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Puzzle 11/06/05: ~ XY

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sun Jun 05, 2011 4:09 pm    Post subject: Puzzle 11/06/05: ~ XY Reply with quote

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

Play this puzzle online at the Daily Sudoku site
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tlanglet



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

PostPosted: Mon Jun 06, 2011 2:49 pm    Post subject: Reply with quote

I stumbled into a nice chain while looking for xy-wings............

(3=4)r9c1-(4=1)r9c6-r3c6=(1-3)r3c4=(3)r123c5; r9c5<>3=9

Ted
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peterj



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

PostPosted: Mon Jun 06, 2011 3:58 pm    Post subject: Reply with quote

An alternative to Ted's chain (which to me looks like an m-wing with a r9 3=1) is this xy-chain...
Quote:
(1=3)r3c4 - (3=4)r3c2 - (4=3)r2c1 - (3=4)r9c1 - (4=1)r9c6 ; r3c6<>1, r79c4<>1
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Jun 06, 2011 5:32 pm    Post subject: Reply with quote

Code:
 after basics
 +--------------------------------------------------------------------------------+
 |  8       1       6       |  4       235     9       |  7       235     23      |
 |  34      5       9       |  6       238     7       |  234     2348    1       |
 |  2       34      7       |  13      358     15      |  3459    345689  34689   |
 |--------------------------+--------------------------+--------------------------|
 |  7       9       348     |  5       1       26      |  234     23468   23468   |
 |  56      348     348     |  9       7       26      |  1       234568  23468   |
 |  1       26      25      |  8       4       3       |  59      7       69      |
 |--------------------------+--------------------------+--------------------------|
 |  9       234     12345   |  123     6       145     |  8       234     7       |
 |  56      23467   2345    |  237     359     8       |  2349    1       2349    |
 |  34      23478   12348   |  1237    39      14      |  6       2349    5       |
 +--------------------------------------------------------------------------------+
 # 109 eliminations remain

This puzzle is interesting because it only has a single XY-Chain, which cracks the puzzle (as peterj discovered).

It also has 2x (nearly identical) M-Wing that crack the puzzle:

Code:
M-Wing 2B: (1=5)r3c6 - r7c6 = (5-1)r7c3 = (1)r9c3   =>  r9c6<>1
M-Wing 3B: (1=5)r3c6 - r7c6 = (5-1)r7c3 = (1)r7c46  =>  r9c6<>1

After that, an extraneous XYZ-Wing still needs a chain to crack the puzzle (like Ted used).
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Marty R.



Joined: 12 Feb 2006
Posts: 5122
Location: Rochester, NY, USA

PostPosted: Tue Jun 07, 2011 4:33 am    Post subject: Reply with quote

The XY-Chain is also what I call an XY-Wing Chain or what others call an Extended XY-Wing, 13-34-34-34-14, where the three 34 cells act as the one pivot cell in an XY-Wing.
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