The Ultimate FISH Guide

Advanced methods and approaches for solving Sudoku puzzles

Postby ronk » Thu Jan 15, 2009 1:02 am

daj95376 wrote:IMO: There are (at least) two ways to view Fish.

1) As NxN Base Sectors by Cover Sectors with fin cells possible in the Base Sectors. The set of all fin cells is called the fin. I use this approach.
...
Fin Cell: A candidate cell that exist in more Base Sectors than Cover Sectors.
...
Fish Elimination: A candidate cell that exists in more Cover sectors than Base sectors, and is a peer to all fin cells.

Nice definitions. However, with N Base Sectors and equal N Cover Sectors and apparently no Fin Sectors, how exactly do you then obtain an unequal number of Base and Cover Sectors for the elimination of a finned fish.

A theoretical or actual example for a smallish fish would be appreciated.
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Postby daj95376 » Thu Jan 15, 2009 5:02 am

ronk wrote:
daj95376 wrote:IMO: There are (at least) two ways to view Fish.

1) As NxN Base Sectors by Cover Sectors with fin cells possible in the Base Sectors. The set of all fin cells is called the fin. I use this approach.
...
Fin Cell: A candidate cell that exist in more Base Sectors than Cover Sectors.
...
Fish Elimination: A candidate cell that exists in more Cover sectors than Base sectors, and is a peer to all fin cells.

Nice definitions. However, with N Base Sectors and equal N Cover Sectors and apparently no Fin Sectors, how exactly do you then obtain an unequal number of Base and Cover Sectors for the elimination of a finned fish.

A theoretical or actual example for a smallish fish would be appreciated.

Thanks Ron!!!

Obi-Wahn had a great idea in his thread here. He just went too far with the concept in my opinion. I posted a reply explaining how his arithmetic could be easily interpreted in an NxN Fish. That reply contains an example that is processed from start to finish.

Note: An exemplar grid for an NxN Fish can be created from the grid in step (1) of my reply.

I'll be glad to answer any questions you have.
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Postby ronk » Thu Jan 15, 2009 5:27 am

daj95376 wrote:Obi-Wahn had a great idea in his thread here. He just went too far with the concept in my opinion. I posted a reply explaining how his arithmetic could be easily interpreted in an NxN Fish.

In that post ...
you wrote:3c) Any candidate cell with a plus value can be eliminated -- provided it's seen by all fin cells.

In order to see an elimination cell, fin cells must share a sector (unit) with the elimination cell, right? Just because you don't call it a Fin Sector doesn't mean a fin sector isn't being used.

Besides, that argument is meaningless when eliminations are presented without the corresponding counts.
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Postby daj95376 » Thu Jan 15, 2009 7:30 am

ronk wrote:In that post ...
you wrote:3c) Any candidate cell with a plus value can be eliminated -- provided it's seen by all fin cells.

You quoted me out of context.

3a) Using the results from step (2), examine the candidate grid from your PM.
3b) Any candidate cell with a minus value must be empty or treated as a fin cell.
3c) Any candidate cell with a plus value can be eliminated -- provided it's seen by all fin cells.

ronk wrote:In order to see an elimination cell, fin cells must share a sector (unit) with the elimination cell, right? Just because you don't call it a Fin Sector doesn't mean a fin sector isn't being used.

Besides, that argument is meaningless when eliminations are presented without the corresponding counts.

Here's an entry from your exemplars table. Yes, the elimination [r5c7] does share a sector with each fin cell. However, the fin cells are not in the same sector. I don't need to go looking for Fin Sectors to make my approach work. The fin cells stand on their own merit.

With Obi-Wahn's approach, I believe that cell [r6c7] will have to be in two Fin Sectors, or else you'll need three Fin Sectors. Also, in mutant fish where two Base Sectors and no Cover Sectors intersect at a fin cell in my approach, then Obi-Wahn's approach would require that a Fin Sector be used multiple times to neutralize my fin cell. Yuck!

Code: Select all
 *  *  X |  .  .  . |  .  *  .
 X *X  / |  /  /  / |  #  X  /
 *  *  X |  .  .  . |  .  *  .
---------+----------+----------
 .  *  / |  .  .  . |  .  *  .
 *  *  X |  *  *  * | **  *  *
 /  X  / |  /  /  / |  #  X  #
---------+----------+----------
 .  *  / |  .  .  . |  .  *  .
 /  X  / |  /  /  / |  #  X  /
 .  *  / |  .  .  . |  .  *  .
 Fig 4Ti: rrrc\rccb
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Postby ronk » Thu Jan 15, 2009 8:41 am

daj95376 wrote:Here's an entry from your exemplars table. Yes, the elimination [r5c7] does share a sector with each fin cell. However, the fin cells are not in the same sector.

Yes, two fin sectors are required for that exemplar.

day95376 wrote:I don't need to go looking for Fin Sectors to make my approach work. The fin cells stand on their own merit.

I think you mean your solver doesn't need to go looking for fin sectors. I'm presenting an approach that human solvers can understand. I don't know a single person that wants to interpret the base/cover counts for 81 cells. Therefore, I see no useful purpose in hanging one's hat on an approach that depends on such counting.

daj95376 wrote:With Obi-Wahn's approach, I believe that cell [r6c7] will have to be in two Fin Sectors, or else you'll need three Fin Sectors. Also, in mutant fish where two Base Sectors and no Cover Sectors intersect at a fin cell in my approach, then Obi-Wahn's approach would require that a Fin Sector be used multiple times to neutralize my fin cell. Yuck!]

I don't use Obi-Wahn's approach, and I have no desire to defend an approach that I don't use.

This is at least the second time we've flogged this dead horse, and I think it's time to give it a rest.
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Postby daj95376 » Tue Feb 17, 2009 4:09 am

I continue to be perplexed by the use of Sashimi. The closest I have in my notes to a description is the following.

Code: Select all
ronk:

take the fin(s) out:
1. if you have a     viable basic fish of the original size -------> Finned  Fish
2. if you have a non-viable basic fish of the original size -------> Sashimi Fish

However, let's look at an example.

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

Code: Select all
 after basics
 *--------------------------------------------------------------------*
 | 24789  1      2489   | 5      6      248    | 478    3      478    |
 | 6      47     48     | 1      9      3      | 478    2      5      |
 | 3      5      248    | 48     248    7      | 6      9      1      |
 |----------------------+----------------------+----------------------|
 | 5      8      7      | 2      1      49     | 49     6      3      |
 | 49     3      6      | 49     7      5      | 1      8      2      |
 | 249    249    1      | 68     3      68     | 5      7      49     |
 |----------------------+----------------------+----------------------|
 | 2789   279    5      | 3      28     1      | 789    4      6      |
 | 1      6      3      | 7      48     489    | 2      5      89     |
 | 24789  2479   2489   | 689    5      2689   | 3      1      789    |
 *--------------------------------------------------------------------*

Code: Select all
 candidate grid for <2>
 +-----------------------------------+
 |  2  .  2  |  .  .  2  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  2  .  |
 |  .  .  2  |  .  2  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  2  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  2  |
 |  2  2  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  2  2  .  |  .  2  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  2  .  .  |
 |  2  2  2  |  .  .  2  |  .  .  .  |
 +-----------------------------------+

Code: Select all
 non-degenerate X-Wing r37\c35
 +-----------------------------------+
 |  .  .  *  |  .  *  .  |  .  .  .  |
 |  .  .  *  |  .  *  .  |  .  .  .  |
 |  /  /  X  |  /  X  /  |  /  /  /  |
 |-----------+-----------+-----------|
 |  .  .  *  |  .  *  .  |  .  .  .  |
 |  .  .  *  |  .  *  .  |  .  .  .  |
 |  .  .  *  |  .  *  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  /  /  X  |  /  X  /  |  /  /  /  |
 |  .  .  *  |  .  *  .  |  .  .  .  |
 |  .  .  *  |  .  *  .  |  .  .  .  |
 +-----------------------------------+

Code: Select all
 after overlaying candidate grid
 Sashimi X-Wing r37\c35 w/fins [r7c12] => [r9c3]<>X
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  /  /  X  |  /  X  /  |  /  /  /  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  #  #  ~  |  /  X  /  |  /  /  /  |
 |  .  .  .  |  .  .  .  |  .  .  .  |
 |  .  . **  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

In this case, Sashimi only applies after overlaying the candidate grid on top of a non-degenerate unfinned fish.

Now, let's look at another example for this same elimination.

Code: Select all
 degenerate 2-Fish c6b1\r19
 +-----------------------------------+
 |  X  X  X  |  *  *  X  |  *  *  *  |
 |  /  /  /  |  .  .  /  |  .  .  .  |
 |  /  /  /  |  .  .  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  *  *  *  |  *  *  X  |  *  *  *  |
 +-----------------------------------+

Code: Select all
 after overlaying candidate grid
 Sashimi 2-Fish c6b1\r19 w/fin [r3c3] => [r9c3]<>X
 +-----------------------------------+
 |  X  ~  X  |  .  .  X  |  .  .  .  |
 |  /  /  /  |  .  .  /  |  .  .  .  |
 |  /  /  #  |  .  .  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  . **  |  .  .  X  |  .  .  .  |
 +-----------------------------------+

In this case, the unfinned fish is degenerate and Sashimi applies to the resulting overlay.

At this point, degenerate/non-degenerate seems to be a property of the unfinned fish, and Sashimi seems to follow from overlaying the candidate grid upon the unfinned fish.

[Edit: changed character used for empty vertex cell in overlay grid.]
Last edited by daj95376 on Tue Feb 17, 2009 2:39 am, edited 2 times in total.
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Postby tarek » Tue Feb 17, 2009 6:01 am

daj95376 wrote:I continue to be perplexed by the use of Sashimi.
This is not surprising knowing that we agreed to disagree about its usage IIRC.

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Postby ronk » Tue Feb 17, 2009 7:04 am

daj95376 wrote:At this point, degenerate/non-degenerate seems to be a property of the unfinned fish, and Sashimi seems to follow from overlaying the candidate grid upon the unfinned fish.

Sort of, if I'm understanding what you're saying. Although I hate to use the term exemplar for this ...

If the "exemplar" is sashimi, then the "resultant overlay" must be sashimi. If the exemplar is non-sashimi, the "resultant overlay" may be sashimi.

tarek wrote:
daj95376 wrote:I continue to be perplexed by the use of Sashimi.
This is not surprising knowing that we agreed to disagree about its usage IIRC.

It doesn't seem like daj is perplexed because of the sashimi versus sashimi finned disagreement.
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Postby tarek » Tue Feb 17, 2009 7:26 am

ronk wrote:
tarek wrote:
daj95376 wrote:I continue to be perplexed by the use of Sashimi.
This is not surprising knowing that we agreed to disagree about its usage IIRC.

It doesn't seem like daj is perplexed because of the sashimi versus sashimi finned disagreement.
You're right. After re-reading what daj has written: It seems that it is an attempt to describe Sashimi from an inside to outside perspective. The current definitions describe it in from an outside to inside perspective. (Re-reading what I just wrote sounds funny:D )

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Postby StrmCkr » Tue Feb 17, 2009 8:07 am

removed
Last edited by StrmCkr on Wed Jun 26, 2013 6:52 am, edited 3 times in total.
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Postby ronk » Tue Feb 17, 2009 10:05 am

StrmCkr wrote:
Code: Select all
 finned xwing
 +-----------------------------------+
 |  *  *  #  |  .  .  X  |  .  .  .  |
 |  /  /  #  |  .  .  /  |  .  .  .  |
 |  /  /  X  |  .  .  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  .  |  .  .  /  |  .  .  .  |
 |  .  .  X  |  .  .  X  |  .  .  .  |
 +-----------------------------------+

Where is the strong link that includes r9c3? And with a strong link (ER) in b1, where is the double cover that causes eliminations in b1?
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Postby StrmCkr » Tue Feb 17, 2009 10:31 am

removed
Last edited by StrmCkr on Wed Jun 26, 2013 6:52 am, edited 2 times in total.
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Postby ronk » Tue Feb 17, 2009 10:10 pm

StrmCkr wrote:2 finned x-wing
Code: Select all
 +-----------------------------------+
 |  *  *  X  |  .  .  X  |  .  .  .  |
 |  /  /  #  |  .  .  /  |  .  .  .  |
 |  /  /  #  |  .  .  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  /  |  .  .  /  |  .  .  .  |
 |  .  .  /  |  .  .  /  |  .  .  .  |
 |  .  .  /  |  .  .  /  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  /  |  .  .  /  |  .  .  .  |
 |  .  .  /  |  .  .  /  |  .  .  .  |
 |  .  .  X  |  .  .  X  |  .  .  .  |
 +-----------------------------------+


remove the x you get sashimi.
remove a # you still have a finned wing.
remove a x+# you have a skyscraper or kyte(in some cases)

And an empty rectangle pattern is required in b1 because ....:?:
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Postby daj95376 » Wed Feb 18, 2009 12:03 am

ronk wrote:If the "exemplar" is sashimi, then the "resultant overlay" must be sashimi. If the exemplar is non-sashimi, the "resultant overlay" may be sashimi.

I think we have the same understanding ... just a slightly different choice of words. In order not to use Sashimi in the context of the exemplar and the resultant overlay, I returned to using degenerate/degenerative for the exemplar and reserving Sashimi for the resultant overlay. This way, there's (hopefully) no question as to what I'm describing.

Tarek: I'm glad that you went back and reread what I had to say. I hope you found it acceptable. As for Sashimi vs. Sashimi finned, I don't think anything I said above influences that discussion. It's still a matter of personal interpretation.
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Postby StrmCkr » Wed Feb 18, 2009 2:05 am

removed
Last edited by StrmCkr on Wed Jun 26, 2013 6:53 am, edited 1 time in total.
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