The New Sudoku Players' Forum

by **tarek** » Sat Oct 28, 2006 1:48 am

Following the explosive increase in the number of different species of fish used by the players, there was a need for a reference thread where fish terms, categories & examples are all in one place. This thread also continues the discussion that started all of this here.

The first post of this thread is the reference...it will evolve over time to reflect any additions, deletions, examples, suggestions or comments offered by the players.

This is a joint & collective effort aimed towards the intermediate & advanced players. I must thank all people who participated (directly or indirectly) in the continuous improvement of this guide

Terminology

Sector:

Line:

Candidate:

Nonet:

Peer:

Fish pattern:

Fish:

(Fish) body:

Fin cell:

Fin Sector:

Remote fin cell (RF cell):

Eventual Elimination(EE):

Fish Eliminations:

Fish Anatomy

Naming of fish:

Fish Name: Fish Special Qualities + Fish Shape + Fish Size

Size of Fish:

Shape of Fish:

Special Qualities of fish:

Fish Physiology

In a Finned Fish:

Any PE that is linked directly (Peer relationship) or indirectly (Other Relationship deduced from the NxN pattern) to ALL fin(s) as described as an eventual eliminatin (EE) & can be safely eliminated.In a Finless Fish:

All PEs are described as EEs and can be safely eliminated
Logic behind Finned fish based eliminations :

Conjecture:

Implications:

Only potential eliminations (#) that can be linked to all fins are called eventual eliminations and can be safely eliminated
Proof:

(#): Refer to the terminology section

Tutorial:

X-wing

A column X-wing consists of two columns where a digit only occurs twice in each column and makes a box. In this example the digit, 4, only appears in columns 5 and 8 in rows 2 and 7.
Code: Select all
5 4 8 | 2 1 . | . 3 9 9 6 3 | . . 8 | 1 . . 2 1 7 | 3 9 . | . 8 . -------+-------+------ 6 . 2 | 1 5 . | 8 9 . 4 . 1 | 8 6 9 | 2 5 . 8 5 9 | . 2 3 | . 1 . -------+-------+------ 3 8 6 | . . . | 9 . . 1 9 4 | 6 3 2 | 5 7 8 7 2 5 | 9 8 . | 3 6 . +-----------+------------------+-----------------+ | 5 4 8 | 2 1 67 | 67 3 9 | | 9 6 3 | 57-4 47X 8 | 1 24X 257-4 | | 2 1 7 | 3 9 456 | 46 8 456 | +-----------+------------------+-----------------+ | 6 37 2 | 1 5 47 | 8 9 347 | | 4 37 1 | 8 6 9 | 2 5 37 | | 8 5 9 | 47 2 3 | 467 1 467 | +-----------+------------------+-----------------+ | 3 8 6 | 57-4 47X 157-4 | 9 24X 12-4 | | 1 9 4 | 6 3 2 | 5 7 8 | | 7 2 5 | 9 8 14 | 3 6 14 | +-----------+------------------+-----------------+

In order for "4" to appear in both columns it must appear in r2c5 and r7c8 or it must appear in r2c8 and r7c5 since it can't appear twice in the same row. If r2c4 were to contain a "4", then neither r2c5 nor r2c8 could contain a "4", therefore r2c4 cannot contain a "4". The same is true for any cell in rows 2 and 7 expect those cells in columns 5 and 8 (r2c9, r7c4, r7c6, and r7c9 cannot contain "4").

In general, let "X" indicate the only places where a digit is located in two columns (the "/"s indicate cells which do not contain the digit). If the "X"s form a box, then the digit can be eliminated from all cells in the rows which contains the "X"s except for those in the two columns. The possible eliminations are indicated with "*". The same thing occurs with row X-wings except that the "/" are in rows and the eliminations are in columns.
Code: Select all
. . . | . / . | . / . * * * | * X * | * X * . . . | . / . | . / . ------+-------+------ . . . | . / . | . / . . . . | . / . | . / . . . . | . / . | . / . ------+-------+------ * * * | * X * | * X * . . . | . / . | . / . . . . | . / . | . / .

Code: Select all
. . . | 9 7 4 | . 6 . 4 1 6 | 5 3 8 | 9 7 2 . 7 . | 1 6 2 | 4 3 . -------+-------+------ 7 2 4 | 8 1 9 | 3 5 6 1 5 3 | 2 4 6 | 7 . . 6 9 8 | 7 5 3 | 2 1 4 -------+-------+------ . 4 . | 3 9 1 | 6 2 . . . 1 | 6 . 7 | 5 4 . . 6 . | 4 . 5 | . . .

the 8 for r3 has only two possible places - c1 , c9. And in r7,
this digit also has only two possible places - which are in the same two Columns
so, those two Rows will definitely provide two 8s in those two Columns; which is the full quota of 8s for any two Columns.
---> exclude 8 in those two Columns outside of those two Rows.

Code: Select all: +-----------------+-----------+-----------------+ | 235-8 38 25 | 9 7 4 | 18 6 15-8 | | 4 1 6 | 5 3 8 | 9 7 2 | | 589* 7 59 | 1 6 2 | 4 3 58* | +-----------------+-----------+-----------------+ | 7 2 4 | 8 1 9 | 3 5 6 | | 1 5 3 | 2 4 6 | 7 89 9-8 | | 6 9 8 | 7 5 3 | 2 1 4 | +-----------------+-----------+-----------------+ | 58* 4 57 | 3 9 1 | 6 2 78* | | 239-8 38 1 | 6 28 7 | 5 4 39-8 | | 239-8 6 279 | 4 28 5 | 18 89 1379-8 | +-----------------+-----------+-----------------+

Exemplars:

This section contains a library of exemplars ... 1-fish thru 6-fish. The exemplars are shown as inverse pairs labeled "Fig nZ" and "Fig nZ inverse" where n = 2, 3, 4, 5 and 6 for x-wings, swordfish, jellyfish, starfish (squirmbag) and whale, respectively. The 'Z' is merely an alphabet letter assigned sequentially starting with 'A'. When only one of an inverse pair is cannibalistic, that cannibalistic fish is always assigned the "Fig nZ inverse" tag.

The exemplars are grouped by the size of the fish, but "Fig nA" and "Fig nA inverse" for each grouping is the basic col\row fish for its size. For these basic fish, the inverse is equivalent to the transpose. The order within each size is basic, franken and mutant.

I tried to maximize symmetry in most of the exemplars. That makes many of them permutations of what we've used elsewhere.

An 'rcb\rcb' tag is also assigned to each figure for the base\cover units. The 'rcb' order is maintained to aid in searching for the existence of an exemplar. The actual row, column and box numbers are not included for the same reason. Where the transpose of a pattern is not identical to the pattern itself -- in rcb terms, the 'rcb\rcb' transpose is also listed.

KEY:

Code: Select all: X = base candidate, which may be missing / = empty cell, a cell that may not have an "X" candidate # = EndoFin * = eventual elimination if all fins are false ** = eventual elimination whether or not a fin is true *X = eventual elimination of base candidate (AutoCannibalistic)

1-FISH:

Code: Select all: . . . | . * . | . . . . . . | . / . | . . . . . . | . * . | . . . . . . | . / . | . . . . . . | . * . | . . . . . . | . / . | . . . ---------+----------+---------- ---------+----------+---------- . . . | / X / | . . . . . . | * X * | . . . . . . | / X / | . . . . . . | * X * | . . . . . . | / X / | . . . . . . | * X * | . . . ---------+----------+---------- ---------+----------+---------- . . . | . * . | . . . . . . | . / . | . . . . . . | . * . | . . . . . . | . / . | . . . . . . | . * . | . . . . . . | . / . | . . . Fig 1A: b\c Fig 1A inverse: c\b b\r transpose r\b transpose Locked candidates 1 Locked candidates 2 Inverse of locked candidates 2 Inverse of locked candidates 1 Box-line interaction Line-box interaction

X-WINGS:

Code: Select all: . / . | . . . | . / . . * . | . . . | . * . * X * | * * * | * X * / X / | / / / | / X / . / . | . . . | . / . . * . | . . . | . * . ---------+----------+---------- ---------+----------+---------- . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . ---------+----------+---------- ---------+----------+---------- . / . | . . . | . / . . * . | . . . | . * . * X * | * * * | * X * / X / | / / / | / X / . / . | . . . | . / . . * . | . . . | . * . Fig 2A: cc\rr Fig 2A inverse: rr\cc (basic) x-wing

Code: Select all: . . . | X * X | . . . . . . | X / X | . . . . . . | X * X | . . . . . . | X / X | . . . . . . | X * X | . . . . . . | X / X | . . . ---------+----------+---------- ---------+----------+---------- . . . | / . / | . . . . . . | * . * | . . . . . . | / . / | . . . . . . | * . * | . . . . . . | / . / | . . . . . . | * . * | . . . ---------+----------+---------- ---------+----------+---------- . . . | X * X | . . . . . . | X / X | . . . . . . | X * X | . . . . . . | X / X | . . . . . . | X * X | . . . . . . | X / X | . . . Fig 2B: cc\bb Fig 2B inverse: bb\cc rr\bb transpose bb\rr transpose franken x-wing Note Fig 2B is equivalent to Fig 1A.

Code: Select all: * X * | . . . | . * . / X / | . . . | . / . X / X | / / / | / X / X *X X | * * * | * X * * X * | . . . | . * . / X / | . . . | . / . ---------+----------+---------- ---------+----------+---------- . / . | . . . | . * . . * . | . . . | . / . . / . | . . . | . * . . * . | . . . | . / . . / . | . . . | . * . . * . | . . . | . / . ---------+----------+---------- ---------+----------+---------- . / . | . . . | . * . . * . | . . . | . / . . # . | . . . | . ** . . ** . | . . . | . # . . / . | . . . | . * . . * . | . . . | . / . Fig 2C: rc\cb Fig 2C inverse: cb\rc rc\rb transpose rb\rc transpose turbot fish (2-stringed kite) turbot fish (ER + conjugate link) sashimi mutant x-wing

Code: Select all: * X * | . . . | . / . / X / | . . . | . * . ** X ** | . . . | . # . # X # | . . . | . ** . * X * | . . . | . / . / X / | . . . | . * . ---------+---------+--------- ---------+---------+--------- . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . ---------+---------+--------- ---------+---------+--------- . / . | . . . | . / . . * . | . . . | . * . * X * | * * * | * X * / X / | / / / | / X / . / . | . . . | . / . . * . | . . . | . * . Fig 2D: cc\rb Fig 2D inverse: rb\cc rr\cb transpose cb\rr transpose turbot fish (skyscraper) turbot fish (ER + conjugate link) sashimi mutant x-wing

SWORDFISH:

Code: Select all: . / . | . / . | . / . . * . | . * . | . * . * X * | * X * | * X * / X / | / X / | / X / . / . | . / . | . / . . * . | . * . | . * . ---------+----------+---------- ---------+----------+---------- . / . | . / . | . / . . * . | . * . | . * . * X * | * X * | * X * / X / | / X / | / X / . / . | . / . | . / . . * . | . * . | . * . ---------+----------+---------- ---------+----------+---------- . / . | . / . | . / . . * . | . * . | . * . * X * | * X * | * X * / X / | / X / | / X / . / . | . / . | . / . . * . | . * . | . * . Fig 3A: ccc\rrr Fig 3A inverse: rrr\ccc (basic) swordfish

Code: Select all: . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . ---------+----------+---------- ---------+----------+---------- * X * | X X X | * X * / X / | X X X | / X / . / . | / / / | . / . . * . | * * * | . * . * X * | X X X | * X * / X / | X X X | / X / ---------+----------+---------- ---------+----------+---------- . / . | . . . | . / . . * . | . . . | . * . * X * | * * * | * X * / X / | / / / | / X / . / . | . . . | . / . . * . | . . . | . * . Fig 3B1: ccb\rrr Fig 3B1 inverse: rrr\ccb rrb\ccc transpose ccc\rrb transpose franken swordfish Equivalents: . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . ---------+----------+---------- ---------+----------+---------- * X * | . . . | * X * / X / | . . . | / X / X / X | / / / | X / X X *X X | * * * | X *X X * X * | . . . | * X * / X / | . . . | / X / ---------+----------+---------- ---------+----------+---------- . / . | . . . | . / . . * . | . . . | . * . * X * | * * * | * X * / X / | / / / | / X / . / . | . . . | . / . . * . | . . . | . * . Fig 3B2: rcc\rbb Fig 3B2 inverse: rbb\rcc rrc\cbb transpose cbb\rrc transpose mutant swordfish

[Example of Fig 3B2 in daj95376's puzzle F001 here]

Fig 3C relabeled 3V since it was discovered to be sashimi (degenerate)

Fig 3D relabeled 3B2 since based on same hidden pattern as 3B1

Code: Select all: / X / | . . . | . / . * X * | . . . | . * . X *X X | * * * | * X * X / X | / / / | / X / / X / | . . . | . / . * X * | . . . | . * . ---------+----------+---------- ---------+----------+---------- . * . | . . . | . / . . / . | . . . | . * . . * . | . . . | . / . . / . | . . . | . * . . * . | . . . | . / . . / . | . . . | . * . ---------+----------+---------- ---------+----------+---------- . * . | . . . | * X * . / . | . . . | / X / / X / | / / / | X / X * X * | * * * | X *X X . * . | . . . | * X * . / . | . . . | / X / Fig 3E: rcb\rcb Fig 3E inverse: rcb\rcb mutant swordfish

[Example from Mike Barker here]

Code: Select all: . . . | . / . | . / . . . . | . * . | . * . * ** * | * X * | * X * / # / | / X / | / X / . . . | . / . | . / . . . . | . * . | . * . ---------+----------+---------- ---------+----------+---------- . . . | . / . | * X * . . . | . * . | / X / / # / | / / / | X / X * ** * | * * * | X *X X . . . | . / . | * X * . . . | . * . | / X / ---------+----------+---------- ---------+----------+---------- . . . | . / . | . / . . . . | . * . | . * . * ** * | * X * | * X * / # / | / X / | / X / . . . | . / . | . / . . . . | . * . | . * . Fig 3V: rcc\rrb Fig 3V inverse: rrb\rcc rrc\ccb transpose ccb\rrc transpose sashimi mutant swordfish (x-wing + 1-fish)

[Example from Mike Barker here]

Fig 3X deleted since it was merely a finned x-wing

Code: Select all: X * * | * X * | * * * X / / | / X / | / / / / . . | . / . | . . . * . . | . * . | . . . / . . | . / . | . . . * . . | . * . | . . . ---------+----------+---------- ---------+----------+---------- / / # | . / . | . . . * * ** | . * . | . . . / / # | . / . | . . . * * ** | . * . | . . . / X X | * X * | * * * *X X X | / X / | / / / ---------+----------+---------- ---------+----------+---------- X * * | . / . | . . . X / / | . * . | . . . X * * | . / . | . . . X / / | . * . | . . . X * ** | . # . | . . . X / # | . ** . | . . . Fig 3Y: ccb\rrb Fig 3Y inverse: rrb\ccb rrb\ccb transpose ccb\rrb transpose sashimi franken swordfish (cascading locked candidates)

[Figure based on daj95376's puzzle #E060]

Code: Select all: . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . . / . | . . . | . / . . * . | . . . | . * . ---------+----------+---------- ---------+----------+---------- * X * | . . . | * X * / X / | . . . | / X / X / X | / / / | X / X X *X X | * * * | X *X X * X * | . . . | * X * / X / | . . . | / X / ---------+----------+---------- ---------+----------+---------- . / . | . . . | * X * . * . | . . . | / X / . # . | . . . | ** X ** . ** . | . . . | # X # . / . | . . . | * X * . * . | . . . | / X / Fig 3Z: rcc\bbb Fig 3Z inverse: bbb\rcc rrc\bbb transpose bbb\rrc transpose sashimi mutant swordfish (cascading locked candidates)

JELLYFISH:

Code: Select all: . / . | / . / | . / . . * . | * . * | . * . * X * | X * X | * X * / X / | X / X | / X / . / . | / . / | . / . . * . | * . * | . * . ---------+----------+---------- ---------+----------+---------- * X * | X * X | * X * / X / | X / X | / X / . / . | / . / | . / . . * . | * . * | . * . * X * | X * X | * X * / X / | X / X | / X / ---------+----------+---------- ---------+----------+---------- . / . | / . / | . / . . * . | * . * | . * . * X * | X * X | * X * / X / | X / X | / X / . / . | / . / | . / . . * . | * . * | . * . Fig 4A: cccc\rrrr Fig 4A inverse: rrrr\cccc (basic) jellyfish

Code: Select all: . * . | X / X | . * . . / . | X * X | . / . . * . | X / X | . * . . / . | X * X | . / . . * . | X / X | . * . . / . | X * X | . / . ---------+----------+---------- ---------+----------+---------- / X / | X / X | / X / * X * | X * X | * X * . * . | * . * | . * . . / . | / . / | . / . / X / | X / X | / X / * X * | X * X | * X * ---------+----------+---------- ---------+----------+---------- . * . | * . * | . * . . / . | / . / | . / . / X / | X / X | / X / * X * | X * X | * X * . * . | * . * | . * . . / . | / . / | . / . Fig 4B1: rrrb\cccc Fig 4B1 inverse: cccc\rrrb cccb\rrrr transpose rrrr\cccb transpose franken jellyfish Equivalents: . * . | . / . | . * . . / . | . * . | . / . . * . | . / . | . * . . / . | . * . | . / . . * . | . / . | . * . . / . | . * . | . / . ---------+----------+---------- ---------+----------+---------- / X / | X / X | / X / * X * | X *X X | * X * . * . | * X * | . * . . / . | / X / | . / . / X / | X / X | / X / * X * | X *X X | * X * ---------+----------+---------- ---------+----------+---------- . * . | * X * | . * . . / . | / X / | . / . / X / | X / X | / X / * X * | X * X | * X * . * . | * X * | . * . . / . | / X / | . / . Fig 4B2: rrrc\ccbb Fig 4B2 inverse: ccbb\rrrc rccc\rrbb transpose rrbb\rccc transpose mutant jellyfish . * . | . / . | . * . . / . | . * . | . / . . * . | . / . | . * . . / . | . * . | . / . . * . | . / . | . * . . / . | . * . | . / . ---------+----------+---------- ---------+----------+---------- / X / | . / . | / X / * X * | . * . | * X * X *X X | * X * | X *X X X / X | / X / | X / X / X / | . / . | / X / * X * | . * . | * X * ---------+----------+---------- ---------+----------+---------- . * . | * X * | . * . . / . | / X / | . / . / X / | X / X | / X / * X * | X *X X | * X * . * . | * X * | . * . . / . | / X / | . / . Fig 4B3: rcbb\rccb Fig 4B3 inverse: rccb\rcbb rcbb\rrcb transpose rrcb\rcbb transpose mutant jellyfish

Code: Select all: . / . | . * . | * X * . * . | . / . | / X / / / / | / X / | X / X * * * | * X * | X *X X . / . | . * . | * X * . * . | . / . | / X / ---------+----------+---------- ---------+----------+---------- . / . | . * . | . / . . * . | . / . | . * . * X * | * * * | * X * / X / | / / / | / X / . / . | . * . | . / . . * . | . / . | . * . ---------+----------+---------- ---------+----------+---------- * X * | . * . | . / . / X / | . / . | . * . X / X | / X / | / / / X *X X | * X * | * * * * X * | . * . | . / . / X / | . / . | . * . Fig 4C: rrcc\rcbb Fig 4C inverse: rcbb\rrcc self-transpose mutant jellyfish

[Figures have diagonal, anti-diagonal and 180-degree rotational symmetry; based on Mike Barker's post here]

Code: Select all: . * . | * . * | . * . . / . | / . / | . / . / X / | X / X | / X / * X * | X * X | * X * . * . | * . * | . * . . / . | / . / | . / . ---------+----------+---------- ---------+----------+---------- . * . | X / X | . * . . / . | X * X | . / . / X / | / / / | / X / * X * | *X * *X | * X * . * . | X / X | . * . . / . | X * X | . / . ---------+----------+---------- ---------+----------+---------- . * . | * . * | . * . . / . | / . / | . / . / X / | X / X | / X / * X * | X * X | * X * . * . | * . * | . * . . / . | / . / | . / . Fig 4D1: rrrb\cccc Fig 4D1 inverse: cccc\rrrb cccb\rrrr transpose rrrr\cccb transpose franken jellyfish Equivalents: . * . | * X * | . * . . / . | / X / | . / . / X / | X / X | / X / * X * | X *X X | * X * . * . | * X * | . * . . / . | / X / | . / . ---------+----------+---------- ---------+----------+---------- . * . | . / . | . * . . / . | . * . | . / . / X / | / / / | / X / * X * | * * * | * X * . * . | . / . | . * . . / . | . * . | . / . ---------+----------+---------- ---------+----------+---------- . * . | * X * | . * . . / . | / X / | . / . / X / | X / X | / X / * X * | X *X X | * X * . * . | * X * | . * . . / . | / X / | . / . Fig 4D2: rrrc\ccbb Fig 4D2 inverse: ccbb\rrrc rccc\rrbb transpose rrbb\rccc transpose mutant jellyfish

[Figure based on Ruud's post here]

Code: Select all: * * . | . . . | . * * / / . | . . . | . / / * * . | . . . | . * * / / . | . . . | . / / X X / | / / / | / X X X X * | * * * | * X X ---------+----------+---------- ---------+----------+---------- X X / | . . . | / X X X X * | . . . | * X X X X / | . . . | / X X X X * | . . . | * X X X X / | . . . | / X X X X * | . . . | * X X ---------+----------+---------- ---------+----------+---------- X X / | / / / | / X X X X * | * * * | * X X * * . | . . . | . * * / / . | . . . | . / / * * . | . . . | . * * / / . | . . . | . / / Fig 4E1: rrbb\cccc Fig 4E1 inverse: cccc\rrbb ccbb\rrrr transpose rrrr\ccbb transpose franken jellyfish Equivalents: * * X | . . . | X * * / / X | . . . | X / / * * X | . . . | X * * / / X | . . . | X / / X X / | / / / | / X X X X *X | * * * | *X X X ---------+----------+---------- ---------+----------+---------- . . / | . . . | / . . . . * | . . . | * . . . . / | . . . | / . . . . * | . . . | * . . . . / | . . . | / . . . . * | . . . | * . . ---------+----------+---------- ---------+----------+---------- X X / | / / / | / X X X X *X | * * * | *X X X * * X | . . . | X * * / / X | . . . | X / / * * X | . . . | X * * / / X | . . . | X / / Fig 4E2: rrcc\bbbb Fig 4E2 inverse: bbbb\rrcc self-transpose mutant jellyfish

Fig 4F: relabeled Fig 4E2, since it's equivalent to Fig 4E1 (which was 4E)

Fig 4G: identified as sashimi and relabeled Fig 4V

Fig 4H: relabeled Fig 4D2, since it's equivalent to Fig 4D1 (which was 4D)

Code: Select all: . / . | * X * | . / . . * . | / X / | . * . . # . | ** X * | . # . . ** . | # X / | . ** . . / . | * X * | . / . . * . | / X / | . * . ---------+----------+---------- ---------+----------+---------- * X * | X / X | * X * / X / | X *X X | / X / . / . | # / / | . / . . * . | ** * * | . * . * X * | X / X | * X * / X / | X *X X | / X / ---------+----------+---------- ---------+----------+---------- . / . | . / . | . / . . * . | . * . | . * . * X * | * X * | * X * / X / | / X / | / X / . / . | . / . | . / . . * . | . * . | . * . Fig 4J: cccb\rrrb Fig 4J inverse: rrrb\cccb 4-fish c258b5\r468b2 4-fish r468b2\c258b5 sashimi mutant jellyfish

Note similarity to Fig 4B2

Code: Select all: . / . | * X * | X X * . * . | / X / | X X / . # . | ** X ** | X X ** . ** . | # X # | X X / . / . | * X * | X X * . * . | / X / | X X / ---------+----------+---------- ---------+----------+---------- . / . | . / . | / / . . * . | . * . | * * . * X * | * X * | X X * / X / | / X / | X X / . / . | . / . | / / . . * . | . * . | * * . ---------+----------+---------- ---------+----------+---------- . / . | . / . | / / . . * . | . * . | * * . * X * | * X * | X X * / X / | / X / | X X / . / . | . / . | / / . . * . | . * . | * * . Fig 4K1: cccc\rrbb Fig 4K1 inverse: rrbb\cccc rrrr\ccbb transpose ccbb\rrrr transpose sashimi franken jellyfish (franken swordfish c278\r58b3 + 1-fish c5\b2) Equivalents (not illustrated): Fig 4K2: ccbb\rrcb Fig 4K2 inverse: rrcb\ccbb rrbb\rccb transpose rccb\rrbb transpose sashimi mutant jellyfish

Code: Select all: / / X | . . . | . / . * * X | . . . | . * . X / *X | * * * | ** X * X *X / | / / / | # X / / / X | . . . | . / . * * X | . . . | . * . ---------+----------+---------- ---------+----------+---------- . / * | . . . | . / . . * / | . . . | . * . / / X | / / / | # / / * * X | * * * | ** * * * X * | * * * | ** X ** / X / | / / / | # X # ---------+----------+---------- ---------+----------+---------- . / * | . . . | . / . . * / | . . . | . * . * X * | * * * | ** X * / X / | / / / | # X / . / * | . . . | . / . . * / | . . . | . * . Fig 4T: rccb\rrrc Fig 4T inverse: rrrc\rccb transpose rrcb\rccc transpose rccc\rrcb sashimi mutant jellyfish

Note similarity to Fig 5T

Code: Select all: . / . | . / . | . * . . * . | . * . | . / . * X * | * X * | * * * / X / | / X / | / / / . / . | . / . | . * . . * . | . * . | . / . ---------+----------+---------- ---------+----------+---------- # @ # | / / / | / X / ** ** ** | * * * | * X * . # . | . / . | . * . . ** . | . * . | . / . * X ** | * X * | * * * / X # | / X / | / / / ---------+----------+---------- ---------+----------+---------- . / . | * X * | . * . . * . | / X / | . / . / / # | X / X | / X / * * ** | X *X X | * X * . / . | * X * | . * . . * . | / X / | . / . Fig 4U: rrcc\rrcb Fig 4U inverse: rrcb\rrcc rrcc\rccb transpose rccb\rrcc transpose sashimi mutant jellyfish

Example: r59c16\r16c9b8+c3b4 here

Code: Select all: / / / | X / X | / # / * * * | X *X X | * ** * . . . | * X * | / . . . . . | / X / | * . . . . . | * X * | / . . . . . | / X / | * . . ---------+----------+---------- ---------+----------+---------- / / / | . / . | / . . * * * | . * . | * . . X X X | * X * | X ** * X X X | / X / | X # / X X X | * X * | X ** * X X X | / X / | X # / ---------+----------+---------- ---------+----------+---------- . . . | . / . | / . . . . . | . * . | * . . . . . | . / . | / . . . . . | . * . | * . . * * * | * X * | X ** * / / / | / X / | X # / Fig 4V: rccb\rrrb Fig 4V inverse: rrrb\rccb rrcb\cccb transpose cccb\rrcb transpose sashimi mutant jellyfish (swordfish + 1-fish)

[Figure based on discussion here]

Code: Select all: . . . | . / / | / X / . . . | . * * | * X * * * * | * X X | / *X X / / / | / X X | *X / X . . . | . / / | / X / . . . | . * * | * X * ---------+----------+---------- ---------+----------+---------- . . . | . / / | / * . . . . | . * * | * / . * * * | * X X | X * * / / / | / X X | X / / . . . | . / / | / * . . . . | . * * | * / . ---------+----------+---------- ---------+----------+---------- . . . | . / / | # ** . . . . | . * * | ** # . * * * | * X X | X ** ** / / / | / X X | X @ # . . . | . / / | # ** . . . . | . * * | ** # . Fig 4W: cccb\rrrc Fig 4W inverse: rrrc\cccb rrrb\rccc transpose rccc\rrrb transpose sashimi mutant jellyfish (swordfish + 1-fish)

[Figure based on daj95376's puzzle E091]

Code: Select all: / X / | . . . | . / . * X * | . . . | . * . X *X X | * * * | * X * X / X | / / / | / X / / X / | . . . | . / . * X * | . . . | . * . ---------+----------+---------- ---------+----------+---------- * * * | ** ** ** | * X * / / / | # # # | / X / . * . | . . . | . / . . / . | . . . | . * . / X / | # # # | / / / * X * | ** ** ** | * * * ---------+----------+---------- ---------+----------+---------- . * . | . . . | * X * . / . | . . . | / X / / X / | / / / | X / X * X * | * * * | X *X X . * . | . . . | * X * . / . | . . . | / X / Fig 4X: rrcb\rrcb Fig 4X inverse: rrcb\rrcb rccb\rccb transpose rccb\rccb transpose sashimi mutant jellyfish (swordfish + 1-fish)

[Figure based on digit 1 in permutation of daj9537's puzzle E060]

Fig 4Y: relabeled Fig 4K to separate franken fish from mutant fish

Code: Select all: / X / | . . . | . / . * X * | . . . | . * . X *X X | * * * | * X * X / X | / / / | / X / / X / | . . . | . / . * X * | . . . | . * . ---------+----------+---------- ---------+----------+---------- . * . | . . . | . / . . / . | . . . | . * . . * . | . . . | . / . . / . | . . . | . * . . * . | . . . | . / . . / . | . . . | . * . ---------+----------+---------- ---------+----------+---------- X *X X | ** ** ** | * *X * X / X | # # # | / / / / / / | # # # | X / X * *X * | ** ** ** | X *X X / X / | . . . | * X * * X * | . . . | / X / Fig 4Z: rcbb\rrcb Fig 4Z inverse: rrcb\rcbb rcbb\rccb transpose rccb\rcbb transpose sashimi mutant swordfish

[Figure based on daj95376's puzzle #E084]

STARFISH (SQUIRMBAG): (a token sampling)

Code: Select all: X * X | * X * | X * X X / X | / X / | X / X / . / | . / . | / . / * . * | . * . | * . * X * X | * X * | X * X X / X | / X / | X / X ---------+----------+---------- ---------+----------+---------- / . / | . / . | / . / * . * | . * . | * . * X * X | * X * | X * X X / X | / X / | X / X / . / | . / . | / . / * . * | . * . | * . * ---------+----------+---------- ---------+----------+---------- X * X | * X * | X * X X / X | / X / | X / X / . / | . / . | / . / * . * | . * . | * . * X * X | * X * | X * X X / X | / X / | X / X Fig 5A: ccccc\rrrrr Fig 5A inverse: rrrrr\ccccc self-transpose (basic) starfish

Code: Select all: . / . | / . / | * / . . * . | * . * | / * . * X * | X * X | * X * / X / | X / X | / X / . / . | / . / | * / . . * . | * . * | / * . ---------+----------+---------- ---------+----------+---------- . / . | X * X | * / . . * . | X / X | / * . / / / | / X / | X / / * * * | * X * | X * * . / . | X * X | * / . . * . | X / X | / * . ---------+----------+---------- ---------+----------+---------- . / . | / . / | * / . . * . | * . * | / * . * X * | X * X | * X * / X / | X / X | / X / * X * | X * X | * X * / X / | X / X | / X / Fig 5B: rcccc\rrrcb Fig 5B inverse: rrrcb\rcccc rrrrc\rcccb transpose rcccb\rrrrc transpose mutant starfish

Code: Select all: / X / | / / / | / / / * X * | * * * | * * * . * / | . / . | / . . . / * | . * . | * . . * * X | * X * | * * * / / X | / X / | / / / ---------+----------+---------- ---------+----------+---------- / X / | X / X | / / / * X * | X *X X | * * * . * / | * X * | / . . . / * | / X / | * . . * * X | * * * | X * * / / X | / / / | X / / ---------+----------+---------- ---------+----------+---------- . * / | . / . | / . . . / * | . * . | * . . * * * | * X * | X * * / / / | / X / | X / / . * / | . / . | / . . . / * | . * . | * . . Fig 5C: rrccc\rrrcb Fig 5C inverse: rrrcb\rrccc rrrcc\rcccb transpose rcccb\rrrcc transpose mutant starfish

Code: Select all: X / X | * X * | * X * X *X X | / X / | / X / / / / | . / . | . / . * * * | . * . | . * . X / X | * X * | * X * X *X X | / X / | / X / ---------+----------+---------- ---------+----------+---------- . / . | . / . | . / . . * . | . * . | . * . * X * | * X * | * X * / X / | / X / | / X / . / . | . / . | . / . . * . | . * . | . * . ---------+----------+---------- ---------+----------+---------- * X * | * X * | X / X / X / | / X / | X *X X . / . | . / . | / / / . * . | . * . | * * * * X * | * X * | X / X / X / | / X / | X *X X Fig 5D: cccbb\rrrrr Fig 5D inverse: rrrrr\cccbb rrrbb\cccccc transpose cccccc\rrrbb transpose franken starfish Exemplars have 180-degree rotational symmetry

[Figure based on daj95376's example here]

Code: Select all: / . / | . / . | . / . * . * | . * . | . * . X * X | * X * | * X * X / X | / X / | / X / / . / | . / . | . / . * . * | . * . | . * . ---------+----------+---------- ---------+----------+---------- X * X | * X * | * X * X / X | / X / | / X / / . / | . / . | . / . * . * | . * . | . * . X * X | * X * | * X * X / X | / X / | / X / ---------+----------+---------- ---------+----------+---------- X * X | * X * | X / X X / X | / X / | X *X X / . / | . / . | / / / * . * | . * . | * * * X * X | * X * | X / X X / X | / X / | X *X X Fig 5E: ccccb\rrrrr Fig 5E inverse: rrrrr\ccccb transpose rrrrb\ccccc transpose ccccc\rrrrb franken starfish Franken (illustrated): c1358b9\r24679 (ccccb\rrrrr) r24679\c1358b9 (rrrrr\ccccb) Franken complement (and transpose): r1358b9\c24679 (rrrrb\ccccc) c24679\r1358b9 (ccccc\rrrrb) Mutant equivalents (one self-transpose and two transpose pairs): r58c58b1\r2c2b568 (rrccb\rcbbb) r2c2b568\r58c58b1 (rcbbb\rrccb) r1358c8\c246b36 (rrrrc\cccbb) c246b36\r1358c8 (cccbb\rrrrc) r8c1358\r246b78 (rcccc\rrrbb) r246b78\r8c1358 (rrrbb\rcccc) r58c8b12\r2c246b6 (rrcbb\rcccb) r2c246b6\r58c8b12 (rcccb\rrcbb) r8c58b14\r246c2b8 (rccbb\rrrcb) r246c2b8\r8c58b14 (rrrcb\rccbb)

[diagonal, anti-diagonal and 180-degree rotational symmetry; based on daj95376's puzzlle AKLM_215(8)]

Code: Select all: / / X | . . . | . / . * * X | . . . | . * . X / *X | * * * | ** X * X * / | / / / | # X / / / X | . . . | . / . * * X | . . . | . * . ---------+----------+---------- ---------+----------+---------- * X * | X X X | ** X ** / X / | X X X | # X # / / X | / / / | # / / * * X | * * * | ** * * * X * | X X X | ** X ** / X / | X X X | # X # ---------+----------+---------- ---------+----------+---------- . / * | . . . | . / . . * / | . . . | . * . * X * | * * * | ** X * / X / | / / / | # X / . / * | . . . | . / . . * / | . . . | . * . Fig 5T: rccbb\rrrrc Fig 5T inverse: rrrrc\rccbb transpose rrcbb\rcccc transpose rcccc\rrcbb sashimi mutant starfish

Note similarity to Fig 4T

Code: Select all: . . . | . . * | X * * . . . | . . / | X / / . . . | . . * | X * * . . . | . . / | X / / / / / | / / X | / X *X * * * | * * X | *X X / ---------+----------+---------- ---------+----------+---------- X X X | / / X | / / X X X X | * * X | * * X * ** * | . . * | / . * / # / | . . / | * . / * ** * | . . * | / . * / # / | . . / | * . / ---------+----------+---------- ---------+----------+---------- X X X | * * * | X * * X X X | / / / | X / / / # / | . . * | / . * * ** * | . . / | * . / / # / | / / X | / / X * ** * | * * X | * * X Fig 5Z: rrrcb\rccbb Fig 5Z inverse: rccbb\rrrcb rcccb\rrcbb transpose rrcbb\rcccb transpose sashimi mutant starfish (jellyfish + 1-fish)

[Figure based on Mike Barker's 1-link mutant swordfish here]

WHALE: (a token sampling)

Code: Select all: X * X | X * X | X * X X / X | X / X | X / X / . / | / . / | / . / * . * | * . * | * . * X * X | X * X | X * X X / X | X / X | X / X ---------+----------+---------- ---------+----------+---------- X * X | X * X | X * X X / X | X / X | X / X / . / | / . / | / . / * . * | * . * | * . * X * X | X * X | X * X X / X | X / X | X / X ---------+----------+---------- ---------+----------+---------- X * X | X * X | X * X X / X | X / X | X / X / . / | / . / | / . / * . * | * . * | * . * X * X | X * X | X * X X / X | X / X | X / X Fig 6A: cccccc\rrrrrr Fig 6A inverse: rrrrrr\cccccc self-transpose (basic) whale

Code: Select all: . / . | * X * | * X * . * . | / X / | / X / / / / | X / X | X / X * * * | X *X X | X *X X . / . | * X * | * X * . * . | / X / | / X / ---------+----------+---------- ---------+----------+---------- * X * | . / . | * X * / X / | . * . | / X / X / X | / / / | X / X X *X X | * * * | X *X X * X * | . / . | * X * / X / | . * . | / X / ---------+----------+---------- ---------+----------+---------- * X * | * X * | . / . / X / | / X / | . * . X / X | X / X | / / / X *X X | X *X X | * * * * X * | * X * | . / . / X / | / X / | . * . Fig 6B: rrrccc\bbbbbb Fig 6B inverse: bbbbbb\rrrccc self-transpose self-transpose mutant whale

[Figure based on Ruud's post here]

Code: Select all: ** * *** | *X X X | ** ** * / / # | / X X | / / / X # # | / / / | X X / X ** ** | *X ** ** | X X * * . . | X / / | * * . / . . | X * * | / / . ----------+----------+---------- ----------+----------+---------- * . . | * . . | * * . / . . | / . . | / / . * . . | * . . | * * . / . . | / . . | / / . X / # | X / / | X X / X * ** | X * * | X X * ----------+----------+---------- ----------+----------+---------- X / # | ** * * | * * . X * ** | / / / | / / . / / @ | *X X X | X X / *X * *** | / X X | X X * / / @ | *X X X | X X / *X * *** | / X X | X X * Fig 6Y: rrrrbb\rccccb Fig 6Y: rccccb\rrrrbb transpose ccccbb\rrrrcb transpose rrrrcb\ccccbb sashimi mutant whale

Above sashimi mutant whale r2689b27\r1c1478b8 plus fins r2c2, r267c3 plus endo-fin r89c3 based on post by daj95376 here.

Code: Select all: / X / | X / X | / / / * X * | X * X | * * * / * . | * / * | . . / * / . | / * / | . . * X * * | * X * | * * X X / / | / X / | / / X ---------+----------+---------- ---------+----------+---------- *X * * | * X * | * * X / / / | / X / | / / X / *X X | X / X | / / / *X / X | X * X | * * * X * * | * / * | . . / X / / | / * / | . . * ---------+----------+---------- ---------+----------+---------- # ** . | X # X | . . # ** # . | X ** X | . . ** # * . | X / X | . . / ** / . | X * X | . . * # * . | X / X | . . / ** / . | X * X | . . * Fig 6Z: rrcccb\rrcccb Fig 6Z inverse: rrcccb\rrcccb (r15c159b8\r34c246b4) (r34c246b4\r15c159b8) rrrccb\rrrccb transpose rrrccb\rrrccb transpose sashimi mutant whale

[Figure based on Obi-Wahn's post here]

True examples: (Type of fish followed by base/cover)

Code: Select all: Finned X-wing r39\c27: 5.....1..2...16.8...35....7...4.8.6...6....9..85..32...5.64.9....91.....3......14 *--------------------------------------------------------------------* | 5 479-6 478 | 23789 2789 2479 | 1 234 2369 | | 2 479 47 | 379 1 6 | 345 8 359 | |#14689 *1469 3 | 5 289 249 |*46 24 7 | |----------------------+----------------------+----------------------| | 179 12379 127 | 4 2579 8 | 357 6 35 | | 47 2347 6 | 27 257 1 | 34578 9 358 | | 479 8 5 | 79 6 3 | 2 47 1 | |----------------------+----------------------+----------------------| | 178 5 1278 | 6 4 27 | 9 237 238 | | 4678 2467 9 | 1 3 27 | 678 5 268 | | 3 *267 278 | 2789 2789 5 |*678 1 4 | *--------------------------------------------------------------------* *-----------------------* | .-6 . | . . . | . . 6 | | . . . | . . . | . . . | |#6*6 / | / / / |*6 / / | |-------+-------+-------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------+-------+-------| | . . . | . . . | . . . | | 6 6 . | . . . | 6 . 6 | | /*6 / | / / / |*6 / / | *-----------------------*

Code: Select all: Mutant Jellyfish r47c14\b4578: ...3.9.7.8..4.....1........2..5..6...3.....4.....1....5.....8......2.1.....7....9 46 2456 2456 | 3 8 9 | 245 7 1 8 2579 23579 | 4 567 1 | 2359 23569 2356 1 4579 34579 | 26 567 2567 | 3459 35689 34568 ----------------------+----------------------+--------------------- 2 *4789 *4789 | 5 *3479 3478 | 6 1 38 *679 3 1 |*2689 67-9 2678 | 2579 4 258 *4679 45678-9 45678-9|*2689 1 234678 | 2379 2389 238 ----------------------+----------------------+--------------------- 5 *24679 *24679 | 1 *3469 346 | 8 236 23467 *34679 4678-9 4678-9 |*689 2 34568 | 1 356 34567 346 1 2468 | 7 3456 34568 | 2345 2356 9 / . . | / . . | . . . / 9 9 | / . . | 9 9 . / 9 9 | / . . | 9 9 . ----------+-----------+---------- / *9 *9 | / *9 . | / / / *9 . . | *9 -9 . | 9 . . *9 -9 -9 | *9 . . | 9 9 . ----------+-----------+---------- / *9 *9 | / *9 . | / / / *9 -9 -9 | *9 . . | . . . . . . | . . . | . . . candidates of r47c14 are covered by b4578 for exclusions r5689c2356. Note there can be no candidates at the intersections of r47c14. The same exclusions are available via grouped single-digit coloring (empty rectangles).

by **Ocean** » Sun Oct 29, 2006 6:30 am

tarek wrote:Following the explosive increase in the number of different species of fish used by the players, there was a need for a reference thread where fish terms, categories & examples are all in one place. This thread also continues the discussion that started all of this here.
(...)
Code: Select all
Types of Fish: 1. basic: N rows * N columns or vv. (no fin) 2a. Finned:N rows * N columns or vv. (with fin, the pattern is limited to "basic fish with extra candidates") 2b. Sashimi: N rows * N columns or vv.(with fin, not limited to 2a) 3. Franken: N (rows+boxes) * N (columns+boxes) or vv. (no fins) 4. Finned franken: N (rows+boxes) * N (columns+boxes) or vv. (with fins) 5. Mutant: N Sectors * N Sectors (no fins) 6. Finned mutant: N sectors * N sectors (with fins) 7. Kraken: Any fish (1-6) that requires life support (information from outside the pattern)

Thanks tarek for starting to construct this aquarium.

My first contribution to the collections is to bring forward a puzzle by Nick70, an exemplar of a rare, or at least little studied species classified as finned mutant: bbbb\rrcc.

Code: Select all: # #Nick70: # ...1....2 .1..5.... ..7...6.. 5....2... .4..6..7. ...5....1 ..2...3.. ....9..8. 3....1... Candidate '8': finned mutant bbbb\rrcc *-----------------------------------------------------------* |*4689 *689 *489 | 1 3 7 |-489 5 2 | | 2 /1 /3 | 489 5 6 | 7 49 #489 | |*489 /5 /7 | 489 2 48 | 6 1 3 | |-------------------+-------------------+-------------------| | 5 3 *89 | 7 1 2 |*489 469 *689 | |*89 /4 /1 | 3 6 89 | 2 /7 /5 | | 7 /2 /6 | 5 48 489 |*89 /3 /1 | |-------------------+-------------------+-------------------| | 1 6789 2 | 468 478 5 | 3 469 4679 | | 46 67 5 | 2 9 3 | 1 8 467 | | 3 6789 489 | 468 478 1 | 5 2 4679 | *-----------------------------------------------------------* *-----------------------------------------------------------* |*4689 *689 *489 | 1 3 7 |*489 5 2 | | 2 /1 /3 | 489 5 6 |/7 /49 *489 | |*489 /5 /7 | 489 2 48 |/6 /1 3 | |-------------------+-------------------+-------------------| | 5 3 *89 | 7 1 2 |*489 469 -689 | |*89 /4 /1 | 3 6 89 | 2 7 5 | | 7 /2 /6 | 5 48 489 |#89 3 1 | |-------------------+-------------------+-------------------| | 1 6789 2 | 468 478 5 | 3 469 4679 | | 46 67 5 | 2 9 3 | 1 8 467 | | 3 6789 489 | 468 478 1 | 5 2 4679 | *-----------------------------------------------------------* First diagram: r1c7<>8. Second diagram: r4c9<>8. Choose any of the two eliminations of an '8', and the puzzle is solved.

by **ronk** » Sun Oct 29, 2006 1:12 pm

Here is an unfinned mutant jellyfish (4-fish) from #61 of the top1465.

Code: Select all: ...3.9.7.8..4.....1........2..5..6...3.....4.....1....5.....8......2.1.....7....9 46 2456 2456 | 3 8 9 | 245 7 1 8 2579 23579 | 4 567 1 | 2359 23569 2356 1 4579 34579 | 26 567 2567 | 3459 35689 34568 ----------------------+----------------------+--------------------- 2 4789 4789 | 5 3479 3478 | 6 1 38 679 3 1 | 2689 679 2678 | 2579 4 258 4679 456789 456789 | 2689 1 234678 | 2379 2389 238 ----------------------+----------------------+--------------------- 5 24679 24679 | 1 3469 346 | 8 236 23467 34679 46789 46789 | 689 2 34568 | 1 356 34567 346 1 2468 | 7 3456 34568 | 2345 2356 9 / . . | / . . | . . . / 9 9 | / . . | 9 9 . / 9 9 | / . . | 9 9 . ----------+-----------+---------- / *9 *9 | / *9 / | / / / *9 . . | *9 -9 . | 9 . . *9 -9 -9 | *9 . . | 9 9 . ----------+-----------+---------- / *9 *9 | / *9 / | / / / *9 -9 -9 | *9 . . | . . . . . . | . . . | . . . r47c14\b4578 nutant jellyfish Key: * = base set candidate / = required no candidate - = exclusion

The candidates of r47c14 are covered by b4578 for exclusions r5689c2356. Note there can be no candidates at the intersections of r47c14. The same exclusions are available via grouped single-digit coloring (empty rectangles).

r56c1=9=r4c23-r4c5=9=r56c4-9-r8c4=9=r7c5-9-r7c23=9=r8c1-9-r56c1= implying r5689c2356<>9

Further steps are required to solve the puzzle.

[edit: correctly show r47c6 as empty cells]

by **Mike Barker** » Sun Oct 29, 2006 2:49 pm

Here's a contribution to the thread on Kraken fish based mostly on the posts in Ruud's ARC thread and Luke's finned X-wing thread. I figure this can serve as a starting point for discussions of style and content for this thread.

In a fish, defined by the cells of "n" units (rows, columns, and/or boxes) containing a given digit (the fish digit), a candidate is eliminated from a cell (the candidate elimination cell or CEC) when its existance allows only n-1 or fewer fish digit candidates to be placed in the "n" units. In a standard fish the CEC directly sees sufficient cells of the fish to prevent placement. In a Kraken fish the CEC can also prevent placement if it is linked to elements of the fish via its tentacles: stong links, grouped strong links, bivalue cells or other ALS, or any other linking element. A single link or a chain of links may be used. In addition, multiple (one, two, or more) links/chains can be used to link to different elements of the fish. When such links are used it is possible for a candidate which is not the fish digit to be eliminated, in which case it is also possible for the CEC to be part of the fish.

In the following examples the fish is r25c25 with fin r8c2 and "x" is the fish digit. In the first example, a strong link and a "direct link" are used to link the fish to possible CECs, r25c9. In this case, either both members of the covering set, c25, must contain a cell from the fish with the fish digit or the fin and one member of the covering set must. One way to view this elimination is that either the fin contains the digit or it does not. If the fin does then c9c8=x because of the strong link. If the fin does not, then the fish is reduced to a basic fish and r25c9<>x. In either case r25c9<>x. In a more general view of the elimination, any cell which is seen by the fin and all fish elements of one of the covering sets, either directly or indirectly, can not contain the fish digit. In this case r8c2-x-r7c3=x=r7c9-r25c9 and either r2c25-x-r2c9 or r5c25-x-r5c9 and the same eliminations occur.

Code: Select all: . . . | . . . | . . . . X . | . X . | . . * . | . | . | . | . . . ---|---+---|---+------- . | . | . | . | . . . . X . | . X . | . . * . | . | . . . | . . . ---|---+-------+------- . | x================x . # . | . . . | . . . . . . | . . . | . . .

In the next example, a grouped strong link and a bivalue cell link the fish to the CECs, r79c9: r8c2=y=r8c78-y-r79c9 and r5c25-x-r5c9-r79c9. In this example the candidate to be eliminated, "y", is not the fish digit.

Code: Select all: . . . | . . . | . . . . X . | . X . | . . . . | . | . | . | . . . ---|---+---|---+------- . | . | . | . | . . . . X . | . X . | . . xy . | . | . . . | . . . ---|---+-------+------- . | . | . . . | . . * . #y=============y y . . . . | . . . | . . *

In the last example, two bivalue/ALS chains link the fish to the CEC, r5c5: r5c2-x-r68c1-z-r8c5-y-r5c5 and r8c2-x-r9c3-w-r8c1-z-r8c5-y-r5c5. In addition, because the CEC directly replaces a fish element "y" is again eliminated. Note that since each fish-to-CEC link estabilishes an independent truth condition, individual links/chains can overlap without restriction.

Code: Select all: . . . | . . . | . . . . X . | . X . | . . . . | . | . | . | . . . ---|---+---|----+------ . | . | . | . | . . . . X . | . Xy . | . . . xw | . | . . . | . . . ---|---+--------+------ . | . | . . . | . . . zw # . | . yz . | . . . . . wx| . . . | . . .

Kraken fish have been used in the past to solve published puzzles. Myth Jellies used a strong link with a 2 finned Swordfish to perform the elimination in Unsolvable #4. The fins of the fish, r5c7 and r9c4, connect to the CEC, r4c8, directly and via the strong link, r9c4-7-r4c6=7=r7c6-7-r4c8.

Code: Select all: +-----------------+--------------------+------------------+ | 179* 489 5 | 3 89 24 | 6 127* 279* | | 1689 2 3 | 5689 7 569 | 159 4 59 | | 679 49 679 | 569 1 24 | 2579 3 8 | +-----------------+--------------------+------------------+ | 3 5 8 | 4 69 679@ | 279 26-7 1 | | 79* 6 4 | 2 5 1 | 379# 8 379* | | 2 1 79 | 679 3 8 | 579 567 4 | +-----------------+--------------------+------------------+ | 4 3 69 | 156789 2 5679@ | 1578 157 567 | | 568 7 2 | 1568 4 56 | 1358 9 356 | | 569 89 1 | 5679# 689 3 | 4 257* 2567* | +-----------------+--------------------+------------------+

Anne Morelot used a Kraken Fish, a two finned swordfish, to advance #5000 from Ruud's Top 50000. In this case the fins/body of the fish connects to the CEC, r4c9, via an ALS, r4c4-9-r4c35-8-r4c9, and a bivalue, r9c2|r8c7-9-r9c8-8-r4c9.

Code: Select all: +--------------------+-------------------+---------------------+ | 3589 589* 35689 | 2579* 2379 1 | 4 3689 2358 | | 7 589* 34589 | 259* 6 345 | 23589* 1 2358 | | 1 2 34569 | 8 359 345 | 7 369 35 | +--------------------+------------------+--------------------+ | 4 3 589@ | 1569* 59@ 2 | 1568 7-8 1578 | | 6 17 2 | 157 8 357 | 135 4 9 | | 589 17 589 | 4 3579 3567 | 13568 2 1358 | +--------------------+------------------+--------------------+ | 238 68 1 | 267 247 9 | 238 5 23478 | | 2359 4 359 | 257 1 578 | 2389# 3789 6 | | 2589 5689# 7 | 3 245 4568 | 128 #89 1248 | +--------------------+------------------+--------------------+

by **Mike Barker** » Sun Oct 29, 2006 2:51 pm

Just for the fun of it here's a Mutant Squirmbag:

Code: Select all: #01: Mutant Squirmbag (r259,c57): r29c138|r5c136|r67c5|r137c7 => r13c8<>7 Cover=r7,c13,b35,fin=r9c8 +-----------------------+------------------+--------------------+ | 5 78 1 | 27 9 4 | 67* 38-7 2368 | | 3478* 2 3478* | 6 18 5 | 9 478* 148 | | 4679 479 4679 | 127 128 3 | 17* 458-7 12458 | +-----------------------+------------------+--------------------+ | 689 589 5689 | 3 56 2 | 4 1 7 | | 17* 3 57* | 159 4 78* | 2 6 89 | | 12467 147 2467 | 19 67* 1678 | 5 389 389 | +-----------------------+------------------+--------------------+ | 13489 145789 3489 | 145 567* 167 | 167* 2 1469 | | 12479 14579 24579 | 1245 3 167 | 8 4579 14569 | | 1247* 6 2457* | 8 12 9 | 3 457# 145 | +-----------------------+------------------+--------------------+

Even more interesting, here's one with two fins:

Code: Select all: #02: Mutant Squirmbag (r15,c24,b9): r1c1568|r5c58|r2379c2|r278c4|r7c789|r89c8 => r9c5<>5 Cover=r7,c58,b12, fins=r9c2,r8c4 +---------------------+-------------------+-------------------+ | 159* 7 14 | 6 1259* 459* | 3 1258* 28 | | 8 13459* 134 | 157* 12379 2459 | 1457 1257 6 | | 6 1345* 2 | 8 137 345 | 1457 9 145 | +---------------------+-------------------+-------------------+ | 129 19 5 | 3 6 7 | 148 128 1248 | | 237 23 8 | 4 25* 1 | 67 2567* 9 | | 4 6 17 | 9 8 25 | 157 3 125 | +---------------------+-------------------+-------------------+ | 12357 125* 9 | 157* 4 36 | 1568* 1568* 158* | | 135 8 1346 | 15# 39 369 | 2 1456* 7 | | 157 145# 167 | 2 17-5 8 | 9 1456* 3 | +---------------------+-------------------+-------------------+

by **Finlip** » Mon Oct 30, 2006 1:29 pm

Ocean wrote:First diagram: r1c7<>8. Second diagram: r4c9<>8.
Choose any of the two eliminations of an '8', and the puzzle is solved.

I was able to see that both your elimination are perfectly all right but fail to understand the terms.

by **Finlip** » Mon Oct 30, 2006 1:41 pm

ronk wrote:/ . . | / . . | . . .
/ 9 9 | / . . | 9 9 .
/ 9 9 | / . . | 9 9 .
----------+-----------+----------
/ *9 *9 | / *9 . | / / /
*9 . . | *9 -9 . | 9 . .
*9 -9 -9 | *9 . . | 9 9 .
----------+-----------+----------
/ *9 *9 | / *9 . | / / /
*9 -9 -9 | *9 . . | . . .
. . . | . . . | . . .

Do you know how I understand this?
If either of r8c23=9, both r4c23<>9 to put a 9 on c1. This forces r4c5 and then r8c4 to be 9 which results in a conflict.

by **Mage** » Mon Oct 30, 2006 6:26 pm

And do you know how I understand it ?

Code: Select all: +---------+---------+---------+ | . . . | . . . | . . . | | . 9 9 | . . . | 9 9 . | as a grouped digit-to-digit loop : | . 9 9 | . . . | 9 9 . | +---------+---------+---------+ r7c5=r7c23 - r8c1=r56c1 - r4c23=r4c5 | . 9——9——————9 . | . . . | | 9 . . | 9 -9 . | 9 . . | | 9 -9 -9 | 9 . . | 9 9 . | +-|-------+---------+---------+ | | 9——9——————9 . | . . . | | 9 -9 -9 | 9 . . | . . . | | . . . | . . . | . . . | +---------+---------+---------+

Mage

by **daj95376** » Mon Oct 30, 2006 6:28 pm

[Edit: withdrawn]

by **daj95376** » Mon Oct 30, 2006 6:58 pm

[Edit: withdrawn]

by **ronk** » Mon Oct 30, 2006 7:23 pm

Mage wrote:r7c5=r7c23 - r8c1=r56c1 - r4c23=r4c5

That explains r5c5<>9. What about r6c23<>9 and r8c23<>9?

by **Myth Jellies** » Tue Oct 31, 2006 12:33 am

ronk wrote:
Mage wrote:r7c5=r7c23 - r8c1=r56c1 - r4c23=r4c5

That explains r5c5<>9. What about r6c23<>9 and r8c23<>9?

It is an AIC loop, so all the weak links can be treated as conjugate.

by **ronk** » Tue Oct 31, 2006 5:34 am

Myth Jellies wrote:It is an AIC loop, so all the weak links can be treated as conjugate.

But of course. I was so focused on the mutant jellyfish, I didn't see the mutant swordfish.

Code: Select all: * * X | . . . | X * * / / X | . . . | X / / * * X | . . . | X * * / / X | . . . | X / / X X / | / / / | / X X X X * | * * * | * X X ----------+----------+--------- ----------+----------+--------- . . / | . . . | / . . . . * | . . . | * . . . . / | . . . | / . . . . * | . . . | * . . . . / | . . . | / . . . . * | . . . | * . . ----------+----------+--------- ----------+----------+--------- X X / | / / / | / X X X X * | * * * | * X X * * X | . . . | X * * / / X | . . . | X / / * * X | . . . | X * * / / X | . . . | X / / rrcc\bbbb mutant jellyfish bbbb\rrcc mutant jellyfish (inverse) * * X | . . . | . * . / / X | . . . | . / . * * X | . . . | . * . / / X | . . . | . / . X X / | / / / | / X / X X * | * * * | * X * ----------+----------+--------- ----------+----------+--------- . . / | . . . | . * . . . * | . . . | . / . . . / | . . . | . * . . . * | . . . | . / . . . / | . . . | . * . . . * | . . . | . / . ----------+----------+--------- ----------+----------+--------- X X / | / / / | / X / X X * | * * * | * X * * * X | . . . | . * . / / X | . . . | . / . * * X | . . . | . * . / / X | . . . | . / . rrc\cbb mutant swordfish cbb\rrc mutant swordfish (inverse)

by **Steve R** » Tue Oct 31, 2006 2:29 pm

Mike

Thank you for your most interesting note of 29th and for presenting it in such a clear way.

One point puzzles me a little; I cannot see the fish element in the third illustrative example:

Code: Select all: . . . | . . . | . . . . X . | . X . | . . . . | . | . | . | . . . ---|---+---|----+------ . | . | . | . | . . . . X . | . Xy . | . . . xw | . | . . . | . . . ---|---+--------+------ . | . | . . . | . . . zw # . | . yz . | . . . . . wx| . . . | . . .

When written as nice loops the first two examples both contain indifferently inferential links which I think of as characteristic of kraken fish. In the first it is r8c2 =x- r2c9; in the second r8c2 =x- r5c9. The nice loop for the third illustration, repeated above, does not contain a link of this kind that I can find. Also, the elimination can, I think, be made irrespective of where the Xy cell is placed in the fifth column.

So my conundrum is whether the third creature is a fish or a red herring. What do you think?

Steve

by **Mike Barker** » Tue Oct 31, 2006 8:48 pm

The example combined two concepts. First the idea that a chain could be used to link the fish to the CEC. Second that the CEC can be part of the fish itself. The two chains are r5c2-x-r68c1-z-r8c5-y- and r8c2-x-r9c3-w-r8c1-z-r8c5-y-. These link to any cell which sees r8c5, including r5c5 which is part of the fish. Another link/chain to r5c5 might be used, but it is not required in this case. Reducion of the covering set for the fish to only r2 occurs if r5c5=y, that is, if the CEC is part of the fish. Not a red herring, but definitely a different kettle of fish. Similar reductions are used with unique rectangles, which is where I got the idea from when developing the Sudoku Unification Model.

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