## The Ultimate FISH Guide

Advanced methods and approaches for solving Sudoku puzzles
daj95376 wrote:To me, the results for T_1only and T_2only seem to imply that the fish getting past Test #1 are often caught by Test #2, but the converse is not true. Test #2 is the more dominant filter!

I was trying to ignore the affect of your Test #1.

The 3:2 ratio doesn't hold up as a generality for most eliminations. Sometimes a high percentage of the possible fish are invalid, and other times it is a very small percentage.

Unless I misinterpreted the impact of 1-finned fish, I don't see how it would be anything other than 3:2. OTOH, I might not be understanding what your GFF is doing.

r6c29b1\r18c18 appears in T_none and T_1only, which implies that it's caught by Test #2. r6c29b1\r158c1 and r6c29b1\r18c1b6 appear in T_12, which implies that they're legitimate fish.

On this point, I think we're saying the same thing.
ronk
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A simple Empty Rectangle elimination and a 2-Fish that fails Test #1 and Test #2.

Code: Select all
` +-----------------------------------+ |  .  8  .  |  .  8  .  |  .  8  .  | |  8  .  .  |  .  8  8  |  .  8  8  | |  .  8  .  |  .  8  8  |  .  .  8  | |-----------+-----------+-----------| |  8  .  .  |  .  .  .  |  .  8  .  | |  8  . *8  | -8  .  8  |  .  .  8  | |  .  8  .  |  8  .  .  |  .  .  .  | |-----------+-----------+-----------| |  .  .  .  |  .  .  .  |  8  .  .  | |  8  8  .  | *8  .  .  |  .  .  .  | |  .  . *8  |  . *8 *8  |  .  .  .  | +-----------------------------------+`

Code: Select all
` 2-Fish c3b8\r9b5  <> X  [r5c4]                   *** fails Test #1 and Test #2 +-----------------------------------------------+ |   .   .   /   |   .   .   .   |   .   .   .   | |   .   .   /   |   .   .   .   |   .   .   .   | |   .   .   /   |   .   .   .   |   .   .   .   | |---------------+---------------+---------------| |   .   .   /   |   *   *   *   |   .   .   .   | |   .   .   #   |  **   *   *   |   .   .   .   | |   .   .   /   |   *   *   *   |   .   .   .   | |---------------+---------------+---------------| |   .   .   /   |   /   /   /   |   .   .   .   | |   .   .   /   |   #   /   /   |   .   .   .   | |   *   *   X   |   X   X   X   |   *   *   *   | +-----------------------------------------------+`
daj95376
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daj95376 wrote:A simple Empty Rectangle elimination and a 2-Fish that fails Test #1 and Test #2.

Code: Select all
` 2-Fish c3b8\r9b5  <> X  [r5c4]                   *** fails Test #1 and Test #2 +-----------------------------------------------+ |   .   .   /   |   .   .   .   |   .   .   .   | |   .   .   /   |   .   .   .   |   .   .   .   | |   .   .   /   |   .   .   .   |   .   .   .   | |---------------+---------------+---------------| |   .   .   /   |   *   *   *   |   .   .   .   | |   .   .   #   |  **   *   *   |   .   .   .   | |   .   .   /   |   *   *   *   |   .   .   .   | |---------------+---------------+---------------| |   .   .   /   |   /   /   /   |   .   .   .   | |   .   .   /   |   #   /   /   |   .   .   .   | |   *   *   X   |   X   X   X   |   *   *   *   | +-----------------------------------------------+`

Since my GFF doesn't even construct a potential fish without at least one base candidate -- i.e., any candidate of the actual pencilmarks in any base unit -- not also "covered" by another cover unit, it never encounters this situation.

This example doesn't even have an 'X' in the pattern for b5, so I'm unclear about where this discussion is supposed to be going.

[edit: "pattern" was "exemplar"]
Last edited by ronk on Thu Mar 06, 2008 7:56 am, edited 1 time in total.
ronk
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ronk wrote:I'm unclear about where this discussion is supposed to be going.

My example in the Programmers Forum was of a 5-Fish that failed Test #1. My example earlier in this thread was of a 4-Fish that failed Test #2.

I thought a trivial example of a 2-Fish that fails both Test #1 and Test #2 might serve to show that you don't need big, complicated fish to run into problems if you don't perform testing equivalent to Test #1 and Test #2.

Unfortunately, I forgot to add this as a comment to the example.
daj95376
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on the previous page, daj95376 (2008.Mar.4/5) wrote:
ronk wrote:Have you ever seen an elimination based on such a fish to be invalid?

Q: Even if Test #1 and/or Test #2 fail for a finned fish,
is the elimination ever invalid?

I suspect the answer is no.

yes, daj95376, you are right, the exclusion is always valid

i like the simple beauty of the fish definition
it does allow such "impossible" fish as your cute example (above) of the Franken X-wing with 2 fins
-- so what? doesn't bother me

Pat

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While testing I came across the following puzzle:
Code: Select all
`.---------------------.---------------------.---------------------.| 9      234    7     | 68     14     5     | 48     3468   1234  || 1      345    2345  | 7      468    238   | 9      68     234   || 8      6      234   | 34     9      123   | 5      7      12    |:---------------------+---------------------+---------------------:| 457    8      45    | 234    347    6     | 1      23     9     || 3      1      6     | 24     5      9     | 248    28     7     || 2      47     9     | 1      3478   378   | 6      5      34    |:---------------------+---------------------+---------------------:| 457    345    1358  | 58     2      1378  | 47     9      6     || 567    9      1235  | 56     367    4     | 27     12     8     || 467    247    128   | 9      168    178   | 3      124    5     |'---------------------'---------------------'---------------------'`

My solver gave me a Template Delete [r9c1]<>4.
The only fish i could find for that elimination was:
Code: Select all
`Finned Mutant Whale: 4 r357c89b4 r69c347b3 f[r4c1] f[r7c1] f[r7c2] => [r9c1]<>4`

(plus a lots of variants, but nothing smaller than Finned Mutant Whale)
Is a Mutant Whale really the smallest possible fish here or can somebody find a smaller one?
hobiwan
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I found 19 finned mutant Whales. Here are the three I found with your base set.

Code: Select all
`6-Fish r357c89b4\r6c347b3+r9|c1|b7final cover sector r9 => 3 fin cellsfinal cover sector c1 => 2 fin cellsfinal cover sector b7 => 2 fin cells`
daj95376
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I always thought, that any fish larger than Jellyfish had a complementary smaller fish. That's obviously not true.
hobiwan
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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.
ronk
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ronk wrote:It may hold for frankens, but I've forgotten.

I don't think it holds for Franken fish, either. There are two mutant 4-Fish for this elimination, but no smaller Franken fish.

Code: Select all
` +-----------------------+ | 1 . . | . . . | . 8 . | | . 5 . | 7 1 . | . 3 6 | | 8 . 6 | 9 . . | . . . | |-------+-------+-------| | . 6 . | 5 . 1 | . . . | | 7 . . | . 8 . | . . 2 | | . . . | 2 . 7 | . 1 . | |-------+-------+-------| | . . . | . . 3 | 8 . 1 | | 9 1 . | . 7 5 | . 6 . | | . 3 . | . . . | . . 7 | +-----------------------+SSTS5-Fish c13459\r1468b8           fF 050\401  <> 4  [r1c2]5-Fish c13459\r468b18           fF 050\302  <> 4  [r1c2]5-Fish c1459b7\r1468b8          fF 041\401  <> 4  [r1c2]5-Fish c1459b7\r468b18          fF 041\302  <> 4  [r1c2]5-Fish c459b47\r1468b8          fF 032\401  <> 4  [r1c2]5-Fish r23579\c2678b8           fF 500\041  <> 4  [r1c2]5-Fish r23579\c678b18           fF 500\032  <> 4  [r1c2]5-Fish r2579b2\c2678b8          fF 401\041  <> 4  [r1c2]5-Fish r2579b2\c678b18          fF 401\032  <> 4  [r1c2]5-Fish r579b23\c2678b8          fF 302\041  <> 4  [r1c2]`
daj95376
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Ah,

A finned mutant whale (Nice catch).......

Are there any new updtaes on the "NO FISH" Puzzles.

tarek

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daj95376 wrote:
ronk wrote:It may hold for frankens, but I've forgotten.

I don't think it holds for Franken fish, either. There are two mutant 4-Fish for this elimination, but no smaller Franken fish.

Why can't a mutant be a complement for a franken?

BTW a complementary fish must first be an equivalent fish, meaning the fish are based on the same empty cells and yield the same eliminations. I could only find five frankens equivalent to the two mutants.
ronk
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ronk wrote:Why can't a mutant be a complement for a franken?

BTW a complementary fish must first be an equivalent fish, meaning the fish are based on the same empty cells and yield the same eliminations. I could only find five frankens equivalent to the two mutants.

I was not aware that fish of different shapes could be considered complementary.

Apparently Sudopedia doesn't agree with your definition of complement. It says this PM has complementary row/column Jellyfish for digit 3. However, the two Jellyfish are not based on the same empty cells, and the eliminations in common are only those in the PM -- not in their exemplars.

Code: Select all
` *-----------------------------------------------------------* | 8     4     9     | 7     6     13    | 135   2     135   | | 2     1     6     | 389   389   5     | 4     7     38    | | 35    35    7     | 2     138   4     | 1358  9     6     | |-------------------+-------------------+-------------------| | 4     8     13    | 139   139   2     | 6     5     7     | | 9     35    1235  | 13    7     6     | 23    8     4     | | 7     6     23    | 4     5     8     | 9     1     23    | |-------------------+-------------------+-------------------| | 1     9     358   | 6     238   7     | 258   4     258   | | 6     7     4     | 5     128   9     | 128   3     128   | | 35    2     358   | 138   4     13    | 7     6     9     | *-----------------------------------------------------------*`

Code: Select all
`  4-Fish c1267\r1359  <> 3  [r1c9],[r3c5],[r59c34]  +-----------------------------------+  |  X  X  *  |  *  *  X  |  X  * **  |  |  /  /  .  |  .  .  /  |  /  .  .  |  |  X  X  *  |  * **  X  |  X  *  *  |  |-----------+-----------+-----------|  |  /  /  .  |  .  .  /  |  /  .  .  |  |  X  X **  | **  *  X  |  X  *  *  |  |  /  /  .  |  .  .  /  |  /  .  .  |  |-----------+-----------+-----------|  |  /  /  .  |  .  .  /  |  /  .  .  |  |  /  /  .  |  .  .  /  |  /  .  .  |  |  X  X **  | **  *  X  |  X  *  *  |  +-----------------------------------+`

Code: Select all
`  4-Fish r2467\c3459  <> 3  [r1c9],[r3c5],[r59c34]  +-----------------------------------+  |  .  .  *  |  *  *  .  |  .  . **  |  |  /  /  X  |  X  X  /  |  /  /  X  |  |  .  .  *  |  * **  .  |  .  .  *  |  |-----------+-----------+-----------|  |  /  /  X  |  X  X  /  |  /  /  X  |  |  .  . **  | **  *  .  |  .  .  *  |  |  /  /  X  |  X  X  /  |  /  /  X  |  |-----------+-----------+-----------|  |  /  /  X  |  X  X  /  |  /  /  X  |  |  .  .  *  |  *  *  .  |  .  .  *  |  |  .  . **  | **  *  .  |  .  .  *  |  +-----------------------------------+`

In any event, since you only found five of my ten frankens to be equivalent to the two mutants, wouldn't that lead to the conclusion that the remaining five frankens don't have a complementary smaller fish?
daj95376
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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.
daj95376
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daj95376 wrote:
ronk wrote:Why can't a mutant be a complement for a franken?

I was not aware that fish of different shapes could be considered complementary.

Don't know that they can, but don't know that they can't either.

daj95376 wrote:
ronk wrote:BTW a complementary fish must first be an equivalent fish, meaning the fish are based on the same empty cells and yield the same eliminations.

Apparently Sudopedia doesn't agree with your definition of complement. It says this PM has complementary row/column Jellyfish for digit 3. However, the two Jellyfish are not based on the same empty cells, and the eliminations in common are only those in the PM -- not in their exemplars.

Agree with the sudopedia example, but not that it's in conflict with my definition. Without considering the PM, the complement of a 4-fish is a 5-fish. Since the complement is not a 5-fish, the PM is being considered, and this consideration should be reflected in the "hidden pattern." IOW both fish exist only if the "hidden pattern" has at least these empty cells ...
Code: Select all
`  +-----------------------------------+   |  .  .  .  |  .  .  .  |  .  .  .  |   |  /  /  .  |  .  .  /  |  /  /  .  |   |  .  .  .  |  .  .  .  |  .  .  .  |   |-----------+-----------+-----------|   |  /  /  .  |  .  .  /  |  /  /  .  |   |  .  .  .  |  .  .  .  |  .  .  .  |   |  /  /  .  |  .  .  /  |  /  /  .  |   |-----------+-----------+-----------|   |  /  /  .  |  .  .  /  |  /  /  .  |   |  /  /  .  |  .  .  /  |  /  .  .  |   |  .  .  .  |  .  .  .  |  .  .  .  |   +-----------------------------------+ `

As you noted, although the potential eliminations for the two fish are different, the actual eliminations on the PM are identical.

daj95376 wrote:
ronk wrote:I could only find five frankens equivalent to the two mutants.

In any event, since you only found five of my ten frankens to be equivalent to the two mutants, wouldn't that lead to the conclusion that the remaining five frankens don't have a complementary smaller fish?

[edit: Ran it again and it came up with six frankens, so I must have miscounted last time. One set of equivalents consists of six frankens and two mutants, the second set has four frankens.]

Every hidden pattern with an elimination due to a valid fish probably has at least one [edit: pair of complementary] fish. However, I don't think I ever claimed that every fish has a complement.
Last edited by ronk on Sun Apr 13, 2008 5:08 pm, edited 2 times in total.
ronk
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