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Puzzle 10/09/05: C

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sun Sep 05, 2010 1:02 am    Post subject: Puzzle 10/09/05: C Reply with quote
Code:
 +-----------------------+
 | . . . | . . . | 3 7 9 |
 | . . . | . 6 . | 1 . . |
 | 3 . 7 | . . . | . . . |
 |-------+-------+-------|
 | 6 . . | 1 5 . | . . 3 |
 | . 5 . | 3 . . | 7 9 . |
 | 9 . . | . . 8 | . . . |
 |-------+-------+-------|
 | . 3 . | . 8 . | . 1 . |
 | 5 . . | . . . | 9 . . |
 | 8 6 . | 5 . . | . . 4 |
 +-----------------------+

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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK
PostPosted: Sun Sep 05, 2010 9:10 am    Post subject: Reply with quote
I don't normally do these sort of moves... (so it may be wrong!)
Quote:
6-cell ADP(56) r3c89|r6c78|r7c79, DP avoided by (2)r3c9 or (4)r6c7
(4=2)r2c8 - ADP(56):(2)r3c9=(4)r6c7 ; r4c8<>4, r3c7<>4
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
PostPosted: Sun Sep 05, 2010 11:29 am    Post subject: Reply with quote
A one step solution :
Quote:
Unique Loop of length 6 (56)[R3C98,R6C87,R7C79] : 2-SIS AIC : SIS[(2)r3c9,(4)r6c7] (42)R4C8 : => r5c9,r2c8<>2

Or the following proof :
Quote:
Remote pairs (24) : => r5c1<>24
3-SIS X Chain (including an Empty Rectangle) : (2)C9B58 : => r3c46<>2
XYZ Wing (12-4), pivot at R1C5 : => r3c5,r5c6<>4
3-SIS- X Chain : (4)C27B2 : => r8c4<>4
5-SIS AIC written as an ALS XY Wing : [(42)R1C1 (21)R1C5] [(19)R9C5 (94)R7C4] (48)R1C4 : "ANP(42=1) ANP(1=94) (48)R1C4" : => r1c4<>4
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Tue Sep 07, 2010 12:30 am    Post subject: Reply with quote
I struggled with this more than any recent puzzle I can remember.

Remote Pairs (24)
Finned X-Wing (2)
XYZ-Wing (124)
AIC; r6c4<>2
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Tue Sep 07, 2010 1:39 am    Post subject: Reply with quote
It does have an XY-rated solution -- dominated by <2> and <4>.

Code:
 r24\c18 Skyscraper                      <> 24   r5c1    Remote Pair

 c59\r35 finned  X-Wing                  <> 2    r3c46

 <12+4>  XYZ-Wing r1c5/r1c1+r3c6         <> 4    r1c4
 <12+4>  XYZ-Wing r1c5/r3c6+r5c5         <> 4    r3c5
 <46+2>  XYZ-Wing r8c4/r6c4+r7c6         <> 2    r7c4    maybe extraneous

 +--------------------------------------------------------------+
 |  24    18    6     |  28    124   5     |  3     7     9     |
 |  24    9     5     |  7     6     3     |  1     24    8     |
 |  3     18    7     |  489   129   14    |  456   56    256   |
 |--------------------+--------------------+--------------------|
 |  6     7     24    |  1     5     9     |  8     24    3     |
 |  1     5     8     |  3     24    246   |  7     9     26    |
 |  9     24    3     |  26    7     8     |  456   56    1     |
 |--------------------+--------------------+--------------------|
 |  7     3     249   |  49    8     24    |  56    1     56    |
 |  5     24    124   |  246   3     1246  |  9     8     7     |
 |  8     6     19    |  5     19    7     |  2     3     4     |
 +--------------------------------------------------------------+
 # 45 eliminations remain

 M-Wing 3B (2=4)r1c1 - r1c5 = (4-2)r5c5 = (2)r13c5  =>  r1c4<>2   -or-
 M-Wing 3B (2=4)r5c5 - r1c5 = (4-2)r1c1 = (2)r1c45  =>  r3c5<>2
 -or-
 W-Wing    (4=2)r1c1 - r1c45 = r13c5 - (2=4)r5c5    =>  r1c5<>4
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