The New Sudoku Players' Forum

[Pat]

SpAce, your comments about the terminology
arose naturally in the present discussion --
but will be lost here.

they would fit well in "The Ultimate FISH Guide"

[SpAce]

Pat, I can't judge if my comments have enough merit to fit in the UFG -- and I don't want to cause unnecessary confusion or beat a dead horse in such a holy reference guide -- but if someone does think so, perhaps a moderator could move this side discussion there?

[tarek]

My own example difficult to argue with that!

In principle I have no problem how you construct the fish. My only worry is the confusion that has/still is around the term sashimi. You have correctly used the word Finned & decided not to use the word sashimi (which is fine, although the fish construct degenerates without the fins). You added the term headless to describe the line that has no 7s which is also fine. So in all these you have done correctly and didn't contradict the definitions.

Although a basic franken fish does the job it doesn't mean that your use wasn't correct. A simple search on solver will tell you how many fish do exist simultaneously which do the same job! You solve regularly & you use different techniques at will so I can't see why you shouldn't use these terms if they are easier to spot & they don't contradict the UFG as long as you can help the people who are going to ask you questions about these terms (with greater knowledge comes greater responsibility )!

tarek

[SpAce]

In principle I have no problem how you construct the fish. My only worry is the confusion that has/still is around the term sashimi. You have correctly used the word Finned & decided not to use the word sashimi (which is fine, although the fish construct degenerates without the fins).

But what does it degenerate into? It seems to me that a Headless fish (at least this example which is pretty much the only one I've seen) would degenerate into a deadly pattern if all fins were removed, so it can't exist without fins in a valid puzzle. That's in conflict with your earlier Sashimi definition:

Sashimi would refer to the ability to reduce the fish to simpler fish in the absence of fins. In these specific terms, you don't need to have fins to have a sashimi fish.

Based on that, would it be even correct to say "Headless Sashimi", if a finless & headless fish would reduce into a deadly pattern instead of a simpler fish (as per your Sashimi definition)? In that light I would also understand better that you insist using "Finned Sashimi" because Sashimi could be finless too (if not very useful). On the other hand, it seems that a Headless fish can't even exist in a finless form, so "Finned Headless" seems actually redundant. So, perhaps Headless should just be "Headless", defined (partly) by its finless form being a deadly pattern, without any other qualifiers like Finned (redundant) or Sashimi (slightly incorrect)? What do you think of these observations?

Although a basic franken fish does the job it doesn't mean that your use wasn't correct. A simple search on solver will tell you how many fish do exist simultaneously which do the same job!

I use mainly Hodoku and it does have an excellent fish finder, but it doesn't report headless fishes (I presume it's because that concept had probably been dropped from the UFG before it was programmed). That's why that variant has remained a bit of a mystery to me, having only seen it mentioned in old discussions. This discussion has already helped a lot in solving that mystery, so thank you! Maybe I'll use Hodoku to find some Franken Fishes and then try to spot the corresponding Headless Fishes to see some more examples.

You solve regularly & you use different techniques at will so I can't see why you shouldn't use these terms if they are easier to spot & they don't contradict the UFG as long as you can help the people who are going to ask you questions about these terms (with greater knowledge comes greater responsibility )!

Well, I'm always glad to help anyone if I can, and I surely don't want to worsen anyone's confusion (including my own) if I can help it (but of course I sometimes fail). I'm still not sure if the headlessness is an actually useful concept worth reviving, or a potentially confusing distraction, but from what I've learned now, I think there's a slight chance that it might in some cases help spotting Franken Fish eliminations by providing an additional POV to the same. I'll have to investigate more to know for sure. Being a poor fisherman in the first place makes it all the more interesting

[tarek]

SpAce, your comments about the terminology
arose naturally in the present discussion --
but will be lost here.

they would fit well in "The Ultimate FISH Guide"

I think that the last exchanges are actually a very good addition to the UFG!!!

But what does it degenerate into? It seems to me that a Headless fish (at least this example which is pretty much the only one I've seen) would degenerate into a deadly pattern if all fins were removed, so it can't exist without fins in a valid puzzle. That's in conflict with your earlier Sashimi definition

This is very interesting ... Not just because the definition of Sashimi is to be looked at but also because this means that the fin(s) must be true. So anything that sees all the fin(s) can be eliminated.

This supports the fact that the headless fish has to be finned as it can't exist in a non finned form which brings us to your second point.
The term "Headless" can be added as a special quality when naming a fish but here is where we need to be careful. In theory a fish could be headless +/- finned +/- sashimi .... if that is not possible (because of what we mentioned above) then it has to be mentioned explicitly to avoid any confusion when we make amendments!

Let me dig deeper & investigate a bit more before making any generalisations. I have no problem revising or amending any definition btw

tarek

[SpAce]

This is very interesting ... Not just because the definition of Sashimi is to be looked at but also because this means that the fin(s) must be true. So anything that sees all the fin(s) can be eliminated. This supports the fact that the headless fish has to be finned as it can't exist in a non finned form

Exactly. That makes me wonder if the Headless Fish type should be considered a fish at all (through that POV -- it's still a valid Franken Fish, of course), because it does not follow the conventional logic of finned fishes: either one or more of the fins is true OR the (finless) fish is true, which is the same logic as with any almost-Pattern. In the case of the Headless variant there's no OR in that statement because the (finless) fish can't be true. Thus the logic is like that of DPs, because the fins act as guardians instead of spoilers (at least one of them must be true). I think it's quite a significant difference: instead of an almost-valid-fish with spoiler-fins we have an almost-illegal-fish with guardian-fins.

Then again, if a finned fish is considered a valid fish form by itself instead of an almost-fish, then I guess the headless variant can be included in the fish family. Otherwise it seems kind of questionable.

I'm not sure yet, but I might be inclined to put the Headless variant into a different family at this point, because the logic used in chains is slightly different between almost-Valid-Patterns and almost-Deadly-Patterns. That's not to say it's a useless concept at all. DPs are very useful in general, so it might not be a bad idea to learn to recognize illegal fish patterns as well and to use their guardians for "dark logic" (as Allan Barker calls it). It just might deserve its own treatment apart from normal fishing.

Let me dig deeper & investigate a bit more before making any generalisations. I have no problem revising or amending any definition btw

Yes, I think this is worth thinking through because it doesn't seem to be as simple as I initially thought.

[SpAce]

Btw, about that Headless Fish example and its Franken Fish counterpart... The Franken Fish I presented was the only one Hodoku found for that situation. I kind of wondered why it was so different from the Headless one, but I generally trust Hodoku's fishing skills much more than my own (for a good reason) so I didn't really doubt it was the only one available. However, now that I looked at it again, I thought I found manually another Franken Fish that actually uses the same cells as the Headless one:

Code: Select all

.------------------.----------------.--------------------.
| 567    2456  247 | 1   8     467  | 456-7   9     3    |
| 1678   468   3   | 5   2479  4679 | 1468   *267  *478  |
| 15678  9     147 | 3   247   467  | 14568  *267  *4578 |
:------------------+----------------+--------------------:
| 138    238   12  | 6   47    38   | 47      5     9    |
| 4      7     5   | 89  39    2    | 68      36    1    |
| 368    368   9   |*47  1     5    | 2      *37    48   |
:------------------+----------------+--------------------:
| 39     34    8   | 2   4579  479  | 57      1     6    |
| 2      1     6   |*78  35    38   | 9       4    *57   |
| 579    45    47  | 49  6     1    | 3       8     2    |
'------------------'----------------'--------------------'

Franken Swordfish: (7)c489\r68b3 => -7 r1c7

So, I wondered why Hodoku missed that one, but then found a setting: "Only one fish per elimination". When I turned that off, Hodoku also found the same fish and quite a few others as well. Yes, it's still a better fisherman than me (However, I'm still wondering why it doesn't report the grouped X-Chain I mentioned.)

[tarek]

Btw, about that Headless Fish example and its Franken Fish counterpart... The Franken Fish I presented was the only one Hodoku found for that situation.

The more I look at this specific headless fish example, the more shaky it looks ... As the fish body is a deadly pattern this defaults to the fin(s) being true which is not what I think should happen.

This awkward situation happens because it was headless ... It is not an equivalent to the Franken fish because it can't eliminate rows 6 and 8 as the franked could. As I said, the more I look at it the bigger the headache.

tarek

[StrmCkr]

edit: As an afterthought, I think I've seen somewhere a definition that says something about all cover sectors coinciding with at least one base candidate, or something like that. Is it in the UFG?

correct r1, couldn't be used as a cover sector as it includes zero base candidates.

Code: Select all

.------------------.----------------.--------------------.
| 567    2456  247 |*1   8     467  | 456-7  *9    *3    |
| 1678   468   3   | 5   2479  4679 | 1468   #267  #478  |
| 15678  9     147 | 3   247   467  | 14568  #267  #4578 |
:------------------+----------------+--------------------:
| 138    238   12  | 6   47    38   | 47      5     9    |
| 4      7     5   | 89  39    2    | 68      36    1    |
| 368    368   9   |*47  1     5    | 2      *37   *48   |
:------------------+----------------+--------------------:
| 39     34    8   | 2   4579  479  | 57      1     6    |
| 2      1     6   |*78  35    38   | 9      *4    *57   |
| 579    45    47  | 49  6     1    | 3       8     2    |
'------------------'----------------'--------------------'

C489/B3R68 => R1C7 <> 7

not sure why you are adding *'s to R1C89 & R6C9, R8C8....
the basic idea for the fish pattern was that not all the x's needed to be present for the eliminations to be sound.
as it would also eliminate R23,C7 <> 7 {if they are present}

to me its making the franken fish needlessly complicated by dissection of each unit used as "finned" or sashimi.

{ sashimi to my understanding is a "fin" location lacking the direct connecting vertices and if all where lacking would create cannibalistic fish }
{finned - to my understanding is "fin" location where the vertices is present + an extra candidate(s)

vertices - is single cell or grouped cells that connect to another sector.
direct vertices - is line of sight to the connection point.
fin - is a subset section of a sector where 1-3 candidates may be present creating a forming the linking vertices. {box * row = 3 cells.}


here another example an extend empty rectangle version with same eliminations.

B6C49 / C7R68B3 -> R1C7<> 7

Code: Select all

+------------------+------------------+---------------------+
| 567    2456  247 | 1     8     467  | 456-7  9     3      |
| 1678   468   3   | 5     2479  4679 | 1468   267   48(7)  |
| 15678  9     147 | 3     247   467  | 14568  267   458(7) |
+------------------+------------------+---------------------+
| 138    238   12  | 6     47    38   | 4(7)   5     9      |
| 4      7     5   | 89    39    2    | 68     36    1      |
| 368    368   9   | 4(7)  1     5    | 2      3(7)  48     |
+------------------+------------------+---------------------+
| 39     34    8   | 2     4579  479  | 57     1     6      |
| 2      1     6   | 8(7)  35    38   | 9      4     5(7)   |
| 579    45    47  | 49    6     1    | 3      8     2      |
+------------------+------------------+---------------------+

Finned Franken Jellyfish: 7 c47b69 r168b3 efr4c7 efr7c7 => r1c7<>7

Code: Select all

+------------------+------------------+-------------------+
| 567    2456  247 | 1     8     467  | 456-7  9     3    |
| 1678   468   3   | 5     2479  4679 | 1468   267   478  |
| 15678  9     147 | 3     247   467  | 14568  267   4578 |
+------------------+------------------+-------------------+
| 138    238   12  | 6     47    38   | 4(7)   5     9    |
| 4      7     5   | 89    39    2    | 68     36    1    |
| 368    368   9   | 4(7)  1     5    | 2      3(7)  48   |
+------------------+------------------+-------------------+
| 39     34    8   | 2     4579  479  | 5(7)   1     6    |
| 2      1     6   | 8(7)  35    38   | 9      4     5(7) |
| 579    45    47  | 49    6     1    | 3      8     2    |
+------------------+------------------+-------------------+

the only oddity i've found not covered by the ufg is this:
when i was coding my version of obi wans fish solver with out recycling base/cover units i noticed all fish have a limitation of +2 max extra fin sectors.
doing that i notices that 1-fish cannot have +2 sectors by default as it would have zero eliminations as all cover digits would be in the base.
but eliminations are applicable: leading to this idea.

inverted fish, where a cover sector has no candidates outside the base.

Code: Select all

.---------------------------------.---------------------------------.---------------------------------.
| 123456789  123456789  123456789 | 23456789   23456789   23456789  | 23456789   23456789   23456789  |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
'---------------------------------'---------------------------------'---------------------------------'

the normal cyclopes fish for R1/B1 -> r2c123,r3c123<>1

can also be written as a b1/R123 {+2 fin sectors}
where R23 in box 1 can be eliminated as r1 has no extra candidates outside the box. {thus the base is limited by contained cover sector}
any other cover sector inside the base sector could be eliminated. {keyed to the cols of the r1.}

this interesting idea is the bases for this topic http://forum.enjoysudoku.com/no-fish-20-19-15-t33873.html
which is still pending testing.

[tarek]

all where lacking would create an auto cannibalistic fish }

I think we agreed to drop the "auto"

Returning to our headless fish, It appears that:
1. A headless fish has to be finned
2. In a headless fish the fin(s) must be true
confirming SpAce's suspicions.

Code: Select all

. . . | . * . | * * -
. . . | . | . | # # -
. . . | . | . | # # -
------+---|---+-|-|--
. . . | . | . | | | .
- - - | - X - | X X -
. . . | . | . | | | .
------+---|---+-|-|--
. . . | . | . | | | .
. . . | . | . | | | .
- - - | - X - | X X -
Headless Swordfish c578/r158
X actual vertix
* absent vertix
# fin
- eventual elimination (EE)

. * . | . * . | * * -
. | . | . | . | # # -
. | . | . | . | # # -
------+---|---+-|-|--
. | . | . | . | | | .
- X - | - X - | X X -
- X - | - X - | X X -
------+---|---+-|-|--
. | . | . | . | | | .
. | . | . | . | | | .
- X - | - X - | X X -
Headless Jellifish c2578/r1568
X actual vertix
* absent vertix
# fin
- eventual elimination (EE)


I made the above to illustrate how our headless fish works. In both examples the headless fish must have the fin(s) true or it would create a deadly pattern (n base sectors with n-1 candidates to fill them). This eventuality would cascade to allow all the eliminations that you would see in the Franken fish (c578/b1r58 & c2578/b1r568) where the fins of the headless fish become vertices in the franken fish. This is why I would favour the Franken fish in this situation and banish this headless creature to deepest part of the ocean!!!

What do you think? If the headless creature is easier to spot, then another quick search would show you the franken nature!!!

edit: As an afterthought, I think I've seen somewhere a definition that says something about all cover sectors coinciding with at least one base candidate, or something like that. Is it in the UFG?

correct r1, couldn't be used as a cover sector as it includes zero base candidates.

Should we say "In a fish cover sector there has to be at least 1 vertex"?


tarek
[Edit: added diagrams]
[Edit2: added the vertex v cover statement]

[SpAce]

Hi tarek! Thanks for the analysis! One quick note on my part. I'd drop the row and extra box eliminations and only accept the single elimination in r1c9 (in your diagrams) when using the headless fish POV. That way it uses the normal finned rc fish logic where the eventual eliminations have to see all fins and be on a cover line, which is pretty easy to understand. (Well, the logic is not exactly normal anyway because there are no true vertices on the eliminating cover line -- a point that still requires further analysis and a review of definitions, I think, before the concept is accepted in the fish family).

I think the main benefit of possibly keeping the headless concept is its similarity to finned basic fishes, and thus easier learning curve for most players, and adding those extra eliminations breaks that benefit by making it actually more complicated to understand than its Franken Fish counterpart. The other eliminations are valid through the Franken Fish POV, of course, but since we're not using that POV, that logic should not be assumed here, imho. Understanding and explaining those eliminations gets really complicated otherwise, and I'd rather drop the whole headless fish concept and stick to Franken Fishes (with which the explanation is simple).

I've recently looked at the old threads where these concepts (headless / franken) were born and this exact point was debated. Even some very smart players seemed to be very confused about those extra eliminations, and the explanations weren't trivial -- except with the Franken Fish POV using boxes as cover sets. Thus I'd reserve those eliminations for the Franken Fish POV, and only use the Headless POV as a possible finding tool for Franken Fishes (or if the single elimination is enough).

[SpAce]

not sure why you are adding *'s to R1C89 & R6C9, R8C8....

Hi StrmCkr! If I remember correctly, I just copy-pasted tarek's diagram from an old thread (which I linked to) -- edit: it was not a copy-paste but effectively the same diagram anyway. Back then at least Myth Jellies also used that style of marking all vertices whether true or virtual. Personally I like it because it makes the fish shape easy to see. I'd like it even better if the true vertex (and maybe fin) candidates were highlighted with brackets or something, so that it would be easier to recognize sashimi and headless variants (and to see the fish digit anyway).

[SpAce]

I guess the whole controversy started here (with the same sample):

http://forum.enjoysudoku.com/post23274.html#p23274

Here's Myth Jellies' explanation of the evolution of the skinny / headless / franken fish. Note the complicated explanations for the extra eliminations:

http://forum.enjoysudoku.com/post23785.html#p23785

Anyway, I think the remaining questions for us here and now are these:

1) Should the Headless variant be accepted as a fish at all? I don't have a definite opinion yet, but I do think it's a bit weird because of the 0 true vertices cover line and the resulting DP+guardians nature. I guess it mainly depends on the definitions of "fish" and possibly more generic definitions of base\cover logic. I think this part should be thought through carefully, so that no inconsistencies are introduced.

2) If the Headless fish is accepted as a fish, which direct eliminations are accepted? I already stated my rather strong opinion on this. I think it should be treated like a basic (rc) finned fish, so only eliminations that are on a cover line and see all fins directly should be accepted. Eliminations that are valid only through the Franken Fish POV or some complicated logic should not be included. Otherwise we lose the main benefit of simplicity, and instead introduce possibly the most complicated fish type to understand and explain.

3) Is the Headless fish equal to a Franken Fish? Based on my answer to the previous question, my answer here is no. Even if they use the exact same cells, the logic is very different and their eliminations don't need to match. The Franken Fish is inherently more powerful, and there's no reason to give the same powers to the Headless Fish. Despite the common history of one evolving from the other, they're logically two different things and should be treated as such. Besides, the current definition of Franken Fish is different from what it was originally, so they're not even directly related any longer.

4) What is the main argument for keeping the Headless fish type? I think there's an agreement on this: it offers a basic finned fish type of POV which might help find eliminations that would otherwise require recognizing a Franken Fish. There are probably many more players who understand basic finned fishes than those who understand Franken Fishes, so it makes a pretty strong argument. For those who are familiar with Franken Fishes, it might still provide another way to find them.

5) How often do they occur? That is, does it make sense to have such a very special case confusing matters and possibly breaking definitions, if it's very rare? I have no idea of their frequency, but I would guess they're not very common.

[StrmCkr]

"Should we say "In a fish cover sector there has to be at least 1 vertex"? "

I know with coding my engine...
when it uses active pencil marks vrs pesduo active marks this little tidbit generates hundreds of thousands of fish that aren't valid. By selecting any of the 27 cover that intersect the base sets and generates lots of errors. (as it could grab spots with off digits as still there)

Specifically when it goes to the nxn+K sections
Like an xwing it would add on extra intersecting sections for 2x2+1 and spit out lots sectors worth of invalid eliminations by the elimination. Rules.

To me the # fins aren't actually covered by any cover sector. Meaning the fish would still have to be a 4x4+1
And include the box anyway. (or row 23)
not exactly how nxn rules work, but that's how nxn+K works.

But still with out base digits included in the selected cover set, the cover set mathematically accounts for 0 placed digits.
However that's actuak digits vrs pesdeo.

So the question is are we talking theoretical fish or practical... If it's theoretical the fish really isn't headless as the * cells are real, then r1 is valid part of the cover and the box or r23 needs to be added for completion. (or used as fin spots as seen in nxn fish)

[SpAce]

Would XSudo allow using a link (cover) that has no candidates connected to the truths (bases)? I don't know because I haven't used that software, but somehow I would bet that such a rogue link wouldn't work. Could someone test that on our sample headless fish?

From what I understand, XSudo is a pretty good reference and might give a hint whether we should consider the headless variant a logically valid structure or not. I'm more and more inclined to think that it's not, and if so, then the concept should only be listed as a possible spotting aid instead of an actual fish type. The fact that the eliminations are valid is no proof of the validity of the logic.