The Ultimate FISH Guide

Advanced methods and approaches for solving Sudoku puzzles

Postby tarek » Sun Apr 13, 2008 7:49 pm

daj95376 wrote:
tarek wrote:Are there any new updtaes on the "NO FISH" Puzzles.

I'm not aware of any changes from the following:

1) Obi-Wahn submitted 21 NoFish puzzles.
2) Puzzles 14 & 21 turned out to be solvable with fish.
3) The other 19 puzzles often had fish present, but they were insufficient to crack the puzzles.
4) I believe that some of the puzzles were later cracked using the Broken Wing technique. I don't know which puzzles still remain unsolved using single-digit techniques.


Thanx,

Mike Barker also posted this on the "Revival of Boken Wings" thread.[url=http://forum.enjoysudoku.com/viewtopic.php?t=5225&start=46] http://forum.enjoysudoku.com/viewtopic.php?t=5225&start=46[/url]

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re: size of complementary fish

Postby Pat » Mon Apr 14, 2008 9:42 am

on the previous page, ronk (2008.Apr.12) wrote:
hobiwan wrote:I always thought, that any fish larger than Jellyfish had a complementary smaller fish. That's obviously not true.


That rule went out the window when the mutants came in.

It may hold for frankens, but I've forgotten.




i'm reminded of the conjecture i posted on page 14 --

Pat (2007.Jan.15) 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
    [ phrasing implies truncating any fraction ]
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Postby daj95376 » Thu Jul 17, 2008 6:11 am

Until today, the largest fish that I found necessary for a PM was of size N=6. Here are two fish for N=7.

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

 +--------------------------------------------------------------------------------+
 |  6       78      2       |  3       478     9       |  1       5       478     |
 |  17      3       18      |  2       4578    578     |  789     489     6       |
 |  9       5       4       |  78      1       6       |  278     3       278     |
 |--------------------------+--------------------------+--------------------------|
 |  2       6       789     |  5       789     4       |  3       789     1       |
 |  4       1       789     |  6789    2       3       |  5       6789    789     |
 |  5       789     3       |  1       6789    78      |  2789    246789  24789   |
 |--------------------------+--------------------------+--------------------------|
 |  3       79      679     |  4       6789    2       |  789     1       5       |
 |  8       4       15      |  79      3       15      |  6       279     279     |
 |  17      2       1569    |  6789    56789   1578    |  4       789     3       |
 +--------------------------------------------------------------------------------+

7-Fish r1458c16b7\r2c2389b5+r9|c5|b8  <> 7  [r9c5]
7-Fish r1458c1b27\r2c234589           <> 7  [r9c5]
7-Fish r18c167b47\r26c23b39+r9|c5|b8  <> 7  [r9c5]
7-Fish r18c16b467\r269c2389+r9|c5|b8  <> 7  [r9c5]

Code: Select all
 +-----------------------+
 | . . . | . . . | 9 4 . |
 | . 6 1 | . 7 4 | 3 . . |
 | . 4 . | 2 . . | . . 1 |
 |-------+-------+-------|
 | . . 9 | 3 1 . | 4 . . |
 | . 3 . | 4 . 2 | . . . |
 | . 2 . | . 9 6 | . . . |
 |-------+-------+-------|
 | 2 9 . | 1 . . | 8 . 4 |
 | 3 . . | . . . | . 1 . |
 | . . 6 | . . . | 2 . 7 |
 +-----------------------+   # P_Set_E: 26

 +-----------------------------------------------------------------------+
 |  7      58     2      |  568    3      1      |  9      4      568    |
 |  589    6      1      |  589    7      4      |  3      258    258    |
 |  589    4      3      |  2      568    589    |  567    5678   1      |
 |-----------------------+-----------------------+-----------------------|
 |  6      57     9      |  3      1      58     |  4      2578   258    |
 |  1      3      578    |  4      58     2      |  567    56789  5689   |
 |  4      2      58     |  7      9      6      |  1      58     3      |
 |-----------------------+-----------------------+-----------------------|
 |  2      9      57     |  1      56     357    |  8      356    4      |
 |  3      578    4      |  5689   2      5789   |  56     1      569    |
 |  58     1      6      |  589    4      3589   |  2      359    7      |
 +-----------------------------------------------------------------------+

7-Fish r67c2479b5\r12458c3b8+r2|c8|b3  <> 5  [r2c8]
7-Fish r67c24b569\r12458c3b8+r2|c8     <> 5  [r2c8]
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Postby Pat » Thu Jul 17, 2008 11:17 am

daj95376 wrote:Until today, the largest fish that I found necessary was of size 6;
here are two of size 7 --


those are finned fish

just to clarify,
my own comment refers to (unfinned) fish
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Postby daj95376 » Tue Jan 13, 2009 12:02 pm

Mini-Glossary wrote:*Fin*: A candidate that occupies a cell within a "Base sector" but not within any "Cover sector".
A Fin cell is the only example where a candidate can be shared by more than one "Base sector"
A fish with fins is a "finned fish". A fish without fins is a finless fish (omitting the "finless" when describing the finless fish is generally practiced)

Does the mini-glossary need to be updated? This fits Myth Jellies POM description.

*Fin*: Candidate cell(s) that exist in more Base sectors than Cover sectors. A fish with a fin is a "finned fish".

*Fish*: A group of candidate cells that can be mapped onto N Base sectors and N Cover sectors.
The candidate cells are divided into vertices, a fin, and potential eliminations.
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Postby ronk » Tue Jan 13, 2009 2:00 pm

Mini-Glossary wrote:*Fin*: A candidate that occupies a cell within a "Base sector" but not within any "Cover sector".
A Fin cell is the only example where a candidate can be shared by more than one "Base sector"


daj, the mini-glossary speaks of the two types of fins, exo-fin and endo-fin ... without actually using the terms, or even saying that there are two types. As a result, the two sentences seem contradictory and are likely to cause confusion.

If you're also referring to something else, I don't see it.
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Postby daj95376 » Tue Jan 13, 2009 3:39 pm

ronk: I was working from an old copy of the mini-glossary. That said, here's my point.

I was recently in a discussion on the definition of fin.

I think this question about the "number of fins" is semantics. Any sort of finned fish has just one fin, but that fin can be comprised of multiple cells.

I thought this was incorrect until I ran across Myth Jellies POM thread where he said the same thing.

This alternate viewpoint on fin seemed to be in direct conflict with the mini-glossary.

Even when you factor in endo-fin cells and exo-fin cells, they could still be viewed as members of the fin.

===== ===== ===== ===== Related Topic

A candidate cell that's in two base sectors and only one cover sector is a fin cell. This conflicts with the fin definition in the mini-glossary.

A candidate cell that's in two cover sectors and only one base sector is an elimination cell. This conflicts with the elimination definition in the mini-glossary.
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Postby ronk » Tue Jan 13, 2009 4:44 pm

daj95376 wrote:I was recently in a discussion on the definition of fin.

I think this question about the "number of fins" is semantics. Any sort of finned fish has just one fin, but that fin can be comprised of multiple cells.

...
Even when you factor in endo-fin cells and exo-fin cells, they could still be viewed as members of the fin.


Fish heresy IMO. For N base sectors (units), [edit: and using a broader definition of cover sector to include "fin sectors"] ...

N cover sectors <=> no fin
N+1 cover sectors <=> one fin
N+2 cover sectors <=> two fins

[edit: I recall Obi-Wahn posting an example with three fins, but efforts to find it have failed. I can't now imagine an example with three fin sectors.]

daj95376 wrote:I thought this was incorrect until I ran across Myth Jellies POM thread where he said the same thing.

Doesn't the POM thread pre-date the Ultimate Fish Guide thread? Things change.

daj95376 wrote:Related Topic

A candidate cell that's in two base sectors and only one cover sector is a fin cell. This conflicts with the fin definition in the mini-glossary.

A candidate cell that's in two base sectors is a fin cell whether or not it's covered, so the mini-glossary seems correct to me. As I stated earlier, however, it would be less confusing if the two types of fin cells were clarified.

daj95376 wrote:A candidate cell that's in two cover sectors and only one base sector is an elimination cell. This conflicts with the elimination definition in the mini-glossary.

Yes, there are two types of eliminations, so the mini-glossary is incomplete.
Last edited by ronk on Tue Jan 13, 2009 8:14 pm, edited 1 time in total.
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Postby tarek » Tue Jan 13, 2009 7:21 pm

ronk wrote:
daj95376 wrote:A candidate cell that's in two cover sectors and only one base sector is an elimination cell. This conflicts with the elimination definition in the mini-glossary.

Yes, there are two types of eliminations, so the mini-glossary is incomplete.
The thread is a collaborative effort. I understand that updates are needed. The mini-golssary should have simple wording but should also be complete.

what are you proposing (I could simply cut & paste if it's best) ?

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Postby ronk » Tue Jan 13, 2009 11:30 pm

tarek wrote:
ronk wrote:Yes, there are two types of eliminations, so the mini-glossary is incomplete.
The mini-golssary should have simple wording but should also be complete.

what are you proposing (I could simply cut & paste if it's best) ?

Using the existing style ...

Proposal wrote:*Potential elimination*: A candidate that 1) occupies a cell within a "Cover sector" but not within a "Base sector", or 2) occupies a cell within one "Base sector" and within two or more "Cover sectors". In finned fish, the potential elimination that becomes a fish elimination should oocupy a cell that SHARES a sector or sectors with each & every fin (this is usually termed "seeing the fin").

While we're at it ...
Proposal wrote:*Fin*: A fin cell is a candidate that 1) occupies a cell within a "Base sector" but not within any "Cover sector", or
2) occupies a cell within two "Base sectors".

A fish with fins is a "finned fish". A fish without fins is a finless fish (omitting the "finless" when describing the finless fish is generally practiced)

daj95376 or anyone, have you ever seen a useful fish with a fin cell in two base sectors and two cover sectors:?: If such creatures exist, this should be modified further.

tarek, I've assumed you don't wish to bring up the exo-fin and endo-fin terms in the mini-glossary.
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Postby daj95376 » Wed Jan 14, 2009 2:28 am

Assuming that the definition of a fin has changed from a collection of cells to individual cells as ronk asserts:

daj suggestion wrote:*Fin*: A candidate cell that exist in more Base sectors than Cover sectors. A fish with one or more fins is a "finned fish".

*Potential Elimination*: A candidate cell that exists in more Cover sectors than Base sectors, and sees all fin cells.


===== ===== =====

ronk: I restrict my solver to using an NxN fish and at most ...

* __ 2x Base Sectors and 1x Cover Sectors, or
* __ 1x Base Sectors and 2x Cover Sectors

Also, I only allow a sector to be used once.
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Postby ronk » Wed Jan 14, 2009 3:08 am

daj95376 wrote:Assuming that the definition of a fin has changed from a collection of cells to individual cells as ronk asserts:

I asserted no such thing. I just didn't think it necessary to say that one fin (aka a fin sector, a fin unit) consists of one or more fin cells in a single sector. Apparently I was wrong.

daj suggestion wrote:*Fin*: A candidate cell that exist in more Base sectors than Cover sectors. A fish with one or more fins is a "finned fish".

*Potential Elimination*: A candidate cell that exists in more Cover sectors than Base sectors, and sees all fin cells.

For the most part, I agree with that. Just change the *Fin* title to *Fin Cell*, add a definition for *Fin Sector*, and that should do it.

I restrict my solver to using an NxN fish and at most ...

* __ 2x Base Sectors and 1x Cover Sectors, or
* __ 1x Base Sectors and 2x Cover Sectors

I have no idea what that means.
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Postby daj95376 » Wed Jan 14, 2009 3:36 am

ronk wrote:
daj95376 wrote:Assuming that the definition of a fin has changed from a collection of cells to individual cells as ronk asserts:

I asserted no such thing. I just didn't think it necessary to say that one fin (aka a fin sector, a fin unit) consists of one or more fin cells in a single sector. Apparently I was wrong.

Since we are discussing definitions, I would think that not saying something is about as wrong as you can get.

As for being wrong, I was wrong in not prefacing my comments about my solver by saying they were why I'd never encountered a fish with 2x Base Sectors and 2x Cover Sectors ... as you'd asked. My apologies for the confusion!

daj95376 or anyone, have you ever seen a useful fish with a fin cell in two base sectors and two cover sectors.

BTW: Since it's possible for the intersection of a row/column base sector and a box base sector to include one or more fin cells, then it's possible that these fin cells are in two fins. (Oh boy, this is getting to be fun!)
Last edited by daj95376 on Wed Jan 14, 2009 12:14 am, edited 3 times in total.
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Postby tarek » Wed Jan 14, 2009 3:44 am

ronk wrote:
daj suggestion wrote:*Fin*: A candidate cell that exist in more Base sectors than Cover sectors. A fish with one or more fins is a "finned fish".

*Potential Elimination*: A candidate cell that exists in more Cover sectors than Base sectors, and sees all fin cells.

For the most part, I agree with that. Just change the *Fin* title to *Fin Cell*, add a definition for *Fin Sector*, and that should do it.
Thanks to both of you.

This should take care of the endo-fin (until the the 2-based-2-covered fin cell appears, probably in a sudoku variant:idea: ).

I will update the head post shortly.

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Postby daj95376 » Thu Jan 15, 2009 12:28 am

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.

2) As Nx(N+k) Base Sectors by Cover Sectors with "k" Cover Sectors called Fin Sectors. Obi-Wahn proposed this approach and ronk uses it. ronk calls a Fin Sector ... a fin.

In (1) there aren't any Fin Sectors, and in (2) there aren't any fin cells.

===== ===== ===== ===== ===== NxN Fish

Sector: wrote:A collective term for row/column/box.

Line: wrote:A collective term for row/column.

Candidate: wrote:One of several possible digits in a sudoku puzzle cell.

Fish: wrote:Candidate cells mapped onto NxN Base Sectors by Cover Sectors.
The candidate cells are divided into vertices, fin cells, and fish eliminations.
The type of sectors forming the Base and Cover Sectors determines fish "Shape" or configuration.
The number of sectors forming the Base and Cover Sectors is usually termed the fish "Size".
The number and type of sectors forming the fish determines the fish.

Vertex: wrote:A candidate cell at the intersection of an equal number of Base Sectors and Cover Sectors.

Fin Cell: wrote:A candidate cell that exist in more Base Sectors than Cover Sectors.
A fish with one or more fin cells is a "finned fish".

Fish Elimination: wrote:A candidate cell that exists in more Cover sectors than Base sectors, and is a peer to all fin cells.

[Edit: corrected a spelling error.]
Last edited by daj95376 on Thu Jan 15, 2009 12:46 am, edited 1 time in total.
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