This is a particularly extreme Sudoku puzzle but the Finned Swordfish is nicely arranged. As discussed in the article on SwordFish it is not necessary for every cell in the 3 by 3 formation to contain the candidate, in this example candidate 3. This SwordFish is a 2-2-3 version since we have 3 twice in the first column, twice in the second column and three times in the third column. It is orientated on the columns since they are the units where candidate 3 occurs at least three times but no more. We are eliminating in the rows.

Now, that said it is not a perfect Swordfish because the centre column 5 contains an extra 3 in J5, which ruins the whole formation. However, the Finned Rule says we can ignore it if we confine the eliminations to the box where the fin is, namely box 8. There is one 3 that we can remove, on G4.

Now, that said it is not a perfect Swordfish because the centre column 5 contains an extra 3 in J5, which ruins the whole formation. However, the Finned Rule says we can ignore it if we confine the eliminations to the box where the fin is, namely box 8. There is one 3 that we can remove, on G4.

Two examples now of the Sashimi variety of Finned SwordFishies.

Figure two is a little more bunched up but we have a 2-2-3 formation based on eliminations in rows. The exceptional candidate 3 which blocks this from being a perfect SwordFish is on G2. But we can invoke the Sashimi observation to ignore the lack of a 3 on H2, one of the corners of the SwordFish. Eliminating in row H and box 7 we an remove the 3 from H1.

The second example illustrates that the Sashimi cell doesn't have to be a clue or a solved cell. The brown cell A6 simply lacks the candidate 7, which had been removed using previous logical strategies. The double fin is in green, A4 and A5. This is quite a restricted SwordFish, which in row orientation is a 1-2-2 formation - but it works!

(Turn Grouped X-Cycles off)

Here is a lovely Sudoku made by Klaus Brenner (April 2012).

Try loading this one. It contains

Try loading this one. It contains

- 1 X-Wing on 6
- 1 Finned-X-Wing on 6
- 1 Swordfish on 9
- 1 Finned Swordfish on 6, brown cell H9 never contained a 6
- 1 Finned Sashimi Swordfish on 6, brown cell G8 never contained a 6

## Comments

## ... by: Robert

On the "Aligned Pair Exclusion" page, I have described a strategy I have implemented in my solver, which I call "dynamic locked sets" - it is a generalisation of the idea of an ALS in an alternating inference chain. Most useful in a forcing net, but it could come up in an AIC as well. I have similarly implemented, within my "forcing net" algorithm, dynamic groups, dynamic finless fish, and dynamic finned fish.

Here are the statistics on how many puzzles in my small database of 245 can be solved using my forcing net software, with its various dynamic options. Every combination is shown, except that there is no easy way to include finned fish without also including unfinned fish.

Basic (no "dynamic" options) - 165

With dynamic groups only - 168

With dynamic locked sets only - 169

With dynamic finless fish only - 167

With dynamic finless fish and dynamic finned fish only - 195

With dynamic groups and dynamic locked sets only - 173

With dynamic groups and dynamic finless fish only - 169

With dynamic groups, dynamic finless fish, and dynamic finned fish only - 203

With dynamic locked sets and dynamic finless fish only - 172

With dynamic locked sets, dynamic finless fish, and dynamic finned fish only - 206

With dynamic groups, dynamic locked sets, and dynamic finless fish only - 173

With dynamic groups, dynamic locked sets, dynamic finless fish, and dynamic finned fish - 209

The final 209 number includes a good number of the "unsolveables", although this technique definitely remains stumped by some other unsolveables.

Granted, 245 is not a huge sample, but based on the results above, I feel like there could be a lot of mileage to be had by incorporating the concept of an "almost (finned) fish" into the AIC algorithm, or its generalisation, a "dynamic (finned) fish" (either in an AIC, or in a general forcing net).

Something to consider :)

## ... by: dontsaymyid

While solving puzzle

080040070000005800040700020063500002200000005800002760010007030009300000050080010

after some singles and finned X-Wing, puzzle gets into this state:

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

| 1569 8 2 | 169 4 1369 | 13569 7 169 |

| 169 3 7 | 16 2 5 | 8 49 1469 |

| 1569 4 16 | 7 1369 8 | 1356 2 136 |

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

| 14 6 3 | 5 7 149 | 149 8 2 |

| 2 7 14 | 8 1369 13469 | 1349 49 5 |

| 8 9 5 | 14 13 2 | 7 6 134 |

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

| 46 1 8 | 2469 5 7 | 2469 3 469 |

| 7 2 9 | 3 16 146 | 46 5 8 |

| 3 5 46 | 2469 8 469 | 2469 1 7 |

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

My solver printed

"Finned Swordfish

On candidate 4. A fish goes from Column 1, 8, and 9 to Row B, D, and G. On Box 6, the fish has two fins E8 and F9. Therefore...

4 taken off from Cell D7."

(Actually this is a sashimi, but it was meaningless to tell sashimi apart from finned one.)

A sashimi swordfish with two non-aligned fins. I used your solver to see how it solves the puzzle, (turned off GXC and ER) but seems like the finned swordfish algorithm does not find this case.

## ... by: Reetou

While solving puzzle 7.9.........4..2.7.2....3...72......3...17.6.9..2...345347..1.929.........1......

After some other steps, puzzle gets into this state:

There is a sashimi swordfish in rows 2, 6, 7 and columns 3, 5, 6 with fin in r2c2 which eliminates 6 from r3c3.

Am I missing something or just found space for improvement of your solver? Which is brilliant anyway.

## ... by: Ludi

## ... by: Rainer

Applying the same logic as in the Finned Sashimi Example 1 to Example 2, I find an 'imperfect' 2-1-2 SwordFish in columns 1, 6 and 7.

Accordingly, A6 in Example 2 has the same role than H2 in Example 1; a cell of the SwordFish that does not contain the candidate.

Thinking in columns the 'fin' would be B6; restricting elimination to the box of the SwordFish, A4 and A5 could be deleted.

The example argues the other way round: A4 and A5 being a 'double fin' and B6 to be deleted!

Where is the fault?