The Ultimate FISH Guide

Advanced methods and approaches for solving Sudoku puzzles

Postby ronk » Wed Dec 13, 2006 8:40 pm

tarek and Mike Barker,

I'm thinking we should start a separate thread just for Kraken fish examples. tarek, if you would rather they be included here ... I'll agree to that. Mike Barker, since you named the "Kraken" you have first dibs on starting it. If you defer, I will start one.
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Postby Mike Barker » Fri Dec 15, 2006 5:51 am

Here's a shot at a description for Frankenfish. Corrections are always appreciated.

Frankenfish came about as a result of studies of larger fish (whales, etc) started by vidarino here. The conclusion of this study was that if two rows or columns of a fish share the same band or stack, then elimination with bigger fins are possible than could otherwise occur. In the following example, if the two rightmost columns were in separate stacks the elimination could not occur. An elimination is possible because the fish's "big fin" which is located in a single box. This is characteristic of Frankenfish: larger fins which are located in one or more boxes. Recognition of a Frankenfish allows for an elimination with a smaller fish than would otherwise be possible. As a result the largest fish currently identified is a Mutant Squirmbag.
Code: Select all
Finned Franken Swordfish: ccc/rrbf
. . . | . / . | X X .
. . . | . # . | X X *
. . . | . / . | X X .
------+-------+------
. . . | . / . | / / .
. . . | . X . | X X .
. . . | . / . | / / .
------+-------+------
. . . | . / . | / / .
. . . | . / . | / / .
. . . | . X . | X X .

If certain cells of the fish do not contain the fish digit then more eliminations are possible. This led to Havard's discovery of the Frankenfish. Rkral demonstrated an even earlier version of this fish. In the following example of a Finless Franken Swordfish, eliminations can occur in two rows and one box. This is different from a basic swordfish where eliminations occur in three rows if the fish is defined by columns and three columns if defined by three rows. Franken fish eliminations occur because the fish digits in the "n" columns (rows) of the fish can also be contained in (covered by) a total of "n" rows and/or boxes (columns and/or boxes). This is the concept of constraint subsets which is further described in the Mutant Fish post.
Code: Select all
Finless Franken Swordfish: ccc/rrb
. . . | . / . | X X *
. . . | . / . | X X *
. . . | . / . | X X *
------+-------+------ 
. . . | . / . | / / .
* * * | * X * | X X *
. . . | . / . | / / .
------+-------+------
. . . | . / . | / / .
* * * | * X * | X X *
. . . | . / . | / / .

Fish with elimination in more than one box are possible resulting in the "skinny" jellyfish in this example:
Code: Select all
Finless Franken Jellyfish: cccc/rrbb
. . . | * X X | X X *
. . . | * X X | X X *
. . . | * X X | X X *
------+-------+-------
. . . | . / / | / / .
* * * | * X X | X X *
. . . | . / / | / / . 
------+-------+-------
. . . | . / / | / / .
. . . | . / / | / / .
* * * | * X X | X X *

There are two other types of finned Franken Swordfish, where the second is also an empty rectangle.
Code: Select all
Finned Franken Swordfish: ccc/rrbf
. . . | . / . | X X .
. . . | . / . | X X .
. . . | . / . | X X .
------+-------+------
. . . | . # . | / / .
. . . | * X * | X X .
. . . | . # . | / / .
------+-------+------
. . . | . / . | / / .
. . . | . / . | / / .
. . . | . X . | X X .

Finned Franken Swordfish: ccc/rrbf
. . . | . / . | X X .
. . . | . / . | X X .
. . . | . / . | X X .
------+-------+------
. . . | . / . | / / .
. . . | . X . | X X .
. . . | . / . | / / .
------+-------+------
. . . | . / . | # # .
. . . | . / . | # # .
. . . | . X . | X X *

Originally Franken Fish were true fish defined by "n" rows or "n" columns. The definition has been expanded to include a form of Mutant Fish where the fish is defined by a total of "n" rows and/or boxes or a total of "n" columns and boxes. For example:
Code: Select all
Finless Franken Swordfish: rrb/ccc
. . . | . * . | X X /
. . . | . * . | X X /
. . . | . * . | X X /
------+-------+------
. . . | . * . | * * .
/ / / | / X / | X X /
. . . | . * . | * * .
------+-------+------
. . . | . * . | * * .
/ / / | / X / | X X /
. . . | . * . | * * .

Exemplars of Franken X-wings (equivalent to locked candidates) and Franken Jellyfish are found in the first post of this thread. If only true fish are considered, then Franken Squirmbags can be found which do not have smaller fish equivalents. These do have smaller mutant equivalents.
Last edited by Mike Barker on Fri Dec 22, 2006 10:16 pm, edited 2 times in total.
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re: ccc bb (finless) Franken Swordfish

Postby Pat » Fri Dec 15, 2006 10:07 am

Mike Barker wrote:
Fish with elimination in more than one box are possible,
resulting in the "skinny" Swordfish in this example:

    (finless) Franken Swordfish
    ccc\rbb
Code: Select all
 . . . | * X * | X X *
 . . . | * X * | X X *
 . . . | * X * | X X *
-------+-------+-------
 . . . | . / . | / / .
 * * * | * X * | X X *
 . . . | . / . | / / .
-------+-------+-------
 . . . | . / . | / / .
 . . . | . / . | / / .
 . . . | . / . | / / .



in a single step, it excludes much of what would otherwise take 3 steps of box-line interaction --
  1. box9 to c9
  2. box6 to r5
  3. c5 to box2
-- but the box-line interactions do give 3 more exclusions --
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Re: re: ccc bb (finless) Franken Swordfish

Postby ronk » Fri Dec 15, 2006 2:09 pm

Pat wrote:
    (finless) Franken Swordfish
    ccc\rbb
in a single step, it excludes much of what would otherwise take 3 steps of box-line interaction --
  1. box9 to c9
  2. box6 to r5
  3. c5 to box2
-- but the box-line interactions do give 3 more exclusions --

If one is going to use a degenerative pattern to do what box-line interactions can do, then one might as well bring on the additional power ... er, fishpower ... of the Mighty Mutant Jellyfish.:)
Code: Select all
 . . . | * X * | X X  *
 . . . | * X * | X X  *
 . . . | * X * | X X  *
-------+-------+--------
 . . . | . / . | / /  *
 * * * | * X * | X X *X
 . . . | . / . | / /  *
-------+-------+--------
 . . . | . / . | / /  X
 . . . | . / . | / /  X
 . . . | . / . | / /  X
 mutant jellyfish cccb\rcbb

Constraints added are b9\c9.

BTW I see no 3rd additional exclusion beyond r4c9 and r6c9.
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Postby Mike Barker » Sat Dec 16, 2006 2:03 am

Tough crowd although after poking fun at degenerate forms myself, I guess I deserved a Mighty Mutant Jellyfish:) . How about this Franken Jellyfish instead? Same idea, just bigger!
Code: Select all
. . . | * X X | X X *
. . . | * X X | X X *
. . . | * X X | X X *
------+-------+-------
. . . | . / / | / / .
* * * | * X X | X X *
. . . | . / / | / / . 
------+-------+-------
. . . | . / / | / / .
. . . | . / / | / / .
* * * | * X X | X X *

Also, the third elimination in the swordfish is r5c5 from the b6/r5 locked candidates which requires the locked candidate steps to be taken in series, not simultaneously.
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Postby tarek » Sun Dec 17, 2006 2:08 am

Apologies for a late reply but I was away for the past week........

I see that the kraken fish thread has started ..... I think it is a good idea...

I'm a bit concerned about using these large fish to represent multiple smaller fish........

It is the same as using 2 sets of naked doubles as one big naked quad................

if a player is going to sopt them, I'm sure the simpler would be spotted first.......

If I'm going for the single step solution then that is a different issue

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ccb rb (finless) Franken Swordfish

Postby Pat » Tue Dec 19, 2006 1:20 pm

the Frankenfish definition allows Boxes in the "base" and/or the "cover"
so i thought i'd try for the extreme case of and --
      (finless) Franken Swordfish
      ccb\rrb
Code: Select all
 . . . | . . . | / . /
 . . . | . . . | / . /
 . . . | . . . | / . /
-------+-------+-------
 * * * | X X X | X * X
 . . . | / / / | / . /
 * * * | X X X | X * X
-------+-------+-------
 . . . | . . . | X * X
 . . . | . . . | X * X
 . . . | . . . | X * X



      -- valid but not interesting -- one more addition to our growing list of "degenerate" cases --
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re: Franken Squirmbags

Postby Pat » Tue Dec 19, 2006 2:58 pm

Mike Barker (2006.Dec.15) wrote:If only true fish are considered,
then Franken Squirmbags can be found which do not have smaller fish equivalents.
These do have smaller Mutant equivalents.


i expect any Franken Squirmbag is complemented by a Franken Jellyfish (or smaller)
    i admit i don't know what you mean by true fish
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example - finned Franken Jellyfish

Postby Pat » Tue Dec 19, 2006 3:14 pm


        finned Franken Jellyfish
        cccc\rrbb
Nick70 (2005.Nov.24) wrote:The following example requires application of this technique [ finned Franken Jellyfish ] a couple of times,
and nothing else more advanced than locked candidates:

- - - - - -[ 19 clues ]

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




[ edit: i've just noticed that Ocean (2006.Oct.29) had already posted this above ( the very first page of the present Topic ) as a finned Mutant Jellyfish bbbb\rrcc -- which is true, it is also a valid example of a Mutant ]


we do need more finless examples

~ Pat
Last edited by Pat on Thu Dec 21, 2006 1:50 pm, edited 1 time in total.
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Re: ccb rb (finless) Franken Swordfish

Postby ronk » Tue Dec 19, 2006 5:02 pm

Pat wrote:
      (finless) Franken Swordfish
      ccb\rrb
Code: Select all
 . . . | . . . | / . /
 . . . | . . . | / . /
 . . . | . . . | / . /
-------+-------+-------
 * * * | X X X | X * X
 . . . | / / / | / . /
 * * * | X X X | X * X
-------+-------+-------
 . . . | . . . | X * X
 . . . | . . . | X * X
 . . . | . . . | X * X


      -- valid but not interesting -- one more addition to our growing list of "degenerate" cases --

Pat, thanks for the newbie. However, a smaller equivalent degenerate fish -- "equivalent" meaning it uses the same empty cells yielding the identical exclusions -- is this franken x-wing.
Code: Select all
 .  .  . |  *  X  * |  .  .  .        .  .  . |  /  X  / |  .  .  .
 .  .  . |  *  X  * |  .  .  .        .  .  . |  /  X  / |  .  .  .
 .  .  . |  *  X  * |  .  .  .        .  .  . |  /  X  / |  .  .  .
---------+----------+----------      ---------+----------+----------
 /  /  / |  .  /  . |  .  .  .        *  *  * |  .  *  . |  .  .  .
 X  X  X |  *  X  * |  *  *  *        X  X  X |  /  X  / |  /  /  /
 /  /  / |  .  /  . |  .  .  .        *  *  * |  .  *  . |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  /  . |  .  .  .        .  .  . |  .  *  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .        .  .  . |  .  *  . |  .  .  .
 .  .  . |  .  /  . |  .  .  .        .  .  . |  .  *  . |  .  .  .
 franken x-wing cb\rb                 inverse franken x-wing rb\cb
 rb\cb transpose                      cb\rb transpose
 degenerate franken x-wing
[edit: As Pat pointed out, r5c5<>X was incorrect in both grids]

It's interesting that the [edit ...] inverse is identical to the transpose for the permutation shown.

As for other degenerates, I'll add this "smallest equivalent" to the library of exemplars for now, but degenerates may not survive an expected pruning effort later.

I see you used the parenthesized "(finless)" to describe "(finless) swordfish." You and I may be the only ones doing so. A word of explanation is in order. "Franken fish" is the only fish that was finned at the time it was named. The "unfinned" adjective is expected to be omitted eventually, as it's just unnatural and awkward when it's the only exception. The "(unfinned)" eases the transition while indicating the expected future omission.
Last edited by ronk on Thu Dec 21, 2006 12:04 pm, edited 1 time in total.
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Postby Mike Barker » Tue Dec 19, 2006 7:49 pm

To me a "true" fish is one with the base set is "n" rows or "n" columns. Claudiarabia's Frauke has some nice examples of finless fish:
Code: Select all
Column Swordfish: r47c2|r27c4|r24c7 => r72c5<>6
+-------------------+--------------------+-------------------+
|   1   248    247  |    3     56   248  |    9    56   478  |
| 239     5   2349  | 2689* 289-6     7  | 3468*    1   348  |
| 379   348      6  |   59    189  1489  |  358    78     2  |
+-------------------+--------------------+-------------------+
|   8   126*  1259  |    4     57   129  |  126*    3   179  |
|  56   124   1249  |   57      3  1289  | 1248    67  1489  |
| 239     7  12349  |  289   1289     6  | 1248   289     5  |
+-------------------+--------------------+-------------------+
|   4  1236*  1235  |  268* 289-6  2389  |    7  2589  1389  |
|  56     9    237  |    1   2678   238  | 2358     4    38  |
| 237   123      8  |  279      4     5  |  123    29     6  |
+-------------------+--------------------+-------------------+

Column Jellyfish: r269c1|r2679c4|r267c5|r679c8 => r2c3<>2,r6c7<>2,r9c27<>2,r7c236<>2
+--------------------+--------------------+--------------------+
|   1    248    247  |    3    56     24  |     9    56   478  |
| 239*     5  349-2  | 2689*  289*     7  |  3468     1   348  |
| 379    348      6  |   59   189    149  |   358    78     2  |
+--------------------+--------------------+--------------------+
|   8    126   1259  |    4    57    129  |   126     3   179  |
|  56    124   1249  |   57     3   1289  |  1248    67  1489  |
| 239*     7   1349  |  289* 1289*     6  | 148-2   289*    5  |
+--------------------+--------------------+--------------------+
|   4  136-2  135-2  |  268*  289* 389-2  |     7  2589* 1389  |
|  56      9    237  |    1    67    238  |  2358     4    38  |
| 237*  13-2      8  |  279*    4      5  |  13-2    29*    6  |
+--------------------+--------------------+--------------------+
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re(2): ccb rb (finless) Franken Swordfish

Postby Pat » Thu Dec 21, 2006 2:59 pm

ronk wrote:
Pat wrote:
      (finless) Franken Swordfish
      ccb\rrb
Code: Select all
 . . . | . . . | / . /
 . . . | . . . | / . /
 . . . | . . . | / . /
-------+-------+-------
 * * * | X X X | X * X
 . . . | / / / | / . /
 * * * | X X X | X * X
-------+-------+-------
 . . . | . . . | X * X
 . . . | . . . | X * X
 . . . | . . . | X * X


      -- valid but not interesting -- one more addition to our growing list of "degenerate" cases --


a smaller equivalent fish -- itself "degenerate" too -- is this Franken X-wing --

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

 franken x-wing cb\rb                 inverse franken x-wing rb\cb
 rb\cb transpose                      cb\rb transpose

            degenerate franken x-wing

ronk, many thanks for pointing out the smaller fish which i managed to miss.


ronk wrote:It's interesting that the "original" pattern -- the leftmost -- and its inverse are both cannibalistic.

my nit-picking of the day:
the Franken X-wing does not exclude r5c5
-- that extra exclusion only occurs when we forget about the X-wing
and use box-line interactions instead.


ronk wrote:I'll add this "smallest equivalent" to the library of exemplars for now,
but degenerates may not survive an expected pruning effort later.

i hope we can retain "degenerates" in the Ultimate "Fish" Catalogue
-- if we prune them away, we'll be re-discovering them a few weeks later, repeating these discussions --
    for the Franken Swordfish,
    it seems there are several "degenerate" cases
    and only one useful (non-degenerate) case ?
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re: we do need more finless examples

Postby Pat » Thu Dec 21, 2006 3:43 pm

Mike Barker wrote:
Pat wrote:we do need more finless examples


claudiarabia's "Frauke" has some nice examples of finless fish

yes it does - thanks.

i should've been more specific -
we need more examples of
finless Franken/Mutant Swordfish/Jellyfish.

~ Pat
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Re: re(2): ccb rb (finless) Franken Swordfish

Postby ronk » Thu Dec 21, 2006 3:55 pm

Pat wrote:
ronk wrote:It's interesting that the "original" pattern -- the leftmost -- and its inverse are both cannibalistic.

my nit-picking of the day:
the Franken X-wing does not exclude r5c5
-- that extra exclusion only occurs when we forget about the X-wing
and use box-line interactions instead.

Thanks, you are correct, and I'll edit my prior post. That both the original and its inverse were cannibalistic was a bit disconcerting, as that seemingly was the first such instance.

ronk wrote:I'll add this "smallest equivalent" to the library of exemplars for now,
but degenerates may not survive an expected pruning effort later.

i hope we can retain "degenerates" in the Ultimate "Fish" Catalogue
-- if we prune them away, we'll be re-discovering them a few weeks later, repeating these discussions --

I made that same comment elsewhere, and is the biggest reason the degenerates are still there. Another reason is that they may become useful for constructing kraken fish. (I certainly hope kraken isn't a proper name that should be capitalized.)

In any case, the harvesting (pruning) wouldn't be happening any time soon. But when (we think) all the wheat is found, I think we should separate the chaff from the wheat. Maybe not discarded, but at least separated.

    for the Franken Swordfish,
    it seems there are several "degenerate" cases
    and only one useful (non-degenerate) case ?

To what degenerate franken swordfish do you refer:?: I see none in the exemplar catalog.
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re: Franken Swordfish - "degenerate" cases

Postby Pat » Thu Dec 21, 2006 4:07 pm

ronk wrote:
Pat wrote:
    for the Franken Swordfish,
    it seems there are several "degenerate" cases
    and only one useful (non-degenerate) case ?

To what degenerate franken swordfish do you refer?
I see none in the exemplar catalog.


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




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



my capitalization follows no rules.
~ Pat
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