## The Ultimate FISH Guide

Advanced methods and approaches for solving Sudoku puzzles
hobiwan wrote:
tarek wrote:IMO, the term sashimi is redundant. Its constant use has plagued fish. I'm not sure why I feel like this, but I'm thinking that others may feel the same .

Definitly! But redefining the term as you propose might open another pandora's box and give you even more trouble. I stand with what I said before:
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`remove the term sashimi from the section "Shapes of fish"add a line that says that any finned fish that degenerates without the fins may be called sashimi`

This has beenmy aim for some time now....

The proposed changes (subject to approval by all) should be following this:

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`Naming of fish:the "Fish name" consists of 4 sections: 1st section describes the Fish degeneration status, the second section describes the Fish Fin(s) status, the third describes the Fish Shape and the fourth section describes the the Fish SizeAny fish therefore can be properly described in terms of DEGENERATION+FINS+SHAPE+SIZE`

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`Size of Fish:1. Cyclopsfish (a.k.a 1-Fish): All elements are in 1 sector * 1 sector2. X-wing (a.k.a 2-Fish): All elements are in 2 sectors * 2 sectors3. Swordfish (a.k.a 3-Fish): All elements are in 3 sectors * 3 sectors4. Jellyfish (a.k.a 4-Fish): All elements are in 4 sectors * 4 sectors5. Starfish (a.k.a Squirmbag a.k.a 5-Fish): All elements are in 5 sectors * 5 sectors6. Whale (a.k.a 6-Fish): All elements are in 6 sectors * 6 sectors7. Leviathan (a.k.a 7-Fish): All elements are in 7 sectors * 7 sectors`

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`Shape of Fish: 1.  Basic: N rows * N columns or vv.2.  Franken: N (rows+boxes) * N (columns+boxes) or vv. 3.  Mutant: N Sectors * N Sectors (Not described in 1-2)4.  Kraken: Any fish (1-3) that requires life support (information from outside the pattern)`

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`Fish Fin(s) status:1. Finned: if the fish has fin(s) (Review mini glossary)2. Unfinned: if the fish doesn't have fin(s) (Review mini glossary)`

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`Fish Degeneration status:1. Sashimi: in the abscence of fins, the fish ultra-structure degenerates into smaller-sized fish or into a single sector candidates.2. non-sashimi: in the abscence of fins, the fish ultra-structure DOESN'T degenerate into smaller-sized fish nor into single sector candidates.`

this would mean that a single is a degenerate form of 1-fish
this will cover all variants that have column-row constraints.

tarek

tarek

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### "hidden single" as a fish of order 1

tarek wrote:this would mean that a single is a degenerate form of 1-fish

a "hidden single" in a row ( or in a column )
is the fish of order 1 --
r\c ( or c\r )
-- i wouldn't call it "degenerate"

Pat

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### Re: "hidden single" as a fish of order 1

Pat wrote:i wouldn't call it "degenerate"

Any hidden single in whatever sector is a 1-fish.....

It falls under the umbrella of "degenerate" because it leaves a single sector candidate.

so in extreme use of the terms a hidden single is a Sashimi unfinned (basic, franken or mutant) 1-fish compared to the Non-Sashimi unfinned (basic, franken or mutant) 1-fish which are Locked candidates.

I know that hidden singles are locked candidates but I hope you can understand what I'm driving at.

tarek

tarek

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tarek, I meant "sashimi instead of finned" (editited my post to make that clear), but I will go with any version that properly defines "sahimi" und yours certainly does that, so no objections.
hobiwan
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tarek wrote:IMO, the term sashimi is redundant. Its constant use has plagued fish.

The only "plague" I'm aware of is that it takes some people a while to realize that a sashimi without a fin cell is not even a fish. With what is the term "sashimi" redundant?

daj95376 wrote:To the best of my knowledge, every Base/Cover Sector must have at least two candidate cells. I don't know if it's assumed or if it's been documented someplace.

Although that statement is not precise for frankens and mutants, I agree ... and it is documented. It's one of the first things I learned about basic fish.

hobiwan wrote:From a practical viewpoint, why should you bother whether the fish degenerates as long as it makes the same eliminations?

The issue is not about the eliminations made, but what the pattern is called. Do we use the term "naked quad" for two naked pairs in a sector? Do we use the term "jellyfish" for two x-wings on a single-digit grid. I think the answers are clearly "no."

Pat wrote:i like the beautiful simplicity of the fish definition.
both of these statements are true --
it is an X-wing.
it is a degenerate X-wing.

That "beauty" is for a single-digit constraint-set definition ... which is not the same as the traditional fish definition.
ronk
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ronk wrote:The only "plague" I'm aware of is that it takes some people a while to realize that a sashimi without a fin cell is not even a fish. With what is the term "sashimi" redundant?
The only useful thing about it was the reason why it was mentioned in the top post in the 1st place....

It provides a bridge between Nonsashimi finned fish basic fish & the more complex fish....

For a biginner it just tells you not be restricted when forming fish to a 2*2*2*.. formation.

otherwise, it has no impact on actual eliminations or even complexity. Finned fish, so waht if it's sashimi or not

What I'm also trying to say is that sashimi doesn't mean Finned & is not restricted to finned fish. the FOF thread didn't restrict the definition. It gave the name for specific variant. I didn't see any "ONLYs" there.

Things not mentioned in the FOF thread don't have to be wrong, redundant or contradictory.

tarek

tarek

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ronk wrote:
hobiwan wrote:From a practical viewpoint, why should you bother whether the fish degenerates as long as it makes the same eliminations?

The issue is not about the eliminations made, but what the pattern is called. Do we use the term "naked quad" for two naked pairs in a sector? Do we use the term "jellyfish" for two x-wings on a single-digit grid. I think the answers are clearly "no."

I think we talk about two different things. I try not to look at what a player would normally do or what seems clear, but to argue strictly from the definition in this thread to make that definition as complete as possible. And since a fish is defined here as N base sectors/N cover sectors your two x-wings are definitely a jellyfish. If you think this is nonsens, you have to add a degeneration constraint to the fish definition.
hobiwan
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My viewpoint -- expanded #1.

I always process N-Tuples, Locked Candidate (1), and Locked Candidate (2) before fish. This means that, if a candidate appears in a sector, then it appears in at least two cells of that sector. It also means that I'll never encounter fish patterns that are equivalent to these techniques.

As far as tarek's Sashimi unfinned fish goes, I think my technique hierarchy will make it extremely unlikely that I ever encounter one. That leaves Sashimi finned fish, which I simply call Sashimi fish.

If the fin cells are removed and the underlying unfinned fish (UUF) doesn't degenerate, then it's correct to say: at least one fin cell is true or else the UUF is true. If the UUF does degenerate, then it's more correct to say: at least one fin cell is true or else degeneration through lesser techniques occurs. To some people, the distinction in these two statements is important.

If degeneration occurs through an initial Hidden Single, like in a Sashimi (finned) X-Wing, then I think the Sashimi label should be included. If degeneration occurs through an initial Locked Candidate (1) or Locked Candidate (2), then I think the Sashimi label should be optional. Finally, if degeneration occurs through any other means, then I think the Sashimi label should be dropped -- even if the actual degeneration is the main point of the discussion.
daj95376
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sashimi means degenerate or self-destructive. Therefore 2 x-wings do not equate with sashimi.

you can combine those 2 x-wings into a Jellyfish to make a single step massive elimination if you choose to.

a sashimi fish is: A fish that in he abscence of fins degenrates into a single smaller fish or into single sector candidates.

how does it degenrate: using fish eliminations up to the level of fish in question.

I know that unfinned sashimi fish are covering up the smaller fish under there. the resultant eliminations remain, however, perfectly valid.

tarek

tarek

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[Withdrawn]
Last edited by daj95376 on Sat Feb 02, 2008 5:33 pm, edited 1 time in total.
daj95376
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### NON-DEGENERACY CONDITION FOR FISH

NON-DEGENERACY CONDITION FOR FISH

I'm very far from being acquainted with the whole fauna of the aquarium, but I occasionally glance at this very active thread and I just fell upon the above question of degeneracy.
I hope the following will help clarify this point.

In my book ("The Hidden Logic of Sudoku"), when I considered (Naked, Hidden and Super-Hidden) subset rules, I wanted to give definitions such that a Pair would never degenerate into a Single, a Triplet would never degenerate into a Pair or a Single, a Quad would never degenerate into a Triplet or worse. I proved that, in order to avoid such degeneracies, these patterns must be defined as follows :

Pair : {1 2} - {1 2} (rather obvious)
Triplet : {1 2 (3)} - {(1) 2 3} - {1 (2) 3} (with all links identical)
Quad : {1 2 (3) (4)} - {(1) 2 3 (4)} - {(1) (2) 3 4} - {1 (2) (3) 4} (with all links identical)

where:
- 1, 2, 3, 4 designate any different numbers,
- {} indicate a cell with all its candidates,
- cells must be different,
- parens indicate optional candidates.

Re-written as:
Pair : {1 2} - {1 2}
Triplet : {1 2 (3)} - {2 3 (1)} - {3 1 (2)} (with all links identical)
Quad : {1 2 (3) (4)} - {2 3 (4) (1)} - {3 4 (1) (2)} - {4 1 (2) (3)} (with all links identical)
this shows how close Pairs, Triplets and Quads are from xy2, xy3 and xy4 chains with no loop (neither global nor inner). Nevertheless (except Pairs), due to the optional candidates, they cannot be replaced by xy-chains. (I've shown that most, but not all, can be replaced by xyzt-chains.)

Now, applying the cn and rc symmetries, we get the general patterns for non-degenerate Swordfish and Jellyfish in rows, where all rows and columns must be different and 1 indicates the presence of the candidate under consideration (optional if between parens):

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` (Non-degenerate) Swordfish:      1 ------- 1 ------- (1)     (1) ------ 1 -------- 1   1 ------ (1) ------- 1(Non-degenerate) Jellysfish:      1 ------- 1 ------- (1) ------- (1)     (1) ------ 1 -------- 1 -------- (1)  (1) ----- (1) ------- 1 --------- 1   1 ------ (1) ------ (1) -------- 1`

Of course, the order of the rows and columns doesn't have to be as shown here.

When all candidates in parens are absent, we get what I used to call the skeletal fish; speaking of fishbones might be more appropriate from a zoological POV though.
I think including these non-degeneracy constraints in the definition of fish would make things simpler when we want to classify them.

Some variants of fish may have an impact on their skeleton, but they shouldn't allow the skeleton to degenerate into that of a smaller fish. I mean that not any candidate of the skeleton can be absent in the variant. Example of an acceptable variant:

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`(Non-degenerate) Finned-Sashimi Jellyfish:      1 ------- 1 ------- (1) ------- (1)     (1) ------ 1 -------- 1 -------- (1)  (1) ----- (1) ------- 1 --------- 1   1 ------ (1) ------ (1) -------- x ---- 1--- (1)where x indicates the missing candidate (and the lower left 1's, the fin, must be in the same block as x).`
denis_berthier
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### re: "hidden single" as a fish of order 1

Pat wrote:
tarek wrote:this would mean that a single is a degenerate form of 1-fish

a "hidden single" in a row ( or in a column )
is the fish of order 1 --
r\c ( or c\r )
-- i wouldn't call it "degenerate"

perhaps i should've been more emphatic in my statement --
this is how i see it --
a fish degenerates
if it contains another, "smaller" fish.
( "smaller" = of lower order;
often of order 1, but that's not a requirement.
)
a fish which degenerates [ verb ]
is called a degenerate [ adjective ] fish.
-- and therefore, a fish of order 1 ( whether a "hidden single" or a box-line interaction )
is never called a degenerate fish.

Pat

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### a _denenerate_ Jellyfish is still a Jellyfish

hobiwan wrote:
ronk wrote:
hobiwan wrote:From a practical viewpoint, why should you bother whether the fish degenerates as long as it makes the same eliminations?

The issue is not about the eliminations made, but what the pattern is called. Do we use the term "naked quad" for two naked pairs in a sector? Do we use the term "jellyfish" for two x-wings on a single-digit grid. I think the answers are clearly "no."

I think we talk about two different things. I try not to look at what a player would normally do or what seems clear, but to argue strictly from the definition in this thread to make that definition as complete as possible. And since a fish is defined here as N base sectors/N cover sectors your two x-wings are definitely a jellyfish. If you think this is nonsens, you have to add a degeneration constraint to the fish definition.

i agree with hobiwan -- a Jellyfish which degenerates into 2 X-wings is still a valid Jellyfish -- not a Jellyfish which i'm likely to use but still valid
indeed if you try gsf's software with only Jellyfish enabled ( i.e. disabling fish of other sizes ),
i'm sure the software will find and use such a Jellyfish

Pat

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Denis Berthier wrote:Now, applying the cn and rc symmetries, we get the general patterns for non-degenerate Swordfish and Jellyfish in rows ...

That's an interesting way to get there.

hobiwan wrote:And since a fish is defined here as N base sectors/N cover sectors your two x-wings are definitely a jellyfish. If you think this is nonsense, you have to add a degeneration constraint to the fish definition.

Pat wrote:i agree with hobiwan -- a Jellyfish which degenerates into 2 X-wings is still a valid Jellyfish -- not a Jellyfish which i'm likely to use but still valid
indeed if you try gsf's software with only Jellyfish enabled ( i.e. disabling fish of other sizes ),
i'm sure the software will find and use such a Jellyfish

You folks have your opinion, but for me ...

When a pattern of order N = R + S subsumes two patterns -- of identical type -- with orders R and S, the pattern order is R if R <= S, else the order is S.
Last edited by ronk on Tue Feb 05, 2008 1:27 am, edited 1 time in total.
ronk
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I think I would agree that two X-wings do not a Jellyfish make. I would also agree with adding a non-degeneracy requirement to fish to make this clear. Also to me sashimi is just a type of finned fish. Its importance is only to make clear to fisherpeople that a fin can exist even without a cell which is part of the main fish. The definition that a sashimi fish degenerates when the fin is removed is a valid technical distinction, but doesn't differentiate three classes of fish, that is, unfinned, finned and sashimi. I only see two, finned and unfinned.
Mike Barker

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