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Vanhagen Extreme Nov 18

 
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tlanglet



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

PostPosted: Thu Nov 18, 2010 3:25 pm    Post subject: Vanhagen Extreme Nov 18 Reply with quote

Another Vanhegan that seems to have numerous chains.....

Code:

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

Play this puzzle online at the Daily Sudoku site

Quote:
(6=9)r4c5-r7c5=r7c78-(9=8)r8c9-r9c7=(8-5)r5c7=r4c7-(5=6)r4c1; r4c6<>6

(3=2)r3c4-(2=1)r3c7-r9c7=(1-6)r9c8=r7c8-(6=3)r7c6; r2c6<>3

Kraken cell (249)r6c3; r4c2<>9
(2)r6c2-(2=9)r5c3;
||
(4)r6c3-(4=9)r6c8-(9=1)r5c8-r9c8=(1-8)r9c7=r8c9-r56c9=(8-5)r5c7=r4c7-(5=6)r4c1-(6=9)r4c5;
||
(9)r6c3;

AXY-wing -369 vertex (69)r4c5, pincers (36)r5c6 & (39)r7c5 with fin (6)r7c5; r7c6<>3
xy-wing =(6)r7c5-(6=8)r9c5-(8=1)r9c7-(1=2)r3c7-(2=3)r3c4-r5c4=(3)r5c6

Ted
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Marty R.



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

PostPosted: Thu Nov 18, 2010 5:39 pm    Post subject: Reply with quote

I often have trouble with Vanhegan extremes, but this wasn't one of them. I did it a second time because I didn't trust myself.

Quote:
XYZ-Wing (369); r9c5<>6
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 18, 2010 6:27 pm    Post subject: Reply with quote

Marty beat me to it! After basics:
Code:
+-------------------+-------------------+-------------------+
| 2     8     3     | 5     1     9     | 6     7     4     |
| 4     1     7     | 6     238   38    | 29    5     39    |
| 9     5     6     | 23    7     4     | 12    8     13    |
+-------------------+-------------------+-------------------+
| 56    479   8     | 19    69    67    | 1459  3     2     |
| 56    79    29    | 12389 4     3678  | 1589  19    1689  |
| 1     3     249   | 289   2689  5     | 7     49    689   |
+-------------------+-------------------+-------------------+
| 8     2     1     | 7     369   36    | 49    469   5     |
| 7     6     49    | 489   5     1     | 3     2     89    |
| 3     49    5     | 489   689   2     | 189   169   7     |
+-------------------+-------------------+-------------------+
Keith
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peterj



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

PostPosted: Thu Nov 18, 2010 6:36 pm    Post subject: Reply with quote

I missed the xyz-wing - I think the "Extreme" rating sent me looking at chains too early.. (Nice spot, Marty Exclamation )

Here's an ANP that also solves it..
Quote:
ANP(49=6)r7c78 - (6=3)r7c6 - r7c5=r2c5 - (3=9)r2c9 ; r8c9<>9

.. or written as a w-wing (for fun)...
w-wing(39)/als ; (946=3)r7c678 - r7c5=r2c5 - (3=9)r2c9
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Thu Nov 18, 2010 7:33 pm    Post subject: Reply with quote

Using Keith's grid and reviewing Peter's chain:

Code:
+-------------------+-------------------+-------------------+
| 2     8     3     | 5     1     9     | 6     7     4     |
| 4     1     7     | 6     238   38    | 29    5     39    |
| 9     5     6     | 23    7     4     | 12    8     13    |
+-------------------+-------------------+-------------------+
| 56    479   8     | 19    69    67    | 1459  3     2     |
| 56    79    29    | 12389 4     3678  | 1589  19    1689  |
| 1     3     249   | 289   2689  5     | 7     49    689   |
+-------------------+-------------------+-------------------+
| 8     2     1     | 7     369   36    | 49    469   5     |
| 7     6     49    | 489   5     1     | 3     2     89    |
| 3     49    5     | 489   689   2     | 189   169   7     |
+-------------------+-------------------+-------------------+

ANP(49=6)r7c78 - (6=3)r7c6 - r7c5=r2c5 - (3=9)r2c9 ; r8c9<>9

I had a feeling that an alternate perspective existed. Finally, it hit me:

Code:
(9)r7c78 = (9-3)r7c5 = r2c5 - (3=9)r2c9 ; r8c9<>9

Which is the "reverse" of an M-Wing Type 3A.



Yes, Congratulations Marty on finding that solitary XYZ-Wing!
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