wed Oct 06, 2010 2:11 pm    Post subject: Reply with quote

Two steps........

Quote:
AUR(67)r29c89 external SIS: r2c5=6, r2c5=7; r2c5<>489
xy-wing 46-8 vertex (46)r3c2; r2c89<>8


This solution is identical to JC's except in reverse order. I also looked for other solutions but they became BBDBers.

Ted
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK

PostPosted: Wed Oct 06, 2010 9:41 pm    Post subject: Reply with quote

A wing...
Quote:
m-wing(49) (4=9)r2c4 - r1c56=(9-4)r1c8=r2c8 ; r2c3<>4
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Marty R.



Joined: 12 Feb 2006
Posts: 5181
Location: Rochester, NY, USA

PostPosted: Thu Oct 07, 2010 4:22 am    Post subject: Reply with quote

I played three ERs, then the XY-Wing on 468, then the 67 UR with pseudo cell 49.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Oct 07, 2010 3:40 pm    Post subject: Reply with quote

peterj wrote:
m-wing(49) (4=9)r2c4 - r1c56=(9-4)r1c8=r2c8 ; r2c3<>4

Although the M-Wing interpretation is sufficient to crack the puzzle, for completeness ... it's a loop that does a lot more damage:

Code:
 +-----------------------------------------------------------------------+
 |  58     456    1      |  3      46789  4789   |  67     46789  2      |
 |  3      2      48     |  49     46789  5      |  1      46789  6789   |
 |  7      46     9      |  1      468    2      |  5      3      68     |
 |-----------------------+-----------------------+-----------------------|
 |  6      459    3      |  7      1      489    |  89     2      589    |
 |  58     459    48     |  2      3459   349    |  67     167    167    |
 |  2      1      7      |  59     589    6      |  3      589    4      |
 |-----------------------+-----------------------+-----------------------|
 |  14     8      6      |  459    4579   479    |  2      159    3      |
 |  14     7      2      |  6      3459   349    |  89     1589   1589   |
 |  9      3      5      |  8      2      1      |  4      67     67     |
 +-----------------------------------------------------------------------+
 # 83 eliminations remain

 M-Loop  B (4=9)r2c4 - r1c56 = (9-4)r1c8 = (4)r2c8  - loop  =>  r2c3<>4, r1c8<>678, r2c5<>49
 -or-
 M-Loop  D (4=9)r2c4 - r2c89 = (9-4)r1c8 = (4)r2c8  - loop  =>  r2c3<>4, r1c8<>678, r2c5<>49
 -also-
 M-Loop  B (6=7)r1c7 - r1c56 = (7-6)r2c5 = (6)r2c89 - loop  =>  r2c5<>489, r3c9<>6, r1c8<>67
 M-Loop  C (6=7)r1c7 - r2c89 = (7-6)r2c5 = (6)r2c89 - loop  =>  r2c5<>489, r3c9<>6, r1c8<>67
____________________________________________________________________________________________

daj's take on continuous loops wrote:
All of the eliminations in a continuous loop come from ERI cell candidates and forcing weak inferences to become strong links.
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK

PostPosted: Thu Oct 07, 2010 5:28 pm    Post subject: Reply with quote

Danny, is an m-loop the same as an m-ring?
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Oct 07, 2010 6:25 pm    Post subject: Reply with quote

peterj wrote:
Danny, is an m-loop the same as an m-ring?

Yes. I have this mental block about using the word "ring". I'll update the labels in my solver and maybe that'll help me to remember. Sorry for the confusion!
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK

PostPosted: Thu Oct 07, 2010 9:10 pm    Post subject: Reply with quote

No confusion! Just learning...
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