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Puzzle 11/05/04: ~ XY+

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Thu May 05, 2011 12:20 am    Post subject: Puzzle 11/05/04: ~ XY+ Reply with quote
FWIW: I've returned to using my rating system.

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

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: Fri May 06, 2011 4:29 pm    Post subject: Reply with quote
A seven-stepper I don't see the need to elaborate unless someone's interested.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Fri May 06, 2011 7:55 pm    Post subject: Reply with quote
Marty R. wrote:
A seven-stepper I don't see the need to elaborate unless someone's interested.

I'd like to know if you encountered a 5-cell XY-Chain and a 4-cell XY-Chain. The presence of two chains in my solver's solution is what prompted me to add the plus (+) to the rating.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Fri May 06, 2011 9:23 pm    Post subject: Reply with quote
Danny, I didn't make a note of the chain lengths. The 1st chain I used set r6c9<>4 and the 2nd one set r3c3<>4. Hope that helps.
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK
PostPosted: Fri May 06, 2011 9:38 pm    Post subject: Reply with quote
I had four steps - with one 4-cell xy-chain...
Code:
xy-wing(69-4) r1c4 ; r1c56<>4, r2c89<>4
kite(4) r4, c5 ; r2c1<>4
w-wing(69)  r1c4, r2c1 ; r2c5<>9
xy-chain (6=4)r1c9 - (4=3)r3c8 - (3=7)r3c6 - (7=6)r3c4 ; r1c4<>6
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Sat May 07, 2011 1:48 am    Post subject: Reply with quote
Marty R. wrote:
Danny, I didn't make a note of the chain lengths. The 1st chain I used set r6c9<>4 and the 2nd one set r3c3<>4. Hope that helps.

Turns out, there's enough alternatives that you may not have needed the 5-cell XY-Chain after all. My solver selected the 5-cell XY-Chain because it thought it was the most "productive". However, that doesn't guarantee that it's absolutely needed. From what I can reconstruct of your solution, two 4-cell XY-Chains were sufficient.

Further proof, that the 5-cell XY-Chain wasn't necessary, is present in Peter's solution. He found a W-Wing, which I forgot to cross-check for being present, and used it to reduce the puzzle's complexity to the point that a 4-cell XY-Chain finished off the puzzle. (Nice find Peter!)

Regards, Danny
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