The New Sudoku Players' Forum

[StrmCkr]

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

[ronk]

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

BTW I think most people would call your example a "kraken x-wing."

[StrmCkr]

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.

[denis_berthier]

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

[StrmCkr]

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

[yzfwsf]

My solver has implemented almost fish strong links. Here almost fish means that any fish of size n has n+1 cover sets.Then these n+1
houses are strongly linked to each other.

[StrmCkr]

Is that new in your solver?

[yzfwsf]

Hi StrmCkr:I thought you do not come to the forum, it seems to be I overthink。
Yes since version 626, at this stage just directly used the relevant strong links in ALS Chain and Forcing Chain, did not think of a good visual representation method, so also not explicitly mentioned in the chain expression equation, if you find the chain diagram in my solver with arrow lines across house then it may be AF strong links (and possibly AFW links).

[StrmCkr]

That is great!
always wanted this on to be relevant

Agreeded visuals are a nightmare as fish can get huge and use many cells.

This one's been my drawing board forever as my fish algo for regular fish can take 20 mins to cycle all 7x7+2 fish
I don't want to know what that be link generating all +1-3 cells almost fish.

Yes I still frequent here,
I've been busy trying to build reddit sudokus wiki to be more encombering as it was very limited and outdated

That and relearning a programing language to swap to a Gui instead of free pascal for my own solver.

Also been testing

Alc, pairs tripples quads

Alc sos (ahs +als)

[yzfwsf]

This one's been my drawing board forever as my fish algo for regular fish can take 20 mins to cycle all 9x9+2 fish
I don't want to know what that be link generating all +1-3 cells almost fish.

For normal fish I use the bitwise algorithm directly, after all Combin(9,4) is not very big, so it is fast, but complex fish is another story, I use the inverse algorithm plus bitwise operations to reduce the size of the combination, but also it will never take more than a minute. For AF strong links, I only look for basic fish, which is fast,and should be milliseconds.
I don't understand what you mean by "9x9+2" and "+1-3".

Code: Select all

*-----------*
|../|./.|/./|
|..x|.x.|/.x|
|..x|.x.|x.x|
|---+---+---|
|..x|.x.|x.x|
|../|./.|/./|
|..x|./.|x.x|
|---+---+---|
|../|./.|/./|
|..x|.x.|/.x|
|../|./.|/./|
*-----------*

xc3579\r23468 is Almost Fish(Jellyfish)，For this almost fish I will generate 10 pairs of strong links.
x(r2c359 == r3c3579); x(r2c359 == r4c3579) ...

[yzfwsf]

Complete the modification of the chain expression, and then figure out how to implement the visual presentation.

ALS Discontinuous Nice Loop: (5=2369)r8c1389 - (9=261)r6c238 - r6c5 = r7c1(c15\r467) - (1=35)r7c58 - r7c12 = 5r8c1 => r8c7<>5

Cell Forcing Chain: Each candidate in r3c9 true in turn will all lead to: r9c7<>5
1r3c9 - 1r23c8 = (1-3)r7c8 = (3-5)r7c5 = 5r9c5
6r3c9 - (6=21)r78c9 - 1r39c9 = 1r3c8(r39\c389) - 5r3c8 = 5r9c5(r39\c578)
8r3c9 - 8r9c9 = 8r9c7

[StrmCkr]

That's slick! I'll check it out later this week/evening


My fish solvers nxn+k based as a find all it builds base first then cover and adds up to, +2 covers sectors
For 7x7+2 out of 27 sectors for digits 1-9 (selectable sectors reduced by solved digits)

I do agree basic fish is fast... All types not so much.

Speedup for me would be not having each number repeat the base/cover process
And adding in a template check to skip numbers that don't have template delete triggers.

I have to fix that typo... My theory code goes to 9x9+2 for some no fish eliminations I was working on off again.

+1-3 extra cells that land outside the fish pattern (a mini sector) for AF linking. Is what I was thinking is possible

From my notes but it's probably more then that

[StrmCkr]

so its not coded into AIC yet? only als+aic

Code: Select all

+---------------------+-----------------------+---------------------+
| 8      5      179   | 49      6      2      | 79      3     149   |
| 1369   369    4     | 9-5(8)  7      39(5)  | 289(5)  1258  129   |
| 2      379    379   | 1       3589   349(5) | 6       578   489   |
+---------------------+-----------------------+---------------------+
| 13469  23469  5     | 29(48)  12389  7      | 289     268   23689 |
| 13679  8      12379 | 259     12359  139(5) | 7(5)    4     2369  |
| 3479   23479  239   | 6       23589  39(45) | 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     |
+---------------------+-----------------------+---------------------+

AIC + almost Fish
(8)r2c4 = r4c4 - (4)r4c4 = r6c6 - (5)r6c6 = [ c67 / r235 ] {finned x-wing} => r2c4 <> 5

[urhegyi]

so its not coded into AIC yet? only als+aic

Code: Select all

+---------------------+-----------------------+---------------------+
| 8      5      179   | 49      6      2      | 79      3     149   |
| 1369   369    4     | 9-5(8)  7      39(5)  | 289(5)  1258  129   |
| 2      379    379   | 1       3589   349(5) | 6       578   489   |
+---------------------+-----------------------+---------------------+
| 13469  23469  5     | 29(48)  12389  7      | 289     268   23689 |
| 13679  8      12379 | 259     12359  139(5) | 7(5)    4     2369  |
| 3479   23479  239   | 6       23589  39(45) | 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     |
+---------------------+-----------------------+---------------------+

AIC + almost Fish
(8)r2c4 = r4c4 - (4)r4c4 = r6c6 - (5)r6c6 = [ c67 / r235 ] {finned x-wing} => r2c4 <> 5

I suppose this is the original sudoku:

Code: Select all

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

What are the (not basic) steps before you found this elimination(R2C4<>5)?

[denis_berthier]

so its not coded into AIC yet? only als+aic

Code: Select all

+---------------------+-----------------------+---------------------+
| 8      5      179   | 49      6      2      | 79      3     149   |
| 1369   369    4     | 9-5(8)  7      39(5)  | 289(5)  1258  129   |
| 2      379    379   | 1       3589   349(5) | 6       578   489   |
+---------------------+-----------------------+---------------------+
| 13469  23469  5     | 29(48)  12389  7      | 289     268   23689 |
| 13679  8      12379 | 259     12359  139(5) | 7(5)    4     2369  |
| 3479   23479  239   | 6       23589  39(45) | 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     |
+---------------------+-----------------------+---------------------+

AIC + almost Fish
(8)r2c4 = r4c4 - (4)r4c4 = r6c6 - (5)r6c6 = [ c67 / r235 ] {finned x-wing} => r2c4 <> 5

Starting with the same resolution state, this elimination is obtained by a z-chain[4]:

Code: Select all

z-chain[4]: c4n8{r2 r4} - b5n4{r4c4 r6c6} - c6n5{r6 r5} - c7n5{r5 .} ==> r2c4≠5