The New Sudoku Players' Forum

[pjb]

Code: Select all

+-------+-------+-------+
| . . . | * . . | . . . |
| . . . | * . . | . . . |
| / X / | X / X | / / / |
+-------+-------+-------+
| . . . | / / / | . . . |
| . . . | / / X | . . . |
| / X / | X / / | / / / |
+-------+-------+-------+
| . . . | * . . | . . . |
| . . . | * . . | . . . |
| . . . | * . . | . . . |
+-------+-------+-------+

Code: Select all

+-------+-------+-------+
| . . . | . * . | . . . |
| / X / | / X / | X / / |
| . . . | . * . | . . . |
+-------+-------+-------+
| / X / | / X / | / / / |
| . * . | . * . | . . . |
| / / X | / X / | X / / |
+-------+-------+-------+
| . . . | . * . | . . . |
| . . . | . * . | . . . |
| . . . | . * . | . . . |
+-------+-------+-------+

Consider these 2 exemplars: X = candidate; / = no candidate; * = candidate eliminations; . = anything.

I encountered them in the base/link triplets section in the "General Logic for Sudoku" at SudokuOne.com.
While Allan Barker explains them using his triplet theory, they can be alternatively explained fairly readily.
In the first, one of the X's in row 3 must be true, and in each case one of the X's in column 4 is forced to be true.
In the second similarly, one of the X's in row 2 must be true, forcing one of the X's in column 5 to be true.
The second looks like a sashimi swordfish, but with extra eliminations. The first I can't put a name to.

Here is an example of the first: (clear basics, then finned X-wing)
1.......2.3..4..5...6...7.....8.2....5..6..3....5.3.....3...1...4..9..6.2.......3

Code: Select all

 1       89      45*    | 67     58     67     | 3      489*   2     
 89      3       7      | 2      4      1      | 69     5      689   
 45      2       6      | 9      3      58     | 7      1      48*     
------------------------+----------------------+---------------------
 3       169     49*    | 8      17     2      | 5      479*   4679*   
 7       5       2      | 4      6      9      | 8      3      1     
 4689    1689    489    | 5      17     3      | 469    2      4679   
------------------------+----------------------+---------------------
 5689    6789    3      | 67     2      45678  | 1      789-4  45789 
 58      4       1      | 3      9      578    | 2      6      578   
 2       6789    589    | 1      58     4678   | 49     789-4  3 

No example for second
Any suggestions for naming/classifying them? Apologies if this is old hat.

Phil

[tarek]

Hi Phil,

Your second example can have 2 different ways to cover the same base sectors. I think this can be referred to as Siamese fish. The eliminations can be explained as a combination of 2 fish

[SpAce]

Code: Select all

+-------+-------+-------+
| . . . | * . . | . . . |
| . . . | * . . | . . . |
| / X / | X / X | / / / |
+-------+-------+-------+
| . . . | / / / | . . . |
| . . . | / / X | . . . |
| / X / | X / / | / / / |
+-------+-------+-------+
| . . . | * . . | . . . |
| . . . | * . . | . . . |
| . . . | * . . | . . . |
+-------+-------+-------+

3x4-Obifish (Rank 1): R36B5\c2446 => -c4

aka Endofinned Franken Swordfish: r36b5\c246 ef:r6c4 => -c4

Transformed with Obi-Wahn's arithmetic (to get rid of duplicate sector / endofin):

Code: Select all

r36b5   \ c2446    +c5
r36c5b5 \ c24456    c456 -> b258
r36c5b5 \ c24b258  -b5
r36c5   \ c24b28
=>

3x4-Obifish (Rank 1): R36C5\c24b28 => -c4

aka Finned Mutant Swordfish: r36c5\c2b28 f:r6c4 => -c4

Code: Select all

+-------+-------+-------+
| . . . | . * . | . . . |
| / X / | / X / | X / / |
| . . . | . * . | . . . |
+-------+-------+-------+
| / X / | / X / | / / / |
| . * . | . * . | . . . |
| / / X | / X / | X / / |
+-------+-------+-------+
| . . . | . * . | . . . |
| . . . | . * . | . . . |
| . . . | . * . | . . . |
+-------+-------+-------+

4x5-Obifish (Rank 1): R2446\c2557b4 => -c5, -r5c2

aka Kraken Swordfish r246\c257 rf:[r6c3 - r4c2 = r4c5] => -c5, -r5c2

Transformed (to get rid of duplicate sectors / kraken chain):

Code: Select all

r2446     \ c2557b4     +r5
r24456    \ r5c2557b4    r456 -> b456
r24b456   \ r5c2557b4   -b4
r24b56    \ r5c2557     +c46
r24c46b56 \ r5c245567     c456 -> b258
r24c46b56 \ r5c257b258  -b5
r24c46b6  \ r5c257b28
=>

5x6-Obifish (Rank 1): R24C46B6\r5c257b28 => -c5, -r5c2

aka Finned Mutant Squirmbag r24c46b6\r5c27b28 f:r4c5 => -c5 (doesn't directly prove -r5c2, but it's easy with simpler fishes)

Here is an example of the first: (clear basics, then finned X-wing)
1.......2.3..4..5...6...7.....8.2....5..6..3....5.3.....3...1...4..9..6.2.......3

Code: Select all

 1       89      45*    | 67     58     67     | 3      489*   2     
 89      3       7      | 2      4      1      | 69     5      689   
 45      2       6      | 9      3      58     | 7      1      48*     
------------------------+----------------------+---------------------
 3       169     49*    | 8      17     2      | 5      479*   4679*   
 7       5       2      | 4      6      9      | 8      3      1     
 4689    1689    489    | 5      17     3      | 469    2      4679   
------------------------+----------------------+---------------------
 5689    6789    3      | 67     2      45678  | 1      789-4  45789 
 58      4       1      | 3      9      578    | 2      6      578   
 2       6789    589    | 1      58     4678   | 49     789-4  3 

3x4-Obifish (Rank 1): (4)R14B3\c3889 => -4 r79c8

aka Endofinned Franken Swordfish: (4)r14b3\c389 ef:r1c8 => -4 r79c8

Transformed (to get rid of duplicate sector / endofin):

Code: Select all

r14b3   \ c3889    +c7
r14c7b3 \ c37889    c789 -> b369
r14c7b3 \ c38b369  -b3
r14c7   \ c38b69
=>

3x4-Obifish (Rank 1): (4)R14C7\c38b69 => -4 r79c8

aka Finned Mutant Swordfish (4)r14c7\c38b6 f:r9c7 => -4 r79c8

--
Edit. Corrected a typo (b4 -> b3). Added transformations. Removed fixed corrections.

[pjb]

SpAce,

Thank you for corrections. Second example didn't match exemplar.

Phil

PS Are these "Obi" fish to be found somewhere deep in the UFG?

[SpAce]

Thank you for corrections. Second example didn't match exemplar.

No problem. (I just noticed a typo in my own.)

PS Are these "Obi" fish to be found somewhere deep in the UFG?

I think there are examples there too, probably called nxm or nxn+k fishes. In any case, the original intro is here. The real nice thing about the Obifish representation is that it allows transforming any fish into its equivalent forms. For example, the endofinned fishes above can be transformed into normal finned fishes which are normally simpler to understand. In most cases it allows to get rid of duplicate sectors in the Obifish form too. I'll add some examples of those transformations once I edit my post anyway to correct the typo. (I actually noticed the typo when transforming -- it's good for that too, because you'll quickly notice if the transformed fish doesn't make sense.)

(Typo corrected, transformations added to previous post.)

[tarek]

Well spotted SpAce,

I obviously didn't go beyond a Jellyfish in the 2nd example. Smaller UFG fish would only explain some of the eliminations but not all of them

Nx(N+k) fish would be a great addition to UFG. It was discussed at point in the past but didn't see the light of day.

tarek

[SpAce]

Well spotted SpAce,

Thanks!

Nx(N+k) fish would be a great addition to UFG. It was discussed at point in the past but didn't see the light of day.

Yes, it would be nice. The notations are shorter and the arithmetic is very handy. I think playing with it improves understanding of fish logic in general.

One suggestion. I'd strongly prefer calling it just NxM or N\M. Nx(N+k) is not only harder to write and more complicated looking, but it also kind of suggests that there are some special fin sectors (+k). While it may seem like that when a finned fish is written as an Obifish and an extra cover sector is added for the fin, it's not really true. All cover sectors are equivalent and can be written in any order (and they can represent many differently finned UFG fishes at once). I think NxM (where N <= M) communicates that concept better.

Also, with Obifishes: Rank=M-N. That's not necessarily true with Allan Barker's set notation because it doesn't allow duplicate sectors. It uses triplets instead, which complicates rank calculations and figuring out valid eliminations. The duplicates in Obifishes may look ugly but they actually simplify things. They also allow transformations, which is not possible with Allan's fishes or the UFG without first transforming them into Obifishes.

Edit. Fixed obvious typo (M <= N) -> (N <= M).

[tarek]

Also, with Obifishes: Rank=M-N. That's not necessarily true with Allan Barker's set notation because it doesn't allow duplicate sectors. It uses triplets instead, which complicates rank calculations and figuring out valid eliminations. The duplicates in Obifishes may look ugly but they actually simplify things. They also allow transformations, which is not possible with Allan's fishes or the UFG without first transforming them into Obifishes.

Your ability to see both side of the coin is impressive & I'm sure people would like to be able to do that. The UFG can be modified with additions if needed. The head post needs to be reviewed keeping in mind the maximum number of characters allowed!

BTW, I've always hated the term squirmbag and always preferred starfish. I have also suggested names for all fish up to n=10 (Last time I mentioned them I got a Flying Circus comment )