Strong links within Fish Patterns:

Advanced methods and approaches for solving Sudoku puzzles

Strong links within Fish Patterns:

Postby StrmCkr » Fri Nov 11, 2011 11:39 am

Properties:
an incomplete Fish size N, with +1 extra Cell
an AIC of any length: where the starting cell is the +1 cell of the fish pattern and Ending cell is with in line of sight of the strong links contained in the fish size N.
elimination occur in the ending cell of the AIC and the digit removed is the Fish candidate.

Code: Select all
 *------------------*                            *----------------------*
 |...|B-x  X   .|...|                            |AB  . .|Ax   /   /|...|
 |...|.    X   .|...|                            |B-x . .|X    X   X|...|
 |...|.    X   .|...|                            |.   . .|/    /   /|...|
 |---+----------+---|                            |-------+----------+---|
 |...|AB   /   .|...|                            |.   . .|.    .   .|...|
 |...|.   AX   .|...|                            |.   . .|.    .   .|...|
 |...|.    /   .|...|                            |.   . .|.    .   .|...|
 |---+----------+---|                            |-------+----------+---|
 |...|.    /   .|...|                            |.   . .|.    .   .|...|
 |...|.    /   .|...|                            |.   . .|.    .   .|...|
 |...|.    /   .|...|                            |.   . .|.    .   .|...|
 *------------------*                            *----------------------*
Strong link between digits B                     Strong link between digits B
Strong link between digits A                     Strong link between digits A
Almost Cyclopes fish on digit X                  Almost Cyclopes fish on digit X
 =>> R1C4 <> x                                    =>> R2C1 <> x


Code: Select all
 *---------------------*                            *---------------------*
 |.  B-x  X|. . .|. X .|                            |.  B-x  X|. . .|. X .|
 |.  .    /|. . .|. / .|                            |.  .    X|. . .|. / .|
 |.  .    /|. . .|. / .|                            |.  .    X|. . .|. / .|
 |---------+-----+-----|                            |---------+-----+-----|
 |.  .    /|. . .|. / .|                            |.  AB   /|. . .|. / .|
 |.  .    /|. . .|. / .|                            |.  .   AX|. . .|. / .|
 |.  .    X|. . .|. X .|                            |.  .    X|. . .|. X .|
 |---------+-----+-----|                            |---------+-----+-----|
 |.  AB   /|. . .|. / .|                            |.  .    /|. . .|. / .|
 |.  .   AX|. . .|. / .|                            |.  .    /|. . .|. / .|
 |.  .    /|. . .|. / .|                            |.  .    /|. . .|. / .|
 *---------------------*                            *---------------------*
Strong link between digits B                        Strong link between digits B
Strong link between digits A                        Strong link between digits A
Almost  X-wing on digit X                           Almost Finned X-wing on digit X
=>> R1C2 <> x                                        =>> R1C2 <> x

Code: Select all
 *-----------------*
 |. .  .|...|. .  .|
 |/ x  /|/x/|/ Ax /|
 |. .  .|...|. .  .|
 |------+---+------|
 |. .  .|/x/|. .  .|
 |. B-x.|xxx|. AB .|
 |. .  .|/x/|. .  .|
 |------+---+------|
 |. .  .|...|. .  .|
 |. .  .|...|. .  .|
 |. .  .|...|. .  .|
 *------------------*
Strong link between digits B
Strong link between digits A
Almost Empty Rectangle on digit X
 =>> R5C2 <> x

Code: Select all
 *---------------------*
 |.  B-x  X|. X .|. X .|
 |.  .    X|. ./.|. / .|
 |.  .    X|. / .|. / .|
 |---------+-----+-----|
 |.  AB   /|. / .|. / .|
 |.  .   AX|. / .|. / .|
 |.  .    X|. X .|. X .|
 |---------+-----+-----|
 |.  .    /|. / .|. / .|
 |.  .    X|. X .|. X .|
 |.  .    /|. / .|. / .|
 *---------------------*
Strong link between digits B
Strong link between digits A
Almost Finned Sword Fish on digit X
 =>> R1C2 <> x
Last edited by StrmCkr on Sat Nov 12, 2011 3:26 am, edited 5 times in total.
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Re: Strong links within Fish Patterns:

Postby ronk » Fri Nov 11, 2011 12:18 pm

Do you have an example, preferably one that occurs after SSTS?

BTW I think most people would call your example a "kraken x-wing."
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Re: Strong links within Fish Patterns:

Postby StrmCkr » Fri Nov 11, 2011 12:36 pm

not after ssts: needs an als-xz to reach the point where i found the move.

Code: Select all
.---------------------.-------------------.-------------------.
| 8      5      179   | 49    6      2    | 79    3     149   |
| 1369   369    4     | 89@-5 7      359@ | 2589@ 1258  129   |
| 2      379    379   | 1     3589   3459@| 6     578   489   |
:---------------------+-------------------+-------------------:
| 13469  23469  5     | 2489@ 12389  7    | 289   268   23689 |
| 13679  8      12379 | 259   12359  1359@| 57@   4     2369  |
| 3479   23479  239   | 6     23589  3459@| 1     57    2389  |
:---------------------+-------------------+-------------------:
| 3479   23479  6     | 279   129    8    | 24    12    5     |
| 579    279    2789  | 2579  4      19   | 3     1268  1268  |
| 45     1      28    | 3     25     6    | 248   9     7     |
'---------------------'-------------------'-------------------'

Code: Select all
(4)R4C4  =  (8)R2C4
||
(8) R4C4 =  (4)R6C6 
                 |
                (5) almost finned fish in cells
                  R2356C6   -  R25C7
 ==>> R24 <> 5


kraken x-wing.
probably, what interests me is the underling logic behind such moves: these simplistic attestations show that its theoretically plausible to build extending logic onto the known fish patterns and compute further eliminations and is probably the fundamental logic behind more advanced version like the bi bi patter seen in the monsters puzzles.
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Re: Strong links within Fish Patterns:

Postby denis_berthier » Sat Nov 12, 2011 10:14 am

StrmCkr wrote:
Code: Select all
(4)R4C4  =  (8)R2C4
||
(8) R4C4 =  (4)R6C6 
                 |
                (5) almost finned fish in cells
                  R2356C6   -  R25C7
 ==>> R24 <> 5


Hi StrmCkr,

Here is an interpretation of this elimination in terms of g-whips:

g-whip[2]: c6n5{r2 r456} - c7n5{r5 .} ==> r2c4 <> 5
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Re: Strong links within Fish Patterns:

Postby StrmCkr » Tue Nov 25, 2014 6:38 am

bump to see if i can get any renewed interest in this idea
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