The New Sudoku Players' Forum

by **tarek** » Mon Nov 12, 2018 10:02 am

SpAce wrote:Would XSudo allow using a link (cover) that has no candidates connected to the truths (bases)?

I don't know as I haven't used Xsudo for years. My guess as a programmer that it wouldn't build it as a basic fish becuase one of the cover sectors doesn't have a base candidtae!

Returning to the question if this headless creature should be considered a UFG fish (albeit a special case) or not:

1. I demonstrated the logic behind the Headless creature elimination. It is based on the fact that the Fish body is false therefore forcing the fin(s) to be true which then forces the elimination that you would see in the basic finned fish setup. The logic is not "Either the fish is true or the fin(s) are true" anymore like in our UFG fish. That is one point against calling it a UFG fish.
2. I also demonstrated how the in this headless creature the fins(s) truthfulness cascades to eliminate all PEs in the cover rows that have vertices which is what a franken fish does. It is therefore a UFG Franken fish in disguise & not an equivalent. That us another point against calling it a UFG fish.

3. It is constructed like a basic finned fish & appears to eliminate like a basic finned fish. That is the only point in favour of calling it a UFG fish

In balance IMO it shouldn't be a UFG fish. With the presence of many non-UFG creatures I can't see why you shouldn't use it if it is easier to spot though. This discussion (which can be referenced if needed) would explain why it is a valid elimination despite not being a UFG fish. It also can be used (pending examples to say otherwise) to catch a more complex UFG fish which would have been difficult to spot otherwise.

Regarding what rule should we use to exclude these creatures from the UFG. StrmCkr used the term "Cover sector that doesn't include a base candidtae" which is very clear & makes it easy for Fish catching programs to miss/skip this creature. I used "cover sector that doesnt include a vertex" so that the rule would also span all Mutant fish constructions (even cannibalistic). We obviously need more examples of these creatures in more complex setups.

For the time being my simple rule to exclude this fish from the UFG would be:

Code: Select all: When candidates are mapped on a n/n base/cover fish construct: If the fish body is false then the creature is not a fish

I will dig into some of my old Human style solver versions to see if I have something already setup to catch Headless creatures (essentially they are badly designed fish catchers :oops:

)

tarek

by **SpAce** » Mon Nov 12, 2018 10:58 am

I think we're very much on the same page here! I'm quite happy if this creature is not counted as a UFG fish.

tarek wrote:
SpAce wrote:Would XSudo allow using a link (cover) that has no candidates connected to the truths (bases)?
I don't know as I haven't used Xsudo for years. My guess as a programmer that it wouldn't build it as a basic fish becuase one of the cover sectors doesn't have a base candidtae!

I would guess so too. Would be nice if someone (StrmCkr?) confirmed it, though. If it works, it should be a rank 1 structure, while the corresponding Franken Fish has rank 0. Anyway, the Xsudo documentation says:

Covering sets are the links that exactly cover the base candidates. A group of covering sets is any group of links containing all candidates in the base sets where no link can be removed and the candidates remain covered.
...
When counting rank or searching for a solution of covering sets: The links must form a group of covering sets, i.e., cover all candidates with no redundancies.

Those points alone suggest that it might be impossible to build our headless fish as an XSudo construct, because the r1 cover set would clearly be redundant (covering zero base candidates).

by **StrmCkr** » Mon Nov 12, 2018 6:13 pm

Code: Select all: +--------------------+-------------------+------------------------+ | 56(7) 2456 24(7) | 1 8 46(7) | 456(-7) 9 3 | | 1678 468 3 | 5 2479 4679 | 1468 26(7) 48(7) | | 15678 9 147 | 3 247 467 | 14568 26(7) 458(7) | +--------------------+-------------------+------------------------+ | 138 238 12 | 6 47 38 | 47 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 | +--------------------+-------------------+------------------------+

it doesn't list it as a fish under its engine, but it can find the elimination

which is very clear & makes it easy for Fish catching programs to miss/skip this creature.

i mentioned earlier a fish engine that uses actual pencil marks the "cover sector that doesn't include a vertex" would skip these creatures as the vertex's are missing. {and not having this rule generates loads of odd errors}

however when i swap my code back to theoretical:
in pseudo pencil mark {where all the cells are active for the base & cover set intersections }
then the creature is found, and its not "headless" {nothings missing}

the problem arises when you start extrapolating the "not all " x's need to be present mentioned in UFG for the fish to function
then you end up with degenerative fish that appears to break the 'cover sector that doesn't include a vertex' rule when the fish was valid in the pseudo stage.

personally I use nxn+k fish as it does away with all the " endo,exo fins cells" and uses K sectors where any of the "n+k" sectors used acts as the "fin sector"
the math for it makes eliminations easily including the ones the "headless fish" seems to have a difficult time explaining.

N x N+K: Show

nxn uses peers of "fin cells" to see the elimination"

U.F.G: Show

I pointed out the limitations of this setup here:
and suggested updating the elimination rules to include those limitations. {how not sure}

anyway long winded post that may have strayed.....I wouldn't include the degenerate "headless fish" example in the UFG as its missing the cover vertex rule
the pseudo fish that it derived from is usable in the ufg as it includes the rule.

Code: Select all: Fraken sword. C489 / R68B3 +------------------+-----------------+----------------+ | 1 1 1 | . 1 1 | -1 (1) (1) | | 1 1 1 | . 1 1 | -1 (1) (1) | | 1 1 1 | . 1 1 | -1 (1) (1) | +------------------+-----------------+----------------+ | 1 1 1 | . 1 1 | 1 . . | | 1 1 1 | . 1 1 | 1 . . | | (-1) (-1) (-1) | (1) (-1) (-1) | (-1) (1) (1) | +------------------+-----------------+----------------+ | 1 1 1 | . 1 1 | 1 . . | | (-1) (-1) (-1) | (1) (-1) (-1) | (-1) (1) (1) | | 1 1 1 | . 1 1 | 1 . . | +------------------+-----------------+----------------+

Code: Select all: C489 / R168 + Box 3 (indicates that r1 is superfluous} +------------------+-----------------+----------------+ | (1) (1) (1) | . (1) (1) | (-1) (1) (1) | | 1 1 1 | . 1 1 | (-1) (1) (1) | | 1 1 1 | . 1 1 | (-1) (1) (1) | +------------------+-----------------+----------------+ | 1 1 1 | . 1 1 | 1 . . | | 1 1 1 | . 1 1 | 1 . . | | (-1) (-1) (-1) | (1) (-1) (-1) | (-1) (1) (1) | +------------------+-----------------+----------------+ | 1 1 1 | . 1 1 | 1 . . | | (-1) (-1) (-1) | (1) (-1) (-1) | (-1) (1) (1) | | 1 1 1 | . 1 1 | 1 . . | +------------------+-----------------+----------------+

Code: Select all: C478/ R12368 {this one wont work under nxn+k or nxn but works in link-sets seen in xsudoku} {R123 coverts to box 1,2,3} box 3 being the key as the other 2 cant be used. +------------------+-----------------+----------------+ | (1) (1) (1) | . (1) (1) | (-1) (1) (1) | | (1) (1) (1) | . (1) (1) | (-1) (1) (1) | | (1) (1) (1) | . (1) (1) | (-1) (1) (1) | +------------------+-----------------+----------------+ | 1 1 1 | . 1 1 | 1 . . | | 1 1 1 | . 1 1 | 1 . . | | (-1) (-1) (-1) | (1) (-1) (-1) | (-1) (1) (1) | +------------------+-----------------+----------------+ | 1 1 1 | . 1 1 | 1 . . | | (-1) (-1) (-1) | (1) (-1) (-1) | (-1) (1) (1) | | 1 1 1 | . 1 1 | 1 . . | +------------------+-----------------+----------------+

in all honesty this is a degenerative case from this starting point.

Code: Select all: Finned Sword fish. R1C489 are all missing from the "headless" fish.

Code: Select all: C489/R168B3 +---------+-----------+--------------+ | 1 1 1 | (1) 1 1 | -1 (1) (1) | | 1 1 1 | . 1 1 | 1 (1) (1) | | 1 1 1 | . 1 1 | 1 (1) (1) | +---------+-----------+--------------+ | 1 1 1 | . 1 1 | 1 . . | | 1 1 1 | . 1 1 | 1 . . | | 1 1 1 | (1) 1 1 | 1 (1) (1) | +---------+-----------+--------------+ | 1 1 1 | . 1 1 | 1 . . | | 1 1 1 | (1) 1 1 | 1 (1) (1) | | 1 1 1 | . 1 1 | 1 . . | +---------+-----------+--------------+

when R1C4 is missing this turns into the fraken sword as r1 is dropped for box 3 exclusively.

by **SpAce** » Mon Nov 12, 2018 11:23 pm

StrmCkr wrote:it doesn't list it as a fish under its engine, but it can find the elimination

Thanks. However, what I really meant was: can you manually build a logic construct using truths and links as implied by the headless fish? I think the truths should be c489 and the links r168b3. The question is, does Xsudo accept that configuration and specifically the link r1? Of course it can find the elimination, but does it accept that specific type of logic to arrive at it? I'd be surprised if it did.

by **StrmCkr** » Tue Nov 13, 2018 12:08 am

Code: Select all: +--------------------+-------------------+------------------------+ | 56(7) 2456 24(7) | 1 8 46(7) | 456(-7) 9 3 | | 1678 468 3 | 5 2479 4679 | 1468 26(7) 48(7) | | 15678 9 147 | 3 247 467 | 14568 26(7) 458(7) | +--------------------+-------------------+------------------------+ | 138 238 12 | 6 47 38 | 47 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 | +--------------------+-------------------+------------------------+

that is a copy using those exact links you requested, done manually. {in previous post}
the fish algorithm it has built in dose not identify it as a valid fish, nor does this copy paste identify it as a "fish" type when pasted in.{ it comes up as a "cannibalistic logic" }
when i remove r1 it shows up as the franken sword.

it can't build it as it has no connecting "links". {thus not found in the fish finder it uses}

by **SpAce** » Tue Nov 13, 2018 6:15 am

StrmCkr wrote:that is a copy using those exact links you requested, done manually. {in previous post}

Ok, thanks!

the fish algorithm it has built in dose not identify it as a valid fish, nor does this copy paste identify it as a "fish" type when pasted in.

That does not surprise me.

{ it comes up as a "cannibalistic logic" }

But this does! How is it cannibalistic? I don't see it eating its own base candidates. The elimination should be in two cover sets only.

when i remove r1 it shows up as the franken sword.

As expected.

it can't build it as it has no connecting "links". {thus not found in the fish finder it uses}

I wouldn't expect the fish finder to recognize it as a valid fish. I'm more interested in what the generic logic engine says about it, and now I'm a bit confused about the results. Based on what you wrote, it seems that it did accept it somehow and produced the elimination, which surprises me. Or did I misunderstand? The cannibalism part is really weird anyhow.

by **StrmCkr** » Tue Nov 13, 2018 6:24 am

Code: Select all: { it comes up as a "cannibalistic logic" }

because its trying to treat R1 as a Base sector not a cover.

by **SpAce** » Tue Nov 13, 2018 7:04 am

StrmCkr wrote:
Code: Select all
{ it comes up as a "cannibalistic logic" }
because its trying to treat R1 as a Base sector not a cover.

Thanks, that's what I thought! So I guess we can conclude that Xsudo doesn't accept the logic of the headless fish after all, if it tries to circumvent it like that. Based on that observation, I would be ready to deem the headless fish logic invalid and thus the creature itself imaginary. Headless chickens may fly but headless fish don't swim! It's good to know, though, that some Franken Fishes are capable of inducing hallucinations of such imaginary monsters. Perhaps that might sometimes help catch one of those *real* frankens, so I'll keep that in mind! Phew. I think I'm ready to let this go now

by **Yogi** » Tue Nov 20, 2018 9:41 pm

.94.3.5276..972814.7..4563996.28.47..27..4....4...7..2.1.4..7984867192537.9.28146
Just when you think you’ve got it sorted! There are other ways to solve this puzzle, but Hodoku lists it as a Sashimi XWing.
I can’t find it in 1, 3 or 5, and I don’t think there is anything else.

by **SpAce** » Wed Nov 21, 2018 6:11 am

Yogi wrote:.94.3.5276..972814.7..4563996.28.47..27..4....4...7..2.1.4..7984867192537.9.28146
Just when you think you’ve got it sorted! There are other ways to solve this puzzle, but Hodoku lists it as a Sashimi XWing.
I can’t find it in 1, 3 or 5, and I don’t think there is anything else.

You're right that it can only be in 1, 3, or 5, as keith's technique would tell us. Btw, thanks for advertising that technique -- it's proved useful in narrowing down the possibilities more quickly! Anyway, since you're using Hodoku, it can just as well tell you where the fish is hiding, right? I don't think you need us for that, and I don't know what further insights I could give for spotting it either (it's not exactly obvious to me either, so don't beat yourself for not seeing it).

As you say, there are other ways to solve this puzzle, and I think it's a bit unfortunate that Hodoku's default solving hierarchy lists the (Finned) Sashimi X-Wing as its first choice here. I'm pretty sure most human solvers would find other techniques easier. An ungrouped X-Chain of length 6 or even Simple Coloring using pure conjugate links would do the trick, and they're definitely easier than spotting a double-finned Sashimi X-Wing, aka Grouped Skyscraper, imho. With a single fin cell it would be just a normal Skyscraper, but the double-fin makes it harder to spot.

PS. This puzzle has a few larger Finned/Sashimi fishes too, so it can be used for generic fishing practice (especially with the help of Hodoku). It also has plenty of Finned Franken/Mutant variants if one wants to look at more complex fish types.

by **StrmCkr** » Thu Nov 22, 2018 9:58 pm

Code: Select all: +--------------------+-----------------+------------+ | 18 9 4 | 168 3 16 | 5 2 7 | | 6 5(3) 5(3) | 9 7 2 | 8 1 4 | | 128 7 128 | 18 4 5 | 6 3 9 | +--------------------+-----------------+------------+ | 9 6 15-3 | 2 8 1(3) | 4 7 15 | | 1358 2 7 | 1356 569 4 | 39 68 15 | | 1358 4 1358 | 1356 569 7 | 39 68 2 | +--------------------+-----------------+------------+ | 25(3) 1 25(3) | 4 56 6(3) | 7 9 8 | | 4 8 6 | 7 1 9 | 2 5 3 | | 7 5(3) 9 | 35 2 8 | 1 4 6 | +--------------------+-----------------+------------+

the sashimi x-wing is the simplest construct by my count,

this is also interesting to use:
2 tentacle eri :

Box 7 + Row 2 & Col 6 -> R4C3 <> 3

by **SpAce** » Fri Nov 23, 2018 6:09 am

StrmCkr wrote:the sashimi x-wing is the simplest construct by my count,

It might be the simplest construct, but probably not the easiest to spot for most human players. They're two different things. At least for me the easiest to spot here is the X-Chain:

(3)r2c3 = r2c2 - r9c2 = r9c4 - r7c6 = (3)r4c6 => -3 r4c3

It has only conjugate links, which makes it even easier to see directly (or findable with pure Simple Coloring, though that's hardly necessary here).

this is also interesting to use:
2 tentacle eri : Box 7 + Row 2 & Col 6 -> R4C3 <> 3

That's a fun pattern! With a bit more symmetry it would look like a crab:

Code: Select all: o----o | | x o | | o | o o o------o o

It's also an example of how structural complexity and difficulty of spotting aren't always tied. This structure (grouped X-Chain of length 6) is clearly more complex than either the Finned Sashimi X-Wing (grouped X-Chain of length 4) or my chain above (ungrouped X-Chain of length 6). Yet it might be the easiest to spot for some players who look for ERIs first and see where they lead (not a bad tactic as ERIs are easy to see). In any case, it's probably quite a bit simpler to understand than the equivalent fish:

Mutant (3x4) Swordfish: (3)r2c6b7\r47c23 => -3 r4c3

Yet another way to see the same elimination (with an extra one):

Code: Select all: .-----------------.----------------.------------. | 18 9 4 | 168 3 16 | 5 2 7 | | 6 35 5-3 | 9 7 2 | 8 1 4 | | 128 7 128 | 18 4 5 | 6 3 9 | :-----------------+----------------+------------: | 9 6 *15-3 | 2 8 *13 | 4 7 15 | | *1358 2 7 | 1356 569 4 | 39 68 15 | | *1358 4 #1358 | 1356 569 7 | 39 68 2 | :-----------------+----------------+------------: | *235 1 #235 | 4 56 *36 | 7 9 8 | | 4 8 6 | 7 1 9 | 2 5 3 | | 7 35 9 | 35 2 8 | 1 4 6 | '-----------------'----------------'------------'

Grouped Oddagon:[(3)r4c6=r7c6=#=r7c1=r56c1=#=(3)r4c3] + Guardians: (#3)r67c3 => -3 r24c3

by **rjamil** » Tue Nov 27, 2018 1:00 pm

Hi,

StrmCkr" wrote:the sashimi x-wing is the simplest construct by my count,

this is also interesting to use:
2 tentacle eri :

Box 7 + Row 2 & Col 6 -> R4C3 <> 3

SpAce wrote:That's a fun pattern! With a bit more symmetry it would look like a crab:
Code: Select all
o----o : : x o : | o | o o o......o o

Note: changed weak link from dashes to dots.

Let me add my (childish) analysis in to some serious discussion as follows:

I have compared above mentioned Crab pattern with Dual Empty Rectangle pattern, which is as follows:

Code: Select all: x--------o : | : | : | o | o o o......x o

May be there is any connection between Crab and Dual Empty Rectangle patterns.

R. Jamil

by **StrmCkr** » Tue Nov 27, 2018 4:19 pm

sure there is a bit of a connection, its all in how the "arms" interact.
i could sit here and manually generate a lot of different size 3 fish, so ill keep this limited...

Code: Select all: +----------------+--------------+------------+ | . -1 . | -1 . -1 | . . . | | . (1) . | (1) . . | . . . | | . -1 . | -1 (1) -1 | . . . | +----------------+--------------+------------+ | . -1 . | . . . | . . . | | . -1 . | . . . | . . . | | . -1 . | . . . | . . . | +----------------+--------------+------------+ | . (1) . | . . . | . . . | | (1) (-1) (1) | -1 (1) -1 | -1 -1 -1 | | . (1) . | . . . | . . . | +----------------+--------------+------------+

Code: Select all: +----------------+--------------+---------+ | . . . | -1 . -1 | . . . | | . (-1) . | . (+1) . | . . . | | . . . | -1 . -1 | . . . | +----------------+--------------+---------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +----------------+--------------+---------+ | . (1) . | . . . | . . . | | (1) (1) (1) | . (-1) . | . . . | | . (1) . | . . . | . . . | +----------------+--------------+---------+

Code: Select all: +---------------+-------------+---------+ | . . . | . . . | . . . | | . (1) . | (1) . . | . . . | | . . . | . . . | . . . | +---------------+-------------+---------+ | . . . | -1 (1) . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +---------------+-------------+---------+ | . (1) . | . . . | . . . | | (1) (1) (1) | . (1) . | . . . | | . (1) . | . . . | . . . | +---------------+-------------+---------+

Code: Select all: +----------------+---------------+------------+ | . . . | . . -1 | . . . | | . (1) . | . (1) . | . . . | | . . . | . . -1 | . . . | +----------------+---------------+------------+ | . . . | . . -1 | . . . | | . . . | . . -1 | . . . | | . . . | . . -1 | . . . | +----------------+---------------+------------+ | . (-1) . | . . (+1) | -1 -1 -1 | | (1) (1) (1) | . (-1) . | . . . | | . (1) . | . . . | . . . | +----------------+---------------+------------+

Code: Select all: +---------------+-------------+---------+ | . (1) . | . (1) . | . . . | | . . . | . 1 -1 | . . . | | . . . | . 1 -1 | . . . | +---------------+-------------+---------+ | . . . | . -1 . | . . . | | . (1) . | . . (1) | . . . | | . . . | . -1 . | . . . | +---------------+-------------+---------+ | . (1) . | . . . | . . . | | (1) (1) (1) | . -1 -1 | . . . | | . (1) . | . . . | . . . | +---------------+-------------+---------+

Code: Select all: +---------------+-------------+---------+ | . . (1) | . . -1 | . . . | | . (1) . | . . . | . . . | | . . . | . . . | . . . | +---------------+-------------+---------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +---------------+-------------+---------+ | . (1) . | . . (1) | . . . | | (1) (1) (1) | . (1) . | . . . | | . (1) . | . . . | . . . | +---------------+-------------+---------+

it gets a bit more awkward when you start considering the possibilities the bi locals could be grouped nodes instead... giving rise to this:
Empty kyte

Code: Select all: +----------------+---------------+------------+ | . (1) . | (1) . (1) | . . . | | . -1 . | -1 (1) -1 | . . . | | . -1 . | -1 (1) -1 | . . . | +----------------+---------------+------------+ | . -1 . | . . . | . . . | | . -1 . | . . . | . . . | | . -1 . | . . . | . . . | +----------------+---------------+------------+ | . (1) . | . . . | . . . | | (1) (-1) (1) | -1 (1) -1 | -1 -1 -1 | | . (1) . | . . . | . . . | +----------------+---------------+------------+

by **rjamil** » Tue Nov 27, 2018 6:14 pm

WOW!!!

But, I need two explanations as follows:

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

I see no difference as compared to exclusions. The only difference is in strong links.

Will the first one be called Reduced Empty Kite and second one be Empty Kite? (But, I think, there is no need to label them separately).

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

Is it Skyscraper Transport move if r46c6 and r79c4 excluded by basic Skyscraper move and r2c46 may be excluded by Transport ERI?

R. Jamil

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