The New Sudoku Players' Forum

[Pat]

we need more examples of

(finless)

Franken/Mutant

Swordfish/Jellyfish

well i should've been more specific — i'd like to see some examples of puzzles where the Franken/Mutant actually solves the puzzle with nothing tougher used — just add Franken/Mutant as the next step beyond the "superior plus" — can be solved by A+B but cannot be solved by A —

A. "Too Easy"

"hidden singles"
"naked singles"

box-to-line exclusions
line-to-box exclusions

"hidden" subsets ( duos and larger )
"naked" subsets ( duos and larger )

basic fish ( X-wing and larger )

B. "Just Right"

Franken ( Swordfish and larger )
Mutant ( Swordfish and larger )

C. "Too Tough"

finned fish
and everything else

— example:

[ 24 clues ]

Code: Select all


 1 . . | . . 6 | . . 5
 . . . | . . . | . . .
 . . . | . 3 . | 6 7 .
-------+-------+------
 . . 7 | 8 4 . | . . 3
 . . . | . 5 9 | . . .
 9 . . | . 6 . | . . .
-------+-------+------
 . . 4 | . 7 . | 2 8 .
 7 . 9 | . . . | . . .
 . 1 2 | 3 . . | 4 . .



[re'born]

— example:

[ 24 clues ]

Code: Select all

 1 . . | . . 6 | . . 5
 . . . | . . . | . . .
 . . . | . 3 . | 6 7 .
-------+-------+------
 . . 7 | 8 4 . | . . 3
 . . . | . 5 9 | . . .
 9 . . | . 6 . | . . .
-------+-------+------
 . . 4 | . 7 . | 2 8 .
 7 . 9 | . . . | . . .
 . 1 2 | 3 . . | 4 . .



I see an empty rectangle here:

Code: Select all

*--------------------------------------------------------------------------------------*
 | 1        7        38       | 249      289      6        | 389      2349     5        |
 | 234568   2345689  3568     | 12459    1289*    7        | 1389*    12349*   12489*   |
 | 2458     24589    58       | 12459    3        12458    | 6        7        12489*   |
 |----------------------------+----------------------------+----------------------------|
 | 256      256      7        | 8        4        12       | 159      12569    3        |
 | 23468    23468    1368     | 127      5        9        | 178      1246     12468    |
 | 9        2458     158      | 127      6        3        | 1578     1245     1248     |
 |----------------------------+----------------------------+----------------------------|
 | 356      356      4        | 1569     7        15       | 2        8        169      |
 | 7        568      9        | 12456    128*     12458    | 135      1356     16-      |
 | 568      1        2        | 3        89       58       | 4        569      7        |
 *--------------------------------------------------------------------------------------*


that eliminates the 1 from r8c9. This solves the puzzle. My question for any of the Ultimate fisherman is what manual algorithm do you use to find Franken/Mutant fish. For typical fish, it is usually fast to do an exhaustive visual search for such patterns (especially if the computer is there to highlight my candidates), but trying to do such searches for the more complicated fish just seems exhausting. Are there any good tips for us amatuer anglers?

[Pat]

Mutant Swordfish

[ 37 clues ]

Code: Select all

 . . . | 3 7 . | 5 6 9
 5 . 9 | 8 2 . | 1 3 7
 . . 7 | 9 . . | . . .
-------+-------+------
 4 . 8 | 6 . 9 | . . 1
 . 7 6 | . . . | 9 . .
 9 . . | 2 . 7 | 6 . 8
-------+-------+------
 . 9 2 | 7 . 3 | . . 6
 7 . . | . 6 . | . 9 .
 6 . . | . 9 . | . . .



[re'born]

Mutant Swordfish

[ 37 clues ]

Code: Select all

 . . . | 3 7 . | 5 6 9
 5 . 9 | 8 2 . | 1 3 7
 . . 7 | 9 . . | . . .
-------+-------+------
 4 . 8 | 6 . 9 | . . 1
 . 7 6 | . . . | 9 . .
 9 . . | 2 . 7 | 6 . 8
-------+-------+------
 . 9 2 | 7 . 3 | . . 6
 7 . . | . 6 . | . 9 .
 6 . . | . 9 . | . . .



I'm not so experienced with these exotic fish, so perhaps someone will correct me if I'm wrong. ronk's original fish seems to be the mutant swordfish r7c49/r5b89 => r5c568, r8c6, r9c68 <>5. Alternatively, there seems to be a franken swordfish r467/c58b4 => r3c5, r5c58, r9c8<>5.

Firstly, is my franken swordfish well-formed? Secondly (assuming a positive response to the first question), they have overlapping eliminations, but not identical ones, so can there be any duality between the two fish?

[ronk]

ronk's original fish seems to be the mutant swordfish r7c49/r5b89 => r5c568, r8c6, r9c68 <>5. Alternatively, there seems to be a franken swordfish r467/c58b4 => r3c5, r5c58, r9c8<>5.

Firstly, is my franken swordfish well-formed? Secondly (assuming a positive response to the first question), they have overlapping eliminations, but not identical ones, so can there be any duality between the two fish?

The following, which includes your properly formed franken swordfish r467\c58b4, all yield identical eliminations.

Code: Select all

   franken swordfish r467\c58b4
   franken jellyfish c469b7\r3589
   franken jellyfish c469b7\r589b2
   franken jellyfish r467b7\c2358
   mutant jellyfish r467c9\c5b469
   mutant jellyfish r7c469\r35b89
   mutant jellyfish r7c469\r5b289

There are also several fish that yield eliminations identical to r7c49\r5b89:

Code: Select all

   franken swordfish c49b7\r589
   mutant swordfish r7c49\r5b89
   franken jellyfish c2349\r589b4
   franken jellyfish c49b27\r3589
   franken jellyfish r3467\c568b4
   franken jellyfish r467b2\c568b4
   mutant jellyfish r37c49\r5b289
   mutant jellyfish r3c49b7\r589b2
   mutant jellyfish r467c4\c8b458
   mutant jellyfish r7c49b2\r35b89

Since it re-uses only r7, the franken jellyfish r467b2\c568b4 is probably the best "dual."

There's so many of these things, it's a good thing they aren't piranha.

[re'born]

ronk's original fish seems to be the mutant swordfish r7c49/r5b89 => r5c568, r8c6, r9c68 <>5. Alternatively, there seems to be a franken swordfish r467/c58b4 => r3c5, r5c58, r9c8<>5.

Firstly, is my franken swordfish well-formed? Secondly (assuming a positive response to the first question), they have overlapping eliminations, but not identical ones, so can there be any duality between the two fish?

The following, which includes your properly formed franken swordfish r467\c58b4, all yield identical eliminations.

Code: Select all

   franken swordfish r467\c58b4
   franken jellyfish c469b7\r3589
   franken jellyfish c469b7\r589b2
   franken jellyfish r467b7\c2358
   mutant jellyfish r467c9\c5b469
   mutant jellyfish r7c469\r35b89
   mutant jellyfish r7c469\r5b289

There are also several fish that yield eliminations identical to r7c49\r5b89:

Code: Select all

   franken swordfish c49b7\r589
   mutant swordfish r7c49\r5b89
   franken jellyfish c2349\r589b4
   franken jellyfish c49b27\r3589
   franken jellyfish r3467\c568b4
   franken jellyfish r467b2\c568b4
   mutant jellyfish r37c49\r5b289
   mutant jellyfish r3c49b7\r589b2
   mutant jellyfish r467c4\c8b458
   mutant jellyfish r7c49b2\r35b89

Since it re-uses only r7, the franken jellyfish r467b2\c568b4 is probably the best "dual."

There's so many of these things, it's a good thing they aren't piranha.

Wow!...um...well, I mean...Wow! I feel rather blind for not seeing how many ways one can make these exclusions. Some of the jellyies are just overkill versions of a swordfish counterpart, but still...wow. Are these generated by your solver ronk? I only ask because I'm curious if this is an exhaustive list.

[Pat]

I'm curious if this is an exhaustive list

this pair are equivalent to each other --

Code: Select all

Franken Swordfish -- ccb\rrr -- c49b7\r589
 Mutant Swordfish -- rcc\rbb -- r7c49\r5b89

this pair are equivalent to each other --

Code: Select all

Franken Swordfish -- rrr\ccb -- r467\c58b4
 Mutant Swordfish -- rbb\rcc -- r7b56\r5c58

the last one is missing from ronk's list,
thus we know it is not exhaustive


on equivalent fish --
Obi-Wahn (2007.Jan.22)

~ Pat

[ronk]

this pair are equivalent to each other --

Code: Select all

Franken Swordfish -- rrr\ccb -- r467\c58b4
 Mutant Swordfish -- rbb\rcc -- r7b56\r5c58

the last one is missing from ronk's list,
thus we know it is not exhaustive

I manually sorted that list based on eliminations, but my "generalized fish finder" (using daj95376's GFF term) wasn't yet counting the eliminations in the intersection of two cover sectors (units ), so I missed about half of them.

Wow! I feel rather blind for not seeing how many ways one can make these exclusions. Some of the jellyies are just overkill versions of a swordfish counterpart, but still...wow.

I'm still astounded by the sheer quantity too, so I know the feeling. As for the overkill, I was trying to show the myriad of possibilies for the same elims ... but as noted above, I missed a few.

Are these generated by your solver ronk? I only ask because I'm curious if this is an exhaustive list.

It's more of a "fish finder" than a solver technique. IMO it's just too slow to incorporate into a solver ... and it's still a work-in-progress anyway.

The exhaustive list (I think) of 36 unfinned swordfish and unfinned jellyfish can be sorted into just two classes ... based on the eliminations they produce.

Code: Select all

18 fish with identical 6 elims r5c568<>5, r8c6<>5 and r9c68<>5:
  frankens:
    swordfish c49b7\r589
    jellyfish r3467\c568b4
    jellyfish r467b2\c568b4
    jellyfish c2349\r589b4
    jellyfish c49b27\r3589
  mutants:
    swordfish r7c49\r5b89
    swordfish r7c4b6\r5c8b8
    jellyfish r37c49\r5b289
    jellyfish r37c4b6\r5c8b28
    jellyfish r37c9b5\r5c56b9
    jellyfish r37b56\r5c568
    jellyfish r3c49b7\r589b2
    jellyfish r467c4\c8b458
    jellyfish r7c49b2\r35b89
    jellyfish r7c4b26\r35c8b8
    jellyfish r7c9b25\r5c56b9
    jellyfish r7b256\r5c568
    jellyfish c4b679\r589c8
   
18 fish with identical 4 elims r3c5<>5, r5c58<>5 and r9c8<>5:
  frankens:
    swordfish r467\c58b4
    jellyfish r3467\c58b24
    jellyfish r467b7\c2358
    jellyfish c469b7\r3589
    jellyfish c469b7\r589b2
  mutants:
    swordfish r7c9b5\r5c5b9
    swordfish r7b56\r5c58
    jellyfish r37c9b5\r5c5b29
    jellyfish r37b56\r5c58b2
    jellyfish r467c9\c5b469
    jellyfish r467b2\r3c58b4
    jellyfish r7c469\r35b89
    jellyfish r7c469\r5b289
    jellyfish r7c46b6\r35c8b8
    jellyfish r7c46b6\r5c8b28
    jellyfish r7c9b25\r35c5b9
    jellyfish r7b256\r35c58
    jellyfish c9b578\r589c5

If one adds all the different finned (including sashimi) swordfish and finned jellyfish, there are in excess of 200 different combinations of base and cover sectors that yield an elimination.

[edit: manually resorted to better align with rcb sequence of GFF]

[re'born]

Fascinating. When Pat first posted your puzzle, with the only annotation being "Mutant Swordfish", I thought, "why doesn't he post the specific fish?" I see now it's because the word 'the' couldn't be more misleading.

[gsf]

The exhaustive list (I think) of 36 unfinned swordfish and unfinned jellyfish can be sorted into just two classes ... based on the eliminations they produce...

Code: Select all

18 fish with identical 6 elims r5c568<>5, r8c6<>5 and r9c68<>5:
18 fish with identical 4 elims r3c5<>5, r5c58<>5 and r9c8<>5:


under the theme of everythings related, these same eliminations, plus an implied placement via those eliminations,
are reached by two groups of x-cycles containing a total of 8 x-cycles (-v2 output in my solver):

Code: Select all

         x-cycle  1  5  4a [55]-[78][75]-
         x-cycle  2  5  6a [56]-[78][75]-[35][36]-  =>  [56]-[35][36]-
         x-cycle  3  5  4a [58]-[75][78]-
     X3  [55][56][58]^5
         x-cycle  4  5  7a [35]-[75][78]-[54][59]-  =>  [35]-[75][78]-
         x-cycle  5  5  4b [36][35]-[59]=
         x-cycle  6  5  3a [86]-[78]=[36]-
         x-cycle  7  5  3a [96]-[78]=[36]-
         x-cycle  8  5  7a [98]-[54][59]-[75][78]-  =>  [98]-[75][78]-
     X5  [35][86][96][98]^5 [36]=5


the -OA option attempts minimize the number of method applications (its not exhaustive),
and produces a solution with 4 x-cycles

Code: Select all

         x-cycle  1  5  4a [55]-[78][75]-
     X1  [55]^5
         x-cycle  1  5  4a [58]-[75][78]-
     X1  [58]^5
         x-cycle  1  5  6a [56]-[78][75]-[35][36]-  =>  [56]-[35][36]-
     X1  [56]^5
         x-cycle  1  5  4b [36][35]-[59]=
     X1  [36]=5


[36]=5 happens to be a singles backdoor, and it looks like all of the eliminations in the first
group may be required for just one cycle in the second group to hit the backdoor
(manually confirmed that all in the first group are required)

this is good for me because I see and code cycles much easier than I see or envision coding fins

[ronk]

two groups of x-cycles containing a total of 8 x-cycles (-v2 output in my solver):

Code: Select all

         x-cycle  1  5  4a [55]-[78][75]-
         x-cycle  2  5  6a [56]-[78][75]-[35][36]-  =>  [56]-[35][36]-
         x-cycle  3  5  4a [58]-[75][78]-
     X3  [55][56][58]^5
         x-cycle  4  5  7a [35]-[75][78]-[54][59]-  =>  [35]-[75][78]-
         x-cycle  5  5  4b [36][35]-[59]=
         x-cycle  6  5  3a [86]-[78]=[36]-
         x-cycle  7  5  3a [96]-[78]=[36]-
         x-cycle  8  5  7a [98]-[54][59]-[75][78]-  =>  [98]-[75][78]-
     X5  [35][86][96][98]^5 [36]=5


To be consistent with some of your statements on cycles, wouldn't those be x-knots

[gsf]

To be consistent with some of your statements on cycles, wouldn't those be x-knots

this refers to y-knots in my solver
an x or y cycle is constructed from edge segments that form paths that sometimes form cycles
when the segments form a cycle they are labeled x-cycle or y-cycle depending on the edge types in the cycle

the construction of a path may lead to a contradition before the cycle collapse is applied
the cycle collapse is what determines the placements/eliminations for a cycle, if any
they are annotated after the => in the -v2 trace and are outlined in the ternay monoid thread

I don't particularly care for y-knots because they are a fallout of a process that was looking for something else
sort of like hitting a backdoor when checking a bivalue cell
my solver only uses them after all x/y cycles (that it could find) have been exhausted

anyway, for this example, only x-cycles were used, no x/y-knots

one way to look at it:

an x/y-cycle is a structure of consistency
it illustrates a consistency in the puzzle, but as a side effect, produces eliminations/placements
x/y-cycles exist and wait to be discovered

an x/y-knot is a structure of inconsistency
x/y-knots only exist when false premises/propositions are asserted
and you don't know they are false until the knot appears

btw, knot is a play on words, not a math structure: its a cycle, knot

[Pat]

6 elims -- r5c568 r8c6 r9c68


Code: Select all

franken swordfish c49b7\r589
 mutant swordfish r7c49\r5b89

 mutant swordfish r7c4b6\r5c8b8




4 elims -- r3c5 r5c58 r9c8


Code: Select all

franken swordfish r467\c58b4
 mutant swordfish r7b56\r5c58

 mutant swordfish r7c9b5\r5c5b9




the 3 Swordfish
may happen to produce -- in this puzzle -- the same 6 exclusions, or the same 4 exclusions;
but they are not equivalent.

the rcb\rcb is not equivalent to the other 2 --
the observation ("/" -- the "hidden pattern") is different,
and the conclusion ("*" -- the exclusion-cells) will differ too.




Fascinating. When Pat first posted your puzzle, with the only annotation being "Mutant Swordfish", I thought, "why doesn't he post the specific fish?" I see now it's because the word 'the' couldn't be more misleading.




i gave it the title "Mutant Swordfish"
merely because that was the fish identified by ronk way back in 2005

and i avoided spelling out the specific fish
so as not to spoil your pleasure in looking for it




I see and code cycles much easier than I see or envision coding fins




forget about the fins --
how about adding (un-finned) Franken and Mutant fish ?
a major difficulty would be to find a spare letter
~ Pat

[ronk]

the 3 Swordfish
may happen to produce -- in this puzzle -- the same 6 exclusions, or the same 4 exclusions;
but they are not equivalent.

I made no claim about equivalence.

the rcb\rcb is not equivalent to the other 2 --
the observation ("/" -- the "hidden pattern") is different,
and the conclusion ("*" -- the exclusion-cells) will differ too.

Obviously, equivalent fish -- different fish based on the same hidden pattern -- have identical exclusions, but non-equivalent fish can have identical exclusions too. It appears that what you said too, so what's your point?

[Pat]

Obviously, equivalent fish -- different fish based on the same hidden pattern -- have identical exclusions, but non-equivalent fish can have identical exclusions too. It appears that what you said too, so what's your point?

non-equivalent fish will generally have different exclusion-cells ("*");
they may happen to produce identical exclusions in a specific puzzle.

i'm not disagreeing with you,
merely clarifying for myself (and just possibly for a visitor from outer space).

~ Pat