The Ultimate FISH Guide

Advanced methods and approaches for solving Sudoku puzzles

Re: Improved definition of a FISH needed ?

Postby JC Van Hay » Sat Jun 12, 2010 6:42 pm

:oops: Fishermen : Should a better definition of a fish be needed in view of the following four examples of Jellyfishes where the eliminations are either correctly predicted or not ? :roll:

Code: Select all
Jellyfish1 r1578/c1245
+-----------------------------------------------+
|   /   1   /   |   /   1   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|---------------+---------------+---------------|
|   .   .   .   |   .   .   .   |   .   .   .   |
|   1   /   /   |   1   /   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|---------------+---------------+---------------|
|   /   1   /   |   /   1   /   |   /   /   /   |
|   1   /   /   |   1   /   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
+-----------------------------------------------+

Jellyfish2 r1578/c1245
+-----------------------------------------------+
|   /   1   /   |   1   /   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|---------------+---------------+---------------|
|   .   .   .   |   .   .   .   |   .   .   .   |
|   1   /   /   |   /   1   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|---------------+---------------+---------------|
|   /   1   /   |   /   1   /   |   /   /   /   |
|   1   /   /   |   1   /   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
+-----------------------------------------------+

Jellyfish3 r1278/c1245
+-----------------------------------------------+
|   1   /   /   |   1   1   /   |   /   /   /   |
|   /   /   /   |   1   /   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|---------------+---------------+---------------|
|   .   .   .   |   .   .   .   |   .   .   .   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|---------------+---------------+---------------|
|   1   1   /   |   1   1   /   |   /   /   /   |
|   1   /   /   |   1   /   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
+-----------------------------------------------+

Jellyfish4 r1578/c1245
+-----------------------------------------------+
|   /   1   /   |   /   1   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|---------------+---------------+---------------|
|   .   .   .   |   .   .   .   |   .   .   .   |
|   1   1   /   |   1   /   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
|---------------+---------------+---------------|
|   /   1   /   |   1   /   /   |   /   /   /   |
|   1   /   /   |   /   1   /   |   /   /   /   |
|   .   .   .   |   .   .   .   |   .   .   .   |
+-----------------------------------------------+
JC
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Re: The Ultimate FISH Guide

Postby daj95376 » Sat Jun 12, 2010 8:33 pm

There are many different aspects associated with applying a fish pattern to a candidate grid. The way I recall the previous discussions, it was a number of people concurrently discussing their own pet aspect ... with little consensus being reached. Let it RIP.

IF talks were to resume, the first thing that I'd suggest is that a real candidate grid must accompany any discussions. That way, we wouldn't have to waste time on scenarios like your Jellyfish2 where the strong links could never appear in a real puzzle.

Jellyfish2:

Code: Select all
(1): r1c2 = r1c4 - r8c4 = r8c1 - r5c1 = r5c5 - r7c5 = r7c2  =>  r7c2,r8c1=1
(1): r1c4 = r1c2 - r7c2 = r7c5 - r5c5 = r5c1 - r8c1 = r8c4  =>  r7c5,r8c4=1
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Re: The Ultimate FISH Guide

Postby tarek » Sun Jun 13, 2010 1:24 pm

I've just updated the head post. The main changes are all to do with formatting & fonts.

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Postby Pat » Mon Jun 14, 2010 1:19 pm

tarek wrote:I've just updated the head post. The main changes are all to do with formatting & fonts.


the main change
is that you've now included the indirectly-finned (remotely-finned) beasts
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Re:

Postby tarek » Mon Jun 14, 2010 1:47 pm

Pat wrote:
tarek wrote:I've just updated the head post. The main changes are all to do with formatting & fonts.


the main change
is that you've now included the indirectly-finned (remotely-finned) beasts

Yes but not in this update ...

If you're under the impression that the head post prior to this update was the May 2009 status (As I thought), the you're mistaken. I was surprised to find that a guardian angel ;) must have updated it to the last recovered update which I posted on the Programmers forum.

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Postby Pat » Mon Jun 14, 2010 4:11 pm

tarek wrote:
If you're under the impression that the head post prior to this update was the May 2009 status (As I thought), the you're mistaken. I was surprised to find that a guardian angel must have updated it to the last recovered update which I posted on the Programmers forum.


oops
yes i see what you mean
Admin edited it -- which left no flag in the "Last edited"
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Re: The Ultimate FISH Guide

Postby tarek » Mon Jun 14, 2010 6:20 pm

Pat wrote:
tarek wrote:
If you're under the impression that the head post prior to this update was the May 2009 status (As I thought), the you're mistaken. I was surprised to find that a guardian angel must have updated it to the last recovered update which I posted on the Programmers forum.


oops
yes i see what you mean
Admin edited it -- which left no flag in the "Last edited"
One thing I forgot to add in this update which I (most likely) added in the last (lost) update was the fish body definition. This has been added along with typo corrections (Thanks to Danny for his effort).

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Re: Improved definition of a FISH needed ?

Postby JC Van Hay » Tue Jun 15, 2010 7:06 pm

Some further comments on the post at the top of the page35:

    Jellyfish1: nothing very special to say about this configuration. It is a combination of 2 XWings; it has 4 solutions; eliminations can be made safely outside the rows r1578 in the columns c1245.

    Jellyfish2: daj, who first drove out such a beast, kindly and calmly re-analyzed it for the "nth times" above and proved that it cannot occur in a real puzzle : Jellyfish2 has no solution because it is autocannibalized twice in the same sector. It may also be viewed as a combination of 2 skyscrapers cannibalizing each other in the same sector (for example b7). It cannot cause eliminations.

    Jellyfish3: it has no solution because it is autocannibalized twice in the same sector (for example r8). It cannot cause eliminations.

    Jellyfish4: it has only 1 solution: (1)r1c5 (1)r7c4 (1)r8c1 (1)r5c2. It leads to the usual eliminations outside the rows r1578 in the columns c1245, to an elimination by autocannibalism in r5c4 and finally to further eliminations by claiming in b4.
All these properties of the 4 fishes are obtained by a complete dissection.

If such a dissection is not done in a real puzzle, one would only miss some eliminations in fishes of the type of jellyfish4, which would be a pity.

However, jellyfish2 and jellyfish3 are not completely ruled out. They may occur in a real puzzle as the unfinned part of a finned fish, in which case the fins form a derived SIS (to prevent the occurrence of the invalid fish), leading either to the elimination of any candidate "seeing" all the fins or to the assignment of the fin if it is the unique fin. But again, all this is only possible after dissecting the unfinned part of the finned fish. Finally, it is very easy to imagine where on the rows of the fish the fins have to be placed to get an elimination or an assignment.

SO WHAT, to dissect or not to dissect finless fishes (to catch an eventual autocannibalization) and/or finned fishes (to catch the correct eliminations). That is the question!

Lastly, it is not at all clear to me if such an analysis is fully implied or not by the guide in the first post of this thread.

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Re: Improved definition of a FISH needed ?

Postby tarek » Tue Jun 15, 2010 7:36 pm

JC Van Hay wrote:Lastly, it is not at all clear to me if such an analysis is fully implied or not by the guide in the first post of this thread.
The logic behind fish eliminations (which is in the 1st post) explains what you're trying to say. As it stands right now ... there is nothing that disallows the use of an "impossible" (fish) body or a Sashimi finless fish. The effect of Remote fins on top of that (as you recall) has started numerous debates which have been lost with the old forum.

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Re: The Ultimate FISH Guide

Postby daj95376 » Tue Jun 15, 2010 10:04 pm

When it comes to fish, I place them into four categories ... all derived from real puzzles:

    1) An unfinned fish where the fish must be valid for the candidate.

    2) A finned fish where none of the fins are true and the fish must be valid for the candidate.

    3) A finned fish where at least one of the fins is true and the fish seems valid for the candidate.

    4) A finned fish where at least one of the fins is true and the fish is not valid for the candidate.
Finding a way to distinguish (3) from (4) could be interesting.

Note: Saying that a fish is not valid for the candidate is not the same (to me) as saying that the fish pattern is illegal/invalid.
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Re: Improved definition of a FISH needed ?

Postby ronk » Tue Jun 15, 2010 10:12 pm

JC Van Hay wrote:Jellyfish4 r1578/c1245
Code: Select all
+-----------------------+
| / 1 / | / 1 / | / / / |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . . . | . . . | . . . |
| 1 1 / | 1 / / | / / / |
| . . . | . . . | . . . |
|-------+-------+-------|
| / 1 / | 1 / / | / / / |
| 1 / / | / 1 / | / / / |
| . . . | . . . | . . . |
+-----------------------+


JC Van Hay wrote:Jellyfish4: it has only 1 solution: (1)r1c5 (1)r7c4 (1)r8c1 (1)r5c2. It leads to the usual eliminations outside the rows r1578 in the columns c1245, to an elimination by autocannibalism in r5c4 and finally to further eliminations by claiming in b4.
All these properties of the 4 fishes are obtained by a complete dissection.

If such a dissection is not done in a real puzzle, one would only miss some eliminations in fishes of the type of jellyfish4, which would be a pity.

Jellyfish? I see sashimi x-wing r18\c25b7 (aka skyscraper) for r7c2<>1 followed by cascading singles.
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Re: The Ultimate FISH Guide

Postby JC Van Hay » Sat Jun 19, 2010 8:42 am

Danny, Tarek and Ronk : I highly appreciate at their fair value all your comments.

I hope you would forgive me the delay in the reply to your posts. I am still struggling to justify the following, even though I can elaborate.

In the possibilty matrix for a single digit, a candidate is eliminated if it leads to an invalid pattern when it is supposed to be true. For the moment, I conjecture that there are only two possibilities : the invalid pattern contains either a skinny fish or an impossible fish (finless, degenerate or not). Consequently, eliminations could then be found either by looking for a (finless or locally finned) fish directly in the possibility matrix or a (finless, degenerate or not) impossible fish while cross-hatching from every candidate (in view of determining a strong set of candidates preventing the occurrence of such a fish). In the cross-hatching process, it is of course supposed that all the peers of a candidate are suppressed.

In all the real puzzles I have examined so far, the conjecture is true and apparently obvious. The concept of a fish would then be preserved while the concept of a remote fin would be unnecessary (even if it may be useful).

Meanwhile, what would be needed : the test of the conjecture in the case of an elimination due to only a remotely finned fish (with local fin(s) or not).

JC

[edit] Add more precise details in the practical consequences of the conjecture.
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Re: The Ultimate FISH Guide

Postby ronk » Wed Jun 23, 2010 3:28 pm

JC Van Hay wrote:In the possibilty matrix for a single digit, a candidate is eliminated if it leads to an invalid pattern when it is supposed to be true. For the moment, I conjecture that there are only two possibilities : the invalid pattern contains either a skinny fish or an impossible fish (finless, degenerate or not). Consequently, eliminations could then be found either by looking for a (finless or locally finned) fish directly in the possibility matrix or a (finless, degenerate or not) impossible fish while cross-hatching from every candidate (in view of determining a strong set of candidates preventing the occurrence of such a fish). In the cross-hatching process, it is of course supposed that all the peers of a candidate are suppressed.

I generally agree with that. In the A revival of Broken Wings, I posted a non-ambiguous method to separate fish from NoFish. Unfortunately, this post was lost with the disk crash and I apparently didn't keep a copy either.

As I recall, for a fish, asserting the target candidate leads to a morph of this simple invalid pattern:

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

For a NoFish, asserting the target candidate leads to a more complex pattern, e.g., a turbot fish with five strong sides, an invalid jellyfish, an invalid whale, and variations of these.

JC Van Hay wrote:In all the real puzzles I have examined so far, the conjecture is true and apparently obvious. The concept of a fish would then be preserved while the concept of a remote fin would be unnecessary (even if it may be useful).

Meanwhile, what would be needed : the test of the conjecture in the case of an elimination due to only a remotely finned fish (with local fin(s) or not).

I've not combined my generalized fish finder ("GFF") and NoFish finder ("NFF") in a single program, so I don't know the answer to your "no remote-fins required" conjecture. The results of such a fishing expedition would be interesting.

[edit: removed superfluous strong link in column 2]
Last edited by ronk on Thu Jul 01, 2010 6:38 pm, edited 1 time in total.
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Re: The Ultimate FISH Guide

Postby daj95376 » Fri Jun 25, 2010 10:19 pm

Tarek #2 (NoFish #23): 12/25/09

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

 +--------------------------------------------------------------------------------+
 |  38      3468    7       |  589     689     2       |  4569    3569    1       |
 |  128     5       246     |  1789    1689    3       |  4679    2679    2467    |
 |  9       136     236     |  157     4       1567    |  567     8       2367    |
 |--------------------------+--------------------------+--------------------------|
 |  58      2       569     |  14589   7       14589   |  3       169     468     |
 |  378     36789   1       |  2489    2389    489     |  46789   2679    5       |
 |  4       3789    359     |  6       12389   1589    |  1789    1279    278     |
 |--------------------------+--------------------------+--------------------------|
 |  157     1479    459     |  3       1689    146789  |  2       1567    678     |
 |  12357   1379    8       |  1279    1269    1679    |  1567    4       367     |
 |  6       1347    234     |  12478   5       1478    |  178     137     9       |
 +--------------------------------------------------------------------------------+
 # 160 eliminations remain

This unfinned Jellyfish is perfectly legal/acceptable even though it contains two Locked Candidate 1 subpatterns.

Code: Select all
 unfinned Jellyfish c1389\r1389
 +-----------------------------------+
 |  X  *  X  |  *  *  *  |  *  X  X  |
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |  X  *  X  |  *  *  *  |  *  X  X  |
 |-----------+-----------+-----------|
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |-----------+-----------+-----------|
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |  X  *  X  |  *  *  *  |  *  X  X  |
 |  X  *  X  |  *  *  *  |  *  X  X  |
 +-----------------------------------+

When it's overlayed on the candidate grid, then coloring on the remaining vertices results in a contradiction.

Code: Select all
 finned Jellyfish c1389\r1389 (overlaying candidate grid)
 +-----------------------------------+
 |  X  *  .  |  .  .  .  |  .  X  .  |
 |  .  .  .  |  .  .  3  |  .  .  .  |
 |  .  *  X  |  .  .  .  |  .  .  X  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  .  |  3  .  .  |
 |  #  3  .  |  .  3  .  |  .  .  .  |
 |  .  3  #  |  .  3  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  3  .  .  |  .  .  .  |
 |  X  *  .  |  .  .  .  |  .  .  X  |
 |  .  *  X  |  .  .  .  |  .  X  .  |
 +-----------------------------------+

So, at least one of the fins must be true.

How can we determine if a candidate grid is unable to support an overlayed unfinned fish pattern?

Are we going to allow the use of fish patterns where the cover set does not intersect the elimination cells? After all, we're now allowing remote/Kraken fin cells that don't directly see the elimination cells. Why does the fish pattern have to contain the elimination cells?
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Re: The Ultimate FISH Guide

Postby JC Van Hay » Sat Jun 26, 2010 7:46 pm

I hope the following may help.
daj95376 wrote:This unfinned Jellyfish is perfectly legal/acceptable even though it contains two Locked Candidate 1 subpatterns.
Code: Select all
 unfinned Jellyfish c1389\r1389
 +-----------------------------------+
 |  X  *  X  |  *  *  *  |  *  X  X  |
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |  X  *  X  |  *  *  *  |  *  X  X  |
 |-----------+-----------+-----------|
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |-----------+-----------+-----------|
 |  /  .  /  |  .  .  .  |  .  /  /  |
 |  X  *  X  |  *  *  *  |  *  X  X  |
 |  X  *  X  |  *  *  *  |  *  X  X  |
 +-----------------------------------+
As X is a base candidate, which may be missing, this statement is only true iff the conditions that make it true or false are clearly and completely given. Further, we don't logically have the right to wave them off on account of the fact that they don't happen in a real valid puzzle, otherwise we could make false deductions with ambiguous almost fishes. Therefore, "this unfinned Jellyfish is perfectly legal/acceptable even though it contains two Locked Candidate 1 subpatterns, except in the case of a combination of 2 competing skyscrapers", for example.
daj95376 wrote:How can we determine if a candidate grid is unable to support an overlayed unfinned fish pattern?
daj95376 wrote:When it comes to fish, I place them into four categories ... all derived from real puzzles:

    1)...

    2)...

    3) A finned fish where at least one of the fins is true and the fish seems valid for the candidate.

    4) A finned fish where at least one of the fins is true and the fish is not valid for the candidate.
Finding a way to distinguish (3) from (4) could be interesting.
By being aware of the possibility of an invalid situation from the very start.
daj95376 wrote:Are we going to allow the use of fish patterns where the cover set does not intersect the elimination cells? After all, we're now allowing remote/Kraken fin cells that don't directly see the elimination cells. Why does the fish pattern have to contain the elimination cells?
What are the cover sets? Truly, IMHO, they are strong sets that must be added to the base sets to take into account all the Sudoku puzzle rules that are necessary to justify an elimination from the given base sets. In the Fish Advanced Solving Technique, it is supposed that the number of cover sets is at least equal to the number of base sets. The excess in number of cover sets are then implicitly distributed among the fins. One hopes that what remains either is useless, implicitly correct, obvious, ... (?) or justifies a NoFish elimination due to a lack of taking into account additional box-line interaction(s). Therefore, the eliminated candidate is implicitly weakly linked to a derived strong set made either of the fins or of some elements of the base sets or of both. However, as there is room for some ambiguity, the question remains : what is effectively, in practice, for a fisherman, the cover sets?
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