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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Sat Sep 16, 2006 9:57 pm Post subject: Counting fairly 


Keith wrote:  Except, in this case ... 
Code:  ++++
 7 23569 569+  238 245+ 248  3458+ 1 46 
 4 235 15+  12378 257+ 6  358+ 9 58= 
 136 356* 8  13 9 14  7 3456* 2 
++++
 5 78 3  6 1 27  248 248 9 
 69 6789 679  4 27 3  1 258 58= 
 2 1 4  9 8 5  6 7 3 
++++
 8 57* 2  17 3 147  9 456* 46 
 1369 369 169  5 246 2489  2348 2348 7 
 369 4 57+  278 267 2789  2358+ 2358 1 
++++ 
The formula is correct. In fact, it's an identity, because there are nine columns and nine rows in the grid. I've marked the "XWing" (r37c28) with asterisks above.
The complement of the XWing lies in columns 3, 5, 7, & 9 (we already have a "5" in columns 1, 4, & 6). So the swordfish (r129c357) is not the entire "fishy complement"  the rest of the complement lies in column 9, and is of order 1.
2 [order of XWing] + (3 + 1) [order of complement] + 3 [# of "5"s already resolved] = 9. dcb 

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keith
Joined: 19 Sep 2005 Posts: 3194 Location: near Detroit, Michigan, USA

Posted: Sat Sep 16, 2006 10:41 pm Post subject: One fish, two fish ... 


David,
I was not disagreeing with the identity. How could I?
What I was observing is that, at the position I posted, there is an easily identifiable Xwing (in R37) and a swordfish in C357. These are not complements (duals) of each other, for the numbers do not add up.
The other point about these dual fishes, is that they make the same eliminations (as I understand it).
These two points can be resolved by recognizing that the strong link in R5 can be added to the Xwing, to make a swordfish in the rows, which has the same eliminations as the swordfish in the columns (mentioned above).
Admittedly, this swordfish on the rows is somewhat degenerate (like me, perhaps), but it is valid.
Perhaps the Xwing has a dual which is some form of (degenerate?) jellyfish (in the columns)? If so, I do not see it.
Another question I have: What is a 1fish? Is it a naked pair (in a row or column)?
May we learn together,
Keith 

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ravel
Joined: 21 Apr 2006 Posts: 536

Posted: Tue Sep 19, 2006 4:09 pm Post subject: Re: One fish, two fish ... 


keith wrote:  Perhaps the Xwing has a dual which is some form of (degenerate?) jellyfish (in the columns)? If so, I do not see it.

As David said, the dual (complement) is the jelly fish in columns 3,5,7,9 and rows 1,2,5,9. It has the swordfish as "subfish".
Quote:  Another question I have: What is a 1fish? Is it a naked pair (in a row or column)?

Maybe i missed something here. A 1fish would be a single. In this case the complement could not lead to an elimination. 

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eddieg
Joined: 12 Jan 2006 Posts: 47 Location: San Diego, CA USA

Posted: Tue Sep 19, 2006 9:24 pm Post subject: 


This was a tought puzzle. Thanks to all that posted hints. 

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