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Puzzle 11/06/30: ~ XY

 
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Thu Jun 30, 2011 4:08 pm    Post subject: Puzzle 11/06/30: ~ XY Reply with quote

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

Play this puzzle online at the Daily Sudoku site
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Fri Jul 01, 2011 3:01 pm    Post subject: Reply with quote

I worked hard on this puzzle and found a couple of weird, messy steps that did not do any significant damage before I found a reasonably clean back breaker...........

almost xy-chain with r2c4(89=3); r78c8<>8
If r2c4=89: (8)r8c7=(8)r2c7-(8=9)r2c4-r5c4=r6c5-(9=8)r6c8;
If r2c4=(3): (3)r2c4-r7c4=r8c5-(3=8)r8c7;

xy-wing (35-8) vertex r3c4; r2c4,r9c6<>8

I would appreciate any suggestion how to combine the two statements for the almost xy-chain.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Fri Jul 01, 2011 3:18 pm    Post subject: Reply with quote

Ted,

Performing a Kraken Cell on r2c4 is a common alternative for your scenario. All you need to do is split your chain at r2c4:

Code:
Kraken Cell r2c4:

read l-to-r:                           ( =9)r2c4-r5c4=r6c5-(9=8)r6c8 -(8)r78c8
read r-to-l: (8)r78c8- (8)r8c7=(8)r2c7-(8= )r2c4
read l-to-r:                           (  3)r2c4-r7c4=r8c5-(3=8)r8c7 -(8)r78c8

You can also perform a 2-String Kite for r2c4<>3, and then use your chain -- which doesn't appear to be an XY-Chain pattern.

Regards, Danny
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Fri Jul 01, 2011 9:18 pm    Post subject: Reply with quote

tlanglet wrote:
I worked hard on this puzzle and found a couple of weird, messy steps that did not do any significant damage before I found a reasonably clean back breaker...........

almost xy-chain with r2c4(89=3); r78c8<>8
If r2c4=89: (8)r8c7=(8)r2c7-(8=9)r2c4-r5c4=r6c5-(9=8)r6c8;
If r2c4=(3): (3)r2c4-r7c4=r8c5-(3=8)r8c7;

xy-wing (35-8) vertex r3c4; r2c4,r9c6<>8

I would appreciate any suggestion how to combine the two statements for the almost xy-chain.

Ted

*Maybe* this'll do it, avoid a net and keep your xy.

(8=3)r8c7-r8c5=r7c4-(3)r2c4=[xy chain that I'm too lazy to notate but lives in the * cells]

Code:
*-----------------------------------------------------------*
 | 589   3     89    | 1589  149   458   | 2     7     6     |
 | 689   7     1     |*389   369   2     |*38    5     4     |
 | 568   2     4     | 358   36    7     | 1     389   89    |
 |-------------------+-------------------+-------------------|
 | 189   68    689   | 4     5     3     | 7     2     189   |
 | 79    5     2     |*79    8     1     | 4     6     3     |
 | 1789  4     3     | 2    *79    6     | 5    *89    189   |
 |-------------------+-------------------+-------------------|
 | 4     18    7     | 138   2     9     | 6     138   5     |
 | 2     9     58    | 6     134   458   |*38    138   7     |
 | 3     168   568   | 1578  17    58    | 9     4     2     |
 *-----------------------------------------------------------*
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Fri Jul 01, 2011 9:49 pm    Post subject: Reply with quote

tlanglet wrote:
almost xy-chain with r2c4(89=3); r78c8<>8
If r2c4=89: (8)r8c7=(8)r2c7-(8=9)r2c4-r5c4=r6c5-(9=8)r6c8;
If r2c4=(3): (3)r2c4-r7c4=r8c5-(3=8)r8c7;
...
I would appreciate any suggestion how to combine the two statements for the almost xy-chain.

I see no clever way to convert the net to a chain. I suppose this does you no good but, in modernized nice-loop notation, it would look like this:

r78c8 -8- r8c7 =8= r2c7 -8- r2c4 {-3- r7c4 =3= r8c5 -3- r8c7 -8- r78c8} -9- r5c4 =9= r6c5 -9- r6c8 -8- r78c8 ==> r78c8<>8
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dejsmith



Joined: 23 Oct 2005
Posts: 42

PostPosted: Fri Jul 01, 2011 10:23 pm    Post subject: Reply with quote

How come you cannot use the Kite in r7/c7 to eliminate the 3 in r2c4? Then why isn't that an XY Chain, starting at r8c7: 83-38-89-97-79-98; & r78c8<>8?

I tried something different using a UR & 2 kites, but did not see the XY Chain. Instead I tried looking for an almost pattern & chose an ANP in r4c3; 89-6. 6 led to a contradiction & 89 solved the puzzle. Was I just lucky & do I have an incorrect understanding of these techniques?

Dave
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sat Jul 02, 2011 4:52 am    Post subject: Reply with quote

Finned X-Wing; r2c4<>3
W-Wing (89), SL 9, c5, flightless with transport; r2c7, r3c4<>8
XY-Wing (385); r1c6, r9c4<>5
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