The Ultimate FISH Guide

Advanced methods and approaches for solving Sudoku puzzles

Postby ronk » Fri Jan 12, 2007 3:37 pm

Obi-Wahn, welcome to this Forum and to this thread.

Obi-Wahn wrote:I'm not sure if you're aware of the locked candidates in r1b2 of Fig. 4G, so r2c5 and r3c5 can be eliminated, too, although that's not part of the fish pattern.

Thanks. Maybe others were aware, but I wasn't. Since the pattern is a composite of a 1-fish and a swordfish, I'll rename it "sashimi mutant jellyfish" and add the useful fin cells as follows:
Code: Select all
 #  #  # |  X  /  X |  /  #  #
 .  .  . |  *  X  * |  /  .  . 
 .  .  . |  *  X  * |  /  .  . 
---------+----------+---------- 
 /  /  / |  .  /  . |  /  .  . 
 X  X  X |  *  X  * |  X  *  *
 X  X  X |  *  X  * |  X  *  *
---------+----------+---------- 
 .  .  . |  .  /  . |  /  .  . 
 .  .  . |  .  /  . |  /  .  . 
 *  *  * |  *  X  * |  X  *  *
 Fig 4G: rccb\rrrb           
 rrcb\cccb transpose       
 sashimi mutant jellyfish

Any one fin cell true will still yield at least one exclusion.

This actual example is r1c57b4/r569b2. I've run this pattern through my program and it came up with two equivalent jellyfish r14c57/r9b256 and r14c7b8/r9c46b6. It's also equivalent with a franken squirmbag c57b134/r23569 or a franken whale c12357b3/r23569b7 along with dozens of other bigger fish, e.g. r1c123b35689/r569c4689b17 (no idea what you would call that).

For non-sashimi (non-degenerate, non-composite) patterns of size N, I think we're interested in equivalents of size N and maybe size N+1. For sashimi, the sheer quantity of sashimi appears overwhelming, so I personally don't plan on pursuing equivalents too.

However, I'm impressed by the patterns you guys can find manually so I'm not sure if you appreciate computerized help.

Within the guidelines stated above, computerized help is welcomed.
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re(2): Franken and equivalent Mutant

Postby Pat » Sun Jan 14, 2007 9:21 am

ronk (2007.Jan.9) wrote:
Code: Select all
 .  *  . |  X  /  X |  .  *  .        .  /  . |  X  *  X |  .  /  .
 .  *  . |  X  /  X |  .  *  .        .  /  . |  X  *  X |  .  /  .
 .  *  . |  X  /  X |  .  *  .        .  /  . |  X  *  X |  .  /  .
---------+----------+----------      ---------+----------+----------
 /  X  / |  X  /  X |  /  X  /        *  X  * |  X  *  X |  *  X  *
 .  *  . |  *  .  * |  .  *  .        .  /  . |  /  .  / |  .  /  .
 /  X  / |  X  /  X |  /  X  /        *  X  * |  X  *  X |  *  X  *
---------+----------+----------      ---------+----------+----------
 .  *  . |  *  .  * |  .  *  .        .  /  . |  /  .  / |  .  /  .
 /  X  / |  X  /  X |  /  X  /        *  X  * |  X  *  X |  *  X  *
 .  *  . |  *  .  * |  .  *  .        .  /  . |  /  .  / |  .  /  .

 Fig 4B1: rrrb\cccc                   Fig 4B1 inverse: cccc\rrrb
 cccb\rrrr transpose                  rrrr\cccb transpose
 franken jellyfish



Equivalent:
Code: Select all
 .  *  . |  .  /  . |  .  *  .        .  /  . |  .  *  . |  .  /  .
 .  *  . |  .  /  . |  .  *  .        .  /  . |  .  *  . |  .  /  .
 .  *  . |  .  /  . |  .  *  .        .  /  . |  .  *  . |  .  /  .
---------+----------+----------      ---------+----------+----------
 /  X  / |  X  /  X |  /  X  /        *  X  * |  X *X  X |  *  X  *
 .  *  . |  *  X  * |  .  *  .        .  /  . |  /  X  / |  .  /  .
 /  X  / |  X  /  X |  /  X  /        *  X  * |  X *X  X |  *  X  *
---------+----------+----------      ---------+----------+----------
 .  *  . |  *  X  * |  .  *  .        .  /  . |  /  X  / |  .  /  .
 /  X  / |  X  /  X |  /  X  /        *  X  * |  X  *  X |  *  X  *
 .  *  . |  *  X  * |  .  *  .        .  /  . |  /  X  / |  .  /  .

 Fig 4B2: rrrc\ccbb                    Fig 4B2 inverse: ccbb\rrrc
 ccbb\rrrc transpose                  rrrc\ccbb transpose
 mutant jellyfish




      beautiful!

      every non-degenerate Franken
      below order 5
      now has an equivalent Mutant
      of same order
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re: 3 equivalent Mutant Jellyfish

Postby Pat » Sun Jan 14, 2007 9:24 am

Obi-Wahn (2007.Jan.12) wrote:
Code: Select all
 /  /  / |  X  /  X |  /  /  /
 .  .  . |  *  X  * |  /  .  . 
 .  .  . |  *  X  * |  /  .  . 
---------+----------+---------- 
 /  /  / |  .  /  . |  /  .  . 
 X  X  X |  *  X  * |  X  *  *
 X  X  X |  *  X  * |  X  *  *
---------+----------+---------- 
 .  .  . |  .  /  . |  /  .  . 
 .  .  . |  .  /  . |  /  .  . 
 *  *  * |  *  X  * |  X  *  *

 Fig 4G: rccb\rrrb
 rrcb\cccb transpose       
 mutant jellyfish


    This example rccb\rrrb
    is
      r1c57b4\r569b2
    I've run this pattern through my program and it came up with two equivalent jellyfish --
      r14c57\r9b256
      r14c7b8\r9c46b6


    nice -- so diagram 4G needs some extra captions?
      rrcc\rbbb
      rrcb\rccb
    (plus: transpose, inverse)
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2-finned Mutant 6th-order

Postby Pat » Sun Jan 14, 2007 9:32 am

ronk (2006.Dec.27) wrote:
    Is this finned leviathan (N=7) for real ?
Code: Select all
 . #1  . | *1  . *1 |  .  .  .
 .  .  1 |  .  .  1 |  .  1  .
*1  .  . |  1 *1  1 |  .  1 *1
---------+----------+----------
 .  .  1 |  . *1  . |  1  . *1
 . *1 *1 | *1  . *1 |  .  .  .
*1  .  1 |  .  .  . |  1  .  .
---------+----------+----------
*1 -1  . |  1 *1  . |  .  1  .
 . #1  . | *1  . *1 | *1  .  .
 .  . #1 | *1  . *1 | *1 *1  .


    finned mutant leviathan r1589c159\r347c46b49
    plus fins r18c2 and r9c3
    implies r7c2<>1

    Is there actually not a smaller fish to make the exclusion r7c2<>1 ?

    i could never find a 7th-order,
    but once you found it -- here's a slight improvement:

      2-finned Mutant 6th-order

      r15c159b8\r347c46b4

      fins = r1c2 + r7c5

      - excludes r7c2
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Postby Obi-Wahn » Sun Jan 14, 2007 7:55 pm

Correct, a Finned Mutant Whale is the smallest fish that excludes r7c2.
r15c159b8/r34c246b4 for example has the fins r7c15:

Code: Select all
 . *1  . | *1  . *1 |  .  .  .
 .  .  1 |  .  .  1 |  .  1  .
*1  .  . |  1 *1  1 |  .  1 *1
---------+----------+----------
 .  .  1 |  . *1  . |  1  . *1
 . *1 *1 | *1  . *1 |  .  .  .
*1  .  1 |  .  .  . |  1  .  .
---------+----------+----------
#1 -1  . | *1 #1  . |  .  1  .
 .  1  . |  1  .  1 |  1  .  .
 .  .  1 |  1  .  1 |  1  1  .

(I think I have to automate the generation of these patterns.)
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Postby tarek » Sun Jan 14, 2007 9:38 pm

The impressive work that you've done Obi-Wahn (most of it on the programmers' forum) will hopefully bring matters clearer to fishermen........

The next updates to the head post should highlight:

1. the FIN as a candidate of the Base Sector(s) that is not a candidate of any of the Cover Sector.
2. Base sectors can share candidates if the shared candidates are trated as fins.
3. Size o fish to include the now popular (whale & leviathan)
4. Definitions of Sector, Line, Box

There is a Swordfish def with examples from mike barker ot be added to the head post.

The latest from ronk was back in Nov 29, anything else that I missed?

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Postby ronk » Sun Jan 14, 2007 10:21 pm

tarek wrote:The next updates to the head post should highlight:
...
3. Size o fish to include the now popular (whale & leviathan)

My leviathan was a mirage. Both Pat and Obi-Wahn identified a smaller whale. But Obi-Wahn posted one here.

There is a Swordfish def with examples from mike barker ot be added to the head post.

The latest from ronk was back in Nov 29, anything else that I missed?

Exemplar catalog updated a little while ago, and I think Mike's swordfish is Fig 3E.
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Postby tarek » Mon Jan 15, 2007 2:47 am

A new update to the head post. An attempt at a mini glossary also.

ronk: I've noticed that some of the exemplars use the sashimi term in the same fish name with another term that describes the fish shape......

The agreement until now was to use sashimi to describe a very specific case of FINNED BASIC fish only, where it replaces the term FINNED altogether. Is this still the case ?

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re: finned Mutant 6th-order

Postby Pat » Mon Jan 15, 2007 12:46 pm

Obi-Wahn (2007.Jan.14) wrote:
    Correct, a Finned Mutant Whale is the smallest fish that excludes r7c2.

    r15c159b8\r34c246b4 for example has the fins r7c15:
Code: Select all
 . *1  . | *1  . *1 |  .  .  .
 .  .  1 |  .  .  1 |  .  1  .
*1  .  . |  1 *1  1 |  .  1 *1
---------+----------+----------
 .  .  1 |  . *1  . |  1  . *1
 . *1 *1 | *1  . *1 |  .  .  .
*1  .  1 |  .  .  . |  1  .  .
---------+----------+----------
#1 -1  . | *1 #1  . |  .  1  .
 .  1  . |  1  .  1 |  1  .  .
 .  .  1 |  1  .  1 |  1  1  .

    I think I have to automate the generation of these patterns.
        this is an improvement over my version,
        as r7c15 is just one fin.


        it seems to me that the greatest fish of interest
        would be of order j_max = 3s/4; usually s = 9
        so
          j_max = 6


      given a definition such as r15c159b8\r34c246b4
      it would be nice indeed to automatically generate the pattern of "/" cells,
      and also the exclusions ("*").

      a 2nd level of automation
      could then match the pattern of "/" against the situation in the puzzle,
      identifying the fin-cells ("#") and whatever exclusions are still available --
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Postby ronk » Mon Jan 15, 2007 1:44 pm

tarek wrote:I've noticed that some of the exemplars use the sashimi term in the same fish name with another term that describes the fish shape......

The agreement until now was to use sashimi to describe a very specific case of FINNED BASIC fish only, where it replaces the term FINNED altogether. Is this still the case ?

I believe so. I started using "sashimi" in lieu of "degenerate" -- or a separate comment to indicate a degenerate pattern -- as explained here. In the exemplar catalog, I've also tried to illustrate as fins all candidate postions that prevent degeneration and still cause an exclusion. This doesn't mean every possible fin cell, but rather only those at the very beginning of a cascading chain.

Consider the following swordfish:
Code: Select all
 X  *  * |  *  X  * |  *  *  *
 /  .  . |  .  /  . |  .  .  .
 /  .  . |  .  /  . |  .  .  .
---------+----------+----------
 /  #  # |  .  /  . |  .  .  .
 /  #  # |  .  /  . |  .  .  .
 /  X  X |  *  X  * |  *  *  *
---------+----------+----------
 X  *  * |  .  /  . |  .  .  .
 X  *  * |  .  /  . |  .  .  .
 X  *  * |  .  /  . |  .  .  .
 Fig 3Y: ccb\rrb
 rrb\ccb transpose
 franken sashimi swordfish

If all the fin cells are false, then all the exclusions shown -- and a few more -- occur due to cascading locked candidates. If any one of the fin cells is true, then exclusions in c2 or c3 can still occur. From another POV, at least one of the fin cells must be true in order to have a "viable" pattern. So the term "sashimi" here seems consistent with prior usage.

However, I should have written "sashimi franken" instead of "franken sashimi."

This seems like an appropriate time to bring attention to the probable deep-sixing of the following two exemplars. Unless someone shows their usefulness, they will be removed in the next version.

Code: Select all
 .  .  . |  *  X  * |  .  .  .        .  .  . |  #  X  # |  .  .  .
 .  .  . |  *  X  * |  .  .  .        .  .  . |  #  X  # |  .  .  .
 .  .  . |  *  X  * |  .  .  .        .  .  . |  #  X  # |  .  .  .
---------+----------+----------      ---------+----------+----------
 #  #  # |  .  /  . |  .  .  .        *  *  * |  .  *  . |  .  .  .
 X  X  X |  *  X  * |  *  *  *        X  X  X |  /  X  / |  /  /  /
 #  #  # |  .  /  . |  .  .  .        *  *  * |  .  *  . |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  /  . |  .  .  .        .  .  . |  .  *  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .        .  .  . |  .  *  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .        .  .  . |  .  *  . |  .  .  .
 Fig 2C: cb\rb                        Fig 2C inverse: rb\cb
 rb\cb transpose                      cb\rb transpose
 franken x-wing (1-fish + 1-fish)

 No combination of fins yields an exclusion, so this pattern should probably be deep-sixed
[Figure based on post by Pat here]

Code: Select all
 .  .  . |  .  /  . |  #  #  X        .  .  . |  .  *  . |  *  *  X
 .  .  . |  .  /  . |  #  #  X        .  .  . |  .  *  . |  *  *  X
 .  .  . |  .  /  . |  #  #  X        .  .  . |  .  *  . |  *  *  X
---------+----------+----------      ---------+----------+----------
 .  .  . |  *  X  * |  .  .  *        .  .  . |  #  X  # |  .  .  /
 .  .  . |  *  X  * |  .  .  *        .  .  . |  #  X  # |  .  .  /
 .  .  . |  *  X  * |  .  .  *        .  .  . |  #  X  # |  .  .  /
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  /  . |  /  /  X        .  .  . |  .  *  . |  *  *  X
 *  *  * |  *  X  * |  X  X *X        /  /  / |  /  X  / |  X  X  /
 .  .  . |  .  /  . |  /  /  X        .  .  . |  .  *  . |  *  *  X
 Fig 3W: cbb\rcb                      Fig 3W inverse: rcb\cbb
 rbb\rcb transpose                    rcb\rbb transpose
 sashimi mutant swordfish

 No combination of fins yields an exclusion, so this pattern should probably be deep-sixed
[Figure based on Pat's post here]
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Re: re: finned Mutant 6th-order

Postby ronk » Mon Jan 15, 2007 3:11 pm

Pat wrote:it seems to me that the greatest fish of interest
would be of order j_max = 3s/4; usually s = 9
so
    j_max = 6

If that conjecture turns out to be valid, why wouldn't a round-up be required, as in 3 * 9 / 4 = 6.75, implying 7 as the max?

Pat wrote:it would be nice indeed to automatically generate the pattern of "/" cells,
and also the exclusions ("*").

a 2nd level of automation
could then match the pattern of "/" against the situation in the puzzle,
identifying the fin-cells ("#") and whatever exclusions are still available

I have mixed feelings about the "automation." For example, with the appearance of Obi-Wahn's solver, it's nice to be able to confirm that we've identified the smallest fish for a given hidden pattern. But simultaneously, my interest in finding exotic fish manually has certainly waned as a result. And I'm even less enthusiastic about documenting new exemplars found by a computer program.
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re: j_max

Postby Pat » Mon Jan 15, 2007 3:27 pm

ronk wrote:
Pat wrote:it seems to me that the greatest fish of interest
would be of order j_max = 3s/4; usually s = 9
so
    j_max = 6

If that conjecture turns out to be valid, why wouldn't a round-up be required, as in 3 * 9 / 4 = 6.75, implying 7 as the max?


    you're right, ronk -- as long as it is mere conjecture, we don't know about the rounding -- what i wrote is part of my conjecture and we'll just have to see if anyone can prove anything here -- obviously i can't!
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re: automation

Postby Pat » Mon Jan 15, 2007 3:31 pm

ronk wrote:I have mixed feelings about the "automation." For example, with the appearance of Obi-Wahn's solver, it's nice to be able to confirm that we've identified the smallest fish for a given hidden pattern. But simultaneously, my interest in finding exotic fish manually has certainly waned as a result. And I'm even less enthusiastic about documenting new exemplars found by a computer program.

    i'm hoping that the software which finds new cases
    will also automatically produce the relevant diagrams,
    minimizing the effort of documentation.
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Re: re: finned Mutant 6th-order

Postby Obi-Wahn » Tue Jan 16, 2007 3:08 am

ronk wrote:I have mixed feelings about the "automation." For example, with the appearance of Obi-Wahn's solver, it's nice to be able to confirm that we've identified the smallest fish for a given hidden pattern. But simultaneously, my interest in finding exotic fish manually has certainly waned as a result. And I'm even less enthusiastic about documenting new exemplars found by a computer program.

Sorry, I didn't have the intention to spoil the fun for you. With "automation" I meant the generation of the diagrams showing vertices, fins and exclusions because I had to edit the post twice missing some cells in the first try.
I know perfectly well what you are feeling. It's like discovering a walkthrough for a new adventure game. Only to know that it is there and you could easily look up the solution totally kills your motivation to spend hours to find the hidden secrets yourself.
That's why I asked if computerized help would be appreciated. Mainly I was curious if maybe all single digit template eliminations can be explained by some kind of fish pattern and since I don't have the ability to spot all these patterns manually it was only natural for me to teach my electronic helper to systematically find them.
On the other hand I would have felt like cheating if I posted solutions to questions here without telling that it was found by my computer program. Besides, without rkral's help on the programmer's forum I wouldn't have been able to find out what I had been missing. So that was the reason why I wrote about my algorithm there in the first place.
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Postby tarek » Tue Jan 16, 2007 4:39 pm

ronk wrote:I started using "sashimi" in lieu of "degenerate" -- or a separate comment to indicate a degenerate pattern -- as explained here. In the exemplar catalog, I've also tried to illustrate as fins all candidate postions that prevent degeneration and still cause an exclusion.


Sashimi returns AGAIN with a vengence.........

This MAY cause confusion when naming & referring to fish.......

I propose to back from my initial position of limiting it to finned basic fish & leave it as a sub-category of Finned fish........

so if someone is keen on using the optional description of sashimi to refer to a sashimi variation (wherever) my suggestion is to use the following term: Sashimi Finned Fish ....... non Sashimi variations could be then referred to as non-Sashimi or Simple......

examples of complete long names of fish names:
Finless basic x-wing (your normal everyday x-wing)
Sashimi Finned basic swordfish
Simple finned mutant jellyfish

The terms above all of a sudden make things a bit clearer, I hope everybody agrees to this so that we could get rid of this curse.

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