First, the swordfish technique is not required to solve this puzzle. (That doesn't mean you are prevented from applying it.)

When looking for a swordfish, the first thing to try and find are three rows that each contain exactly two occurences of a given candidate. If you can't find any rows that satisfy this condition, look for columns that might.

In your puzzle, looking at the candidate 2's, we have the following.

- Code: Select all
` . . . | . . . | . . .`

. . . | . . . | . . .

. . . | . . . | . . .

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

. . . | . . . | . . .

. 2 2 | . . . | . . .

. . . | . . . | . . .

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

. . . | . . . | . . .

. . 2 | . 2 . | . . .

. 2 2 | . 2 . | . . .

Row 5 has two candidate 2's and row 8 has two candidate 2's, but row 9 has

three candidate 2's. We can't find a swordfish by looking at the rows, so lets try the columns. Column 2 has two candidate 2's and column 5 has two candidate 2's but column 3 has

three candidate 2's. So there is not a swordfish present in the candidate 2's.

Let's look at the candidate 6's.

- Code: Select all
` . . . | . . . | . . .`

. . . | . . . | . . .

. . . | . . . | . . .

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

. . . | . . . | . . .

. . . | . . . | 6 . 6

. . . | . . . | . . .

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

. 6 . | . . . | 6 . .

. . . | . . . | . . .

. 6 . | . . . | 6 . .

Let's look at the columns first. Column 2 has two candidate 6's but column 7 has

three candidate 6's and column 9 has

one candidate 6. We can't find a swordfish by looking at the columns, so lets try the rows. Row 5 has two candidate 6's, row 7 has two candidate 6's, and row 9 has two candidate 6's. The first set of conditions are satisfied!

When looking for a swordfish, once you have found three rows that each contain exactly two occurences of a given candidate, these three rows must share exactly three columns and each shared column must contain exactly two candidates in the rows being examined. (Or vice versa, found three columns... these three columns must share exactly three rows and each shared row must contain exactly two candidates in the columns being examined.)

Let's look at the rows of candidate 6's. The three rows (5, 7, and 9) share three columns (2, 7, and 9) but only column 2 contains exactly two candidate 6's in the rows being examined. Since the second condition cannot be satisifed, there is not a swordfish present in the candidate 6's.

I hope this explanation helped show why there isn't a swordfish present (at this point in the puzzle). If I have some more time, I'll post an example (with another detailed explanation) of a puzzle that requires the swordfish technique.

Update: Corrected a mistake.