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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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 Posted: Sat Sep 16, 2006 9:57 pm Post subject: Counting fairly |
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| 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 "X-Wing" (r37c28) with asterisks above.
The complement of the X-Wing 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 X-Wing] + (3 + 1) [order of complement] + 3 [# of "5"s already resolved] = 9. dcb |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Sep 16, 2006 10:41 pm Post subject: One fish, two fish ... |
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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 X-wing (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 X-wing, 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 X-wing 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 1-fish? 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
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| Posted: Tue Sep 19, 2006 4:09 pm Post subject: Re: One fish, two fish ... |
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| keith wrote: | Perhaps the X-wing has a dual which is some form of (degenerate?) jellyfish (in the columns)? If so, I do not see it.
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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 1-fish? Is it a naked pair (in a row or column)?
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Maybe i missed something here. A 1-fish 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
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| Posted: Tue Sep 19, 2006 9:24 pm Post subject: |
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| This was a tought puzzle. Thanks to all that posted hints. |
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