The Ultimate FISH Guide

Advanced methods and approaches for solving Sudoku puzzles

Postby Ruud » Thu Nov 16, 2006 4:13 am

ronk wrote:What is(are) the exclusion(s) for this hidden pattern?

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

A finned cascading locked candidates move?

Without the fin:
Code: Select all
 /  /  X  |  .  .  .  |  /  /  /
 /  /  X  |  .  .  .  |  /  /  /
 *  *  *  |  *  *  *  |  X  X  X
----------+-----------+----------
 .  .  *  |  .  .  .  |  .  .  . 
 .  .  *  |  .  .  .  |  .  .  .
 .  .  *  |  .  .  .  |  .  .  .
----------+-----------+----------
 X  X  *  |  *  *  *  |  *  *  *
 /  /  *  |  .  .  .  |  .  .  .
 /  /  *  |  .  .  .  |  .  .  .

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Postby Ruud » Thu Nov 16, 2006 4:59 am

There's always a bigger fish...:D

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  /  |  .  *  .
mutant whale bbbbbb * rrrccc
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Postby Myth Jellies » Thu Nov 16, 2006 5:33 am

Pilot fish, or how about remora?

Image

Any of several marine fishes of the family Echeneidae, having on the head a sucking disk with which they attach themselves to sharks, whales, sea turtles, or the hulls of ships. Also called shark sucker, suckerfish, suckfish
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Postby Havard » Thu Nov 16, 2006 11:26 am

Ruud wrote:
Code: Select all
 /  /  X  |  .  .  .  |  /  /  /
 /  /  X  |  .  .  .  |  #  /  /
 .  .  .  |  .  .  .  |  X  X  X
----------+-----------+----------
 .  .  .  |  .  .  .  |  .  .  . 
 .  .  .  |  .  .  .  |  .  .  .
 .  .  .  |  .  .  .  |  .  .  .
----------+-----------+----------
 X  X  .  |  .  .  .  |  *  .  .
 /  /  .  |  .  .  .  |  .  .  .
 /  /  .  |  .  .  .  |  .  .  .



You realize of course that this is also three Empty Rectangles?:)
Code: Select all
 X  X  .  |  .  .  .  |  .  X  X
 X  X  .  |  .  .  .  |  .  X  X
 .  .  +  |  .  .  .  |  +  .  .
----------+-----------+----------
 .  .  .  |  .  .  .  |  .  .  . 
 .  .  .  |  .  .  .  |  .  .  .
 .  .  .  |  .  .  .  |  .  .  .
----------+-----------+----------
 .  .  +  |  .  .  .  |  *  .  .
 X  X  .  |  .  .  .  |  .  .  .
 X  X  .  |  .  .  .  |  .  .  .


so your fish can also look like this:
Code: Select all
 /  /  X  |  .  .  .  |  #  /  /
 /  /  X  |  .  .  .  |  #  /  /
 X  X  X  |  .  .  .  |  X  X  X
----------+-----------+----------
 .  .  .  |  .  .  .  |  .  .  . 
 .  .  .  |  .  .  .  |  .  .  .
 .  .  .  |  .  .  .  |  .  .  .
----------+-----------+----------
 X  X  X  |  .  .  .  |  *  .  .
 /  /  X  |  .  .  .  |  .  .  .
 /  /  X  |  .  .  .  |  .  .  .


As I expressed in an earlier post, ( http://forum.enjoysudoku.com/viewtopic.php?p=37270#p37270 )
you can (with mutants) make fish out of every possible grouped x-cycle, but is not this just redoing all the work that has been done on these cycles? Is it not much more interesting to look at the fish that can not be expressed as a grouped x-cycle?

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Postby ronk » Thu Nov 16, 2006 12:59 pm

Havard wrote:so your fish can also look like this:
Code: Select all
 /  /  X  |  .  .  .  |  #  /  /
 /  /  X  |  .  .  .  |  #  /  /
 X  X  X  |  .  .  .  |  X  X  X
----------+-----------+----------
 .  .  .  |  .  .  .  |  .  .  . 
 .  .  .  |  .  .  .  |  .  .  .
 .  .  .  |  .  .  .  |  .  .  .
----------+-----------+----------
 X  X  X  |  .  .  .  |  *  .  .
 /  /  X  |  .  .  .  |  .  .  .
 /  /  X  |  .  .  .  |  .  .  .

Or this ...
Code: Select all
 /  /  X  | .  .  .  |  X  /  /
 /  /  X  | .  .  .  |  X  /  /
 X  X *X  | *  *  *  |  X  X  X
----------+----------+----------
 .  .  *  | .  .  .  |  *  .  .
 .  .  *  | .  .  .  |  *  .  .
 .  .  *  | .  .  .  |  *  .  .
----------+----------+----------
 X  X *X  | *  *  *  |**X  X  X
 /  /  X  | .  .  .  |  X  #  #
 /  /  X  | .  .  .  |  X  #  #
 finned mutant jellyfish bbbb\rrcc

... which I didn't realize when I posed my question. As such, it was already in the library of exemplars, and I apologize for covering (pun) old ground here.

As I expressed in an earlier post, ( http://forum.enjoysudoku.com/viewtopic.php?p=37270#p37270 )
you can (with mutants) make fish out of every possible grouped x-cycle, but is not this just redoing all the work that has been done on these cycles?

Of course, but I'm also interested in having a complete library of exemplars, that is, fish viewed as constraint sets. Is it not human nature to repeat ourselves once in a while?:)

Is it not much more interesting to look at the fish that can not be expressed as a grouped x-cycle?

Again "of course" ... and that will happen too. Sometimes a fisherman must exercise a little patience.
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Postby Havard » Thu Nov 16, 2006 2:49 pm

ronk wrote:
Havard wrote:so your fish can also look like this:
Code: Select all
 /  /  X  |  .  .  .  |  #  /  /
 /  /  X  |  .  .  .  |  #  /  /
 X  X  X  |  .  .  .  |  X  X  X
----------+-----------+----------
 .  .  .  |  .  .  .  |  .  .  . 
 .  .  .  |  .  .  .  |  .  .  .
 .  .  .  |  .  .  .  |  .  .  .
----------+-----------+----------
 X  X  X  |  .  .  .  |  *  .  .
 /  /  X  |  .  .  .  |  .  .  .
 /  /  X  |  .  .  .  |  .  .  .

Or this ...
Code: Select all
 /  /  X  | .  .  .  |  X  /  /
 /  /  X  | .  .  .  |  X  /  /
 X  X *X  | *  *  *  |  X  X  X
----------+----------+----------
 .  .  *  | .  .  .  |  *  .  .
 .  .  *  | .  .  .  |  *  .  .
 .  .  *  | .  .  .  |  *  .  .
----------+----------+----------
 X  X *X  | *  *  *  |**X  X  X
 /  /  X  | .  .  .  |  X  #  #
 /  /  X  | .  .  .  |  X  #  #
 finned mutant jellyfish bbbb\rrcc


With the dfference, of course that the first example is a swordfish, and the other one is a Jellyfish!:)

I admire your determination to document all possible samples, but in my head that will amount to a lot of combinations?

(and I had thought that you would recognise patience in the fact that I have not bugged you once about that output you know...):D

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Postby ronk » Thu Nov 16, 2006 6:19 pm

Havard wrote:I admire your determination to document all possible samples, but in my head that will amount to a lot of combinations?
If there are so many, why have only two additions been suggested? (Both by Ruud.)

(and I had thought that you would recognise patience in the fact that I have not bugged you once about that output you know...):D
Over several hours, I studied every single grid and every single logical expression. Tersely speaking, the deductions appeared complete and flawless ... but the logic expressions are too verbose. Unfortunately, the computer containing my suggested expressions is currently out-of-service.
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Postby tarek » Thu Nov 16, 2006 11:47 pm

I updated the diagrams in the head post as per ronk's updates.


I like the Remora theme........ but doesn't it serve only to tell us that 2 steps can be combined into 1.........

would the remora be destroyed by the acts of the Host-fish alone...... if not, then it is more of a symbiotic relationship rather than parasitic.

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Postby Ruud » Fri Nov 17, 2006 12:35 am

These Remora actually aid in performing additional eliminations. That brings us to:

Image

Remoraid:D

[disclaimer] this post should not be taken too seriously.
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Postby Mike Barker » Fri Nov 17, 2006 2:56 am

I think that the remora (formerly known as Siamese Fish, aka as a remoraid:) ) are really more than just parasites. Consider the first known sighting of such a fish (see here). The fish is a finned Franken Jellyfish with the fins in box 6. This clearly allows the eliminations in r46c9, but what about the eliminations in r6c46? Since these don't see the fins then they shouldn't occur. The reason, of course, is the remora X-wing in c25 which allows the eliminations. I think it is important to identify these otherwise its hard to understand why some eliminations occur, for example, r1c9 in Ruud's fish.

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


In response to
Ronk wrote:1. IMO Siamese fish should be peers of equal size.
2. Most unfinned N-fish probably contain a finned fish of size N-1. Are we going to call them all Siamese?
3. It would also be desirable for the twins to be "inseparable" ... if that even applies to fish.

1. Remora do not have to be equal size (although they can).
2. Even if #2 is true, the only time a remora comes into play is when it is required in order to explain an elimination as in the above example or in Ruud's example and then it should be clearly called out.
3. I agree. Anytime a fish is composed of two seperable fish then I wouldn't refer to it as the larger fish. So although Ruud's Franken Squirmbag is cute:) , its not a real fish:( . In fact it is a basic jellyfish!

On a different topic, the mutant Jellyfish in the first post is also a classic example of a finless Frankenfish:
Code: Select all
+--------------------------+---------------------+---------------------+
|    46     2456     2456  |    3     8       9  |  245      7      1  |
|     8     2579    23579  |    4   567       1  | 2359* 23569*  2356  |
|     1     4579    34579  |   26   567    2567  | 3459* 35689* 34568  |
+--------------------------+---------------------+---------------------+
|     2     4789     4789  |    5  3479    3478  |    6      1     38  |
|   679*       3        1  | 2689* 67-9    2678  | 2579*     4    258  |
|  4679* 45678-9  45678-9  | 2689*    1  234678  | 2379*  2389*   238  |
+--------------------------+---------------------+---------------------+
|     5    24679    24679  |    1  3469     346  |    8    236  23467  |
| 34679*  4678-9   4678-9  |  689*    2   34568  |    1    356  34567  |
|   346        1     2468  |    7  3456   34568  | 2345   2356      9  |
+--------------------------+---------------------+---------------------+
cccc/rrrb
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Postby daj95376 » Fri Nov 17, 2006 6:54 am

I'm not trying to be a troublemaker. I have a real question. Is a finless Frankenfish preferable to a Kraken Swordfish?

Code: Select all
#                    Swordfish [r568C147] => eliminations
# fin cell [r2c7] => Swordfish [R347c235] => eliminations
# fin cell [r3c7] => Swordfish [R247c235] => eliminations
*-----------------------------------------------------------------------------*
| 46      2456    2456    | 3       8       9       | 245     7       1       |
| 8       2579    23579   | 4       567     1       |#2359    23569   2356    |
| 1       4579    34579   | 26      567     2567    |#3459    35689   34568   |
|-------------------------+-------------------------+-------------------------|
| 2       4789    4789    | 5       3479    3478    | 6       1       38      |
|*679     3       1       |*2689    67-9    2678    |*2579    4       258     |
|*4679    45678-9 45678-9 |*2689    1       234678  |*2379    2389    238     |
|-------------------------+-------------------------+-------------------------|
| 5       24679   24679   | 1       3469    346     | 8       236     23467   |
|*34679   4678-9  4678-9  |*689     2       34568   | 1       356     34567   |
| 346     1       2468    | 7       3456    34568   | 2345    2356    9       |
*-----------------------------------------------------------------------------*

There's also a Kraken Jellyfish in [R2347c2357] whose fin cells force the Swordfish [r568C147], but I doubt if it is of any importance. Since I'm not familiar with all of the fish variants in this thread, how should I select from the few that I do (halfway) know?
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Postby tarek » Fri Nov 17, 2006 7:32 am

Mike Barker wrote:On a different topic, the mutant Jellyfish in the first post is also a classic example of a finless Frankenfish
Good catch...


daj95376 wrote:Since I'm not familiar with all of the fish variants in this thread, how should I select from the few that I do (halfway) know?
The list of types of fish in the first post is also a difficulty ranking....... choose the one with lowest ranking 1st (easiest).......

IMO that means that kraken fish should be last, if another fish is present

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Postby Myth Jellies » Fri Nov 17, 2006 8:29 am

The real remora fish is not really a parasite. It just uses the sucker on its head to hitch a ride on a bigger fish and then it feeds on the scraps that the bigger fish leaves behind.
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Postby ronk » Fri Nov 17, 2006 6:20 pm

The 'rcb\rcb' notation

Let's take a look at a current rcb\rcb exemplar.
Code: Select all
 /  X  / | .  .  . | .  /  .
 X *X  X | *  *  * | *  X  *
 /  X  / | .  .  . | .  /  .
---------+---------+---------
 .  *  . | .  .  . | .  /  .
 .  *  . | .  .  . | .  /  .
 .  *  . | .  .  . | .  /  .
---------+---------+---------
 .  *  . | .  .  . | *  X  *
 /  X  / | /  /  / | X  /  X
 .  *  . | .  .  . | *  X  *

 mutant swordfish r8c8b1\r2c2b9

The cells in the base set are:

base = r8c8b1 = {r8c123456789, r123456789c8, r123c123}

The cells in the cover set are:

cover = r1c2b9 = {r2c123456789, r123456789c2, r789c789}

Removing -- subtracting -- the cover from the base we get:

base\cover = r8c8b1\r1c2b9 = {r8c13456, r13456c8, r13c13}

That result is, with the exception of a missing r8c8, all the required empty cells that validate the exclusions. Missing cell(s) only occur in the problematic cases of intersecting base sectors (rows, columns, boxes).

In the mathematics of set theory, I've seen two symbols for subtraction (aka the relative complement): 1) the minus sign ('-') and 2) the backslash ('\').

I discarded the minus sign for two reasons: 1) it's easily interpreted as a hyphen with no mathematical significance and 2) the backslash was then a unique character in an exemplar. So the backslash was not chosen arbitrarily.
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Postby ronk » Fri Nov 17, 2006 9:35 pm

tarek wrote:
Mike Barker wrote:On a different topic, the mutant Jellyfish in the first post is also a classic example of a finless Frankenfish
Good catch...

There are at least four interpretations based on single-digit constraint sets ... for the same eliminations.

Original puzzle (#61 of top1465):
Code: Select all
...3.9.7.8..4.....1........2..5..6...3.....4.....1....5.....8......

After SSTS with 25 cells completed, I posted a mutant jellyfish here. Myth Jellies pointed out a smaller mutant swordfish here. Mike Barker posted a franken jellyfish here. There is also a classic example of a franken swordfish. All are finless.

Here's the set of four.
Code: Select all
 /  .  . |  /  .  . |  .  .  .        /  .  . |  .  .  . |  .  .  .
 /  9  9 |  /  .  . |  9  9  .        /  9  9 |  .  .  . |  9  9  .
 /  9  9 |  /  .  . |  9  9  .        /  9  9 |  .  .  . |  9  9  .
---------+----------+----------      ---------+----------+----------
 / *9 *9 |  / *9  . |  /  /  /        / *9 *9 |  / *9  / |  /  /  /
*9  .  . | *9 -9  . |  9  .  .       *9  .  . |  9 -9  . |  9  .  .
*9 -9 -9 | *9  .  . |  9  9  .       *9 -9 -9 |  9  .  . |  9  9  .
---------+----------+----------      ---------+----------+----------
 / *9 *9 |  / *9  . |  /  /  /        / *9 *9 |  / *9  / |  /  /  /
*9 -9 -9 | *9  .  . |  .  .  .       *9 -9 -9 |  9  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  .  .  .
 mutant jellyfish r47c14\b4578        mutant swordfish r47c1\c5b47
                   

 /  .  . |  /  .  . |  .  .  .        /  .  . |  .  .  . |  .  .  .
 /  9  9 |  /  .  . | *9 *9  .        / *9 *9 |  .  .  . |  9  9  .
 /  9  9 |  /  .  . | *9 *9  .        / *9 *9 |  .  .  . |  9  9  .
---------+----------+----------      ---------+----------+----------
 /  9  9 |  /  9  . |  /  /  .        / *9 *9 |  / *9  / |  /  /  /
*9  .  . | *9 -9  . | *9  .  .        9  .  . |  9 -9  . |  9  .  .
*9 -9 -9 | *9  .  . | *9 *9  .        9 -9 -9 |  9  .  . |  9  9  .
---------+----------+----------      ---------+----------+----------
 /  9  9 |  /  9  . |  /  /  .        / *9 *9 |  / *9  / |  /  /  /
*9 -9 -9 | *9  .  . |  .  .  .        9 -9 -9 |  9  .  . |  .  .  .
 /  .  . |  /  .  . |  /  /  .        .  .  . |  .  .  . |  .  .  .
 franken jellyfish c1478\r568b3       franken swordfish r47b1\c235

Considering the two givens at r1c6 (b2) and r9c9, the franken jellyfish and franken swordfish are duals. Can you see why?

daj deserves honorable mention for his kraken jellyfish here.

But Havard will likely tell us such a multiplicity of interpretations wouldn't happen if we were dealing with a "true fish" ... and that may be true.:D

[edit: removed incorrect empty cells in b5 of mutant jellyfish]
Last edited by ronk on Fri Nov 17, 2006 10:09 pm, edited 1 time in total.
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