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I have candidate 3 of no more than three occurrences per row, in rows 5, 6 and 7, which line up in columns 1, 2 and 9. When I try in Simple Sudoku to eliminate candidate 3 in r9c9, the solver says: "invalid move". Why?

A Swordfish is when all candidates for digit X in 3 rows are located in only 3 columns. You can also switch around all occurrences of rows and columns in the definition and still be a swordfish.

Your example has three rows (R567) with candidates for 3 in four columns (C1279), so it is not a swordfish.

Note: Your example is a finned swordfish, which is a slightly more complex kind of fish; however it doesn't produce any eliminations.

You might be making things a bit hard for yourself. From the position of the puzzle it solves in singles. The first one is r5c9, which has the only 1 in Column 9.

Leren

You're right Leren. There is indeed a hidden single in r5c9 but somehow I missed it and stumbled upon this pattern which after all isn't a SF (thanks to Jason) but a finned one. Good Grief!

fdh319 wrote:You're right Leren. There is indeed a hidden single in r5c9 but somehow I missed it and stumbled upon this pattern which after all isn't a SF (thanks to Jason) but a finned one. Good Grief!

Here are some good teaching sites that explain Swordfish (and lots of other moves) with visual worked examples. here and here.

Leren

<EDIT>

Repeating what I said on another recent Swordfish thread here are some practice puzzles with Swordfish moves as the only non-basic move to solve.

Code: Select all

1......345..3.2.78...8........6.5..3..5...4..3.....6.298.2.6.1.............78.9.. | 4 r247 c235
..5.7.2.........498....5.7.91...6..7.4.9.8..2..645..8..8..................1.43... | 2 r369 c124
3.15..............74...6.3..8.6.7..4...9.....27..5..8......126.........861..23.5. | 9 r369 c379
.31..6..56....7......59....8..1....27.......3.4...38..12763.........1.....84..3.. | 9 r247 c678
..........8..63..4..2.....8..5.......46..25.....9...3172...54.......7.93.932....5 | 1 r258 c145
..6..........756.....2.3591.5..149.38..9.2.....37......25..94..9...2..3.......... | 7 r147 c189
.......5..46.518.....9..4.6.3.8......2.3..6.9417..9.......68.142.......85.1...... | 7 r358 c568
6.913...........1...4...5.74..8...798.2.............6......3..82....19.3...4296.. | 5 r148 c236
16.54..7...8..1.3..3.8.....7...5..696..9.2.57.............3..4........16...1645.. | 2 r239 c158

They are all row based and not finned. The information to the right of the | symbol tells you the Swordfish digit and the rows and columns in which they can be found.

Leren

Hi Leren,
Excellent. I'll do my best to catch up.
Now, going back to my trivial puzzle, I found two unproductive patterns. Here's the first one, filtered on 7. Guess this is a legitimate SF. Isn't it?

But here's the second, filtered on 9. Is this still a legitimate SW?

Yes, they both look like Swordfish patterns in both rows and columns but there are no eliminations available either way.

If you look at the solved cells you'll see that there are six 7's and six 9's, which is why there could not be any eliminations.

For example, looking at the row Swordfish in 7's you'll see that 7 has been resolved in Rows 1,2,3,4,7 & 8, which are the rows where eliminations from an incomplete row Swordfish in the remaining three rows 2, 3 & 6 would come from.

"Completed" fish patterns are quite common towards the end of a puzzle.

If you try the first example puzzle, after some obvious singles you'll come to a Swordfish in 4's in Rows 2, 4 and 7 for an astounding 11 eliminations in Columns 2, 3 and 5. Here is a PM for that move:

Code: Select all

*---------------------------------------------------------------------------------*
| 1       679      8        | 5       679     79       | 2       3       4        |
| 5      *469     *469      | 3      *469     2        | 1       7       8        |
| 247     237-4    237-4    | 8       17-4    147      | 5       6       9        |
|---------------------------+--------------------------+--------------------------|
| 8      *124     *124      | 6      *124     5        | 7       9       3        |
| 267     267      5        | 9       237     37       | 4       8       1        |
| 3       179-4    179-4    | 14      17-4    8        | 6       5       2        |
|---------------------------+--------------------------+--------------------------|
| 9       8       *47       | 2      *45      6        | 3       1       57       |
| 2467    123567-4 12367-4  | 14      1359-4  1349     | 8       24      567      |
| 246     12356-4  1236-4   | 7       8       134      | 9       24      56       |
*---------------------------------------------------------------------------------*

Swordfish in 4's r247 c235 => - 4 r368c235, r9c35 !

Leren

Great explanation Leren! I thought the fish lay dormant. Now I know they were lying there for a reason. The final six numbers plus the SF's possibilities in both above cases add up nicely to nine! Also, I can see there is no difference between the SF with two possibilities per row and the other with three possibilities per row. Great!