Obi's original

notes/discussion topic on the programs forums has some insight not mentioned in his opening post.

in a N x( N + K) fish all cover sectors used can be interpreted as Fin sectors: iterating all combinations for the base x cover + Finns will yield the same result as treating all

sectors as Finns

ronk wrote:The exclusions of finned fish are those that see all the fin cells. Remora exclusions were not included then and should not be included now IMO. However, it's unfortunate that a better exemplar was not posted back then, one without a remora.

the n x n +k fish process dose not use Finn Cells or specific fin sectors: it treats all sectors used as possible fins.

my generalized rules/ interpretation of Obi-Wahn mathematics eliminates the need for actually counting as well,

based on more of his notes from the programers forum.

that cells to be counted more then once require to be seen in combinations of Rows,Cols,Boxs sectors : all i do is keep track of individual cover sectors

{ for n+1 fish they need to be double covered, for n+2 fish triple covered. }

eliminations are pretty simplistic as described here in this quote;

Pat wrote:ab wrote:This idea does look interesting, but I can't find the thread where you define what you mean by base and cover in this context. Maybe someone can enlighten me?

The Ultimate FISH Guide should provide all the "fish" terminology

"base" and "cover" —

for any specific digit,

a "fish" of order j

is defined by a "base" of j units

and a "cover" of j units,

where the observation is —

A. each unit of the "base" can only have the digit somewhere in the "cover", and

B. the digit cannot occur in the overlap of units of the "base" [ new forFranken andMutant ]

thus we know that the "base" will provide the digit j times in the "cover",

and the conclusion is —

exclude the digit in the "cover" outside the "base"

beyond the "fish" exclusion,

if there's overlap in the "cover" [ i.e. new for Franken and Mutant ]

we have an extra type of exclusion —

exclude the digit in the overlap of units of the "cover";

Obi-Wahn's idea extends this new type of exclusion

by considering order j\J,

where the "cover" is increased to J units ( j < J )

my algorithms is based using

Sets because i use set logic: adding the same base/cover sectors dose not change my "counting".

my logic construct is basically this order:

- Code: Select all
` base[set] x cover[set] <> [ no active units ]`

active base[set] - ( base[set] x cover[set] ) = [ no active units ]

then

if N = N

then

Cover[set] - (base[set] x cover[set] ) = [ set of cells to eliminate ] {basic fish eliminations}

if n = n or K =1 { eliminations from overlapping cells, in cover not in base }

then

((Row Cover[set] x Box cover[set] ) + (Row_cover[set] x col cover[set]) + (Box cover[set] x Col cover [set]) ) - base[set] = [set of cells that are double covered and can be eliminated]

if k > 1 { eliminations from overlapping cells, in cover not in base }

then

( Row cover[set] * box cover[set] * col cover [set]) - base[set] = [set of cells that are tipple covered and can be eliminated]

originally i was confirming you comment that to mimic your fish's elimination that more then one nxn+k fish was required to duplicate the results of your 1 fish: i confirmed this fact by using two different cover sectors however my code identified R1C7 in both cases as an elimination: i was discussing the results with daj that R1c7 is eliminated in you original grid: which he confirmed by cross testing obiwan's mathematics

hence this whole discussion:

daj95376 wrote:During recent discussions with

StrmCkr about the following

ronk exemplar, StrmCkr pointed out that an additional elimination was present from the Nx(N+1) Fish perspective.

- Code: Select all
` * * * | X *X X | * ** *`

. . . | / X / | * . .

. . . | / X / | * . .

---------+----------+----------

* * * | . * . | * . .

X X X | / X / | X / /

X X X | / X / | X / /

---------+----------+----------

. . . | . * . | ** . .

. . . | . * . | ** . .

/ / / | / X / | X # /

mutant jellyfish r569b2\r1c57b4 plus fin r9c8, implies r1c8, r78c7<>X

When the unfinned mutant Jellyfish is processed using Obi-Wahn's arithmetic, then r1c7's count stands out from the general exemplar.

- Code: Select all
` unfinned mutant Jellyfish r569b2\r1c57b4`

+-----------------------------------------------+

| * * * | X *X X | +2 * * |

| . . . | / X / | * . . |

| . . . | / X / | * . . |

|---------------+---------------+---------------|

| * * * | . * . | * . . |

| X X X | / X / | X / / |

| X X X | / X / | X / / |

|---------------+---------------+---------------|

| . . . | . * . | * . . |

| . . . | . * . | * . . |

| / / / | / X / | X / / |

+-----------------------------------------------+

Now, let's add either [c8] or [b9] to create the following Nx(N+1) Fish containing r9c8.

- Code: Select all
` mutant Jellyfish r569b2\r1c57b4+c8 => r1c78<>X`

+-----------------------------------------------+

| . . . | X +1 X | +2 +2 . |

| . . . | / X / | . . . |

| . . . | / X / | . . . |

|---------------+---------------+---------------|

| . . . | . . . | . . . |

| X X X | / X / | X X / |

| X X X | / X / | X X / |

|---------------+---------------+---------------|

| . . . | . . . | . . . |

| . . . | . . . | . . . |

| / / / | / X / | X X / |

+-----------------------------------------------+

- Code: Select all
` mutant Jellyfish r569b2\r1c57b4+b9 => r178c7<>X`

+-----------------------------------------------+

| . . . | X +1 X | +2 . . |

| . . . | / X / | . . . |

| . . . | / X / | . . . |

|---------------+---------------+---------------|

| . . . | . . . | . . . |

| X X X | / X / | X / / |

| X X X | / X / | X / / |

|---------------+---------------+---------------|

| . . . | . . . | +2 . . |

| . . . | . . . | +2 . . |

| / / / | / X / | X X X |

+-----------------------------------------------+

In both cases, r1c7 is included in the eliminations.

Some do, some teach, the rest look it up.