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September 12 Very hard
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David Bryant



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

PostPosted: Sat Sep 16, 2006 9:57 pm    Post subject: Counting fairly Reply with quote

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: 3175
Location: near Detroit, Michigan, USA

PostPosted: Sat Sep 16, 2006 10:41 pm    Post subject: One fish, two fish ... Reply with quote

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

PostPosted: Tue Sep 19, 2006 4:09 pm    Post subject: Re: One fish, two fish ... Reply with quote

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.

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)?

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

PostPosted: Tue Sep 19, 2006 9:24 pm    Post subject: Reply with quote

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