¹Definition: A swordfish is similar to an X-Wing, except that the Swordfish is a 3x3 instead of a 2x2 configuration of a single candidate. The candidate must occur in three lanes no more than three times in each lane, with all occurences lined up on the cross-lanes.

²Look For: A lane with only two or three of a given candidate, with a second and third parallel lane of two or three of the same candidate, where the cross-lanes of all three lanes line-up.
Note that there only needs to be two occurences of the candidate on a lane, so this configuration, with only two on each lane, would still be a valid Swordfish, as would be any other configuration that had no more than three of the candidate per lane, all occupying no more than three cross-lanes. In such cases, all nine cells are still considered part of the Swordfish, even the ones that don't contain the candidate.

³Consequence: Similar, again, to the X-Wing, wherever the given candidate appears in the cross-lanes (outside of the nine Swordfish cells themselves) the candidate can be erased.

⁴Why it Works: With the given configuration (3x3), if the candidate were to appear in another lane of one of the three cross-lanes, it wouldn't leave enough cross-lanes for the candidate in the three lanes. For instance, in our example, if C1 were to solve to a 5, then we'd only have two columns left for the 5 in the Swordfish rows (3, 5, and 7). But in three rows a given candidate needs three different columns in which to grow up to be three Big Numbers.

⁵If we put a 5 in G3, and a 5 in E5, then when we get to row 7 there would be no place for its 5 to go!

⁶On the other hand, going back to the example, let's see what happens if one of the Swordfish cells solves to a 5: say C3. This would cause all 5's in column C as well as those in row 3 to be erased. This leaves us with an X-Wing of 5's in rows 5 & 7, columns E & G. We already know, from our X-Wing tutorial, that this means a 5 must appear in two diagonal corners of this X-Wing, and so can be erased from any other rows in these two columns.

⁷An X-Wing appears no matter which of the nine 5's in the Swordfish you wish to try out as a Big Number.

⁸All of which leads to the same conclusion: in columns C, E, and G candidate 5 will solve to row 3, 5, or 7. Therefore, any 5 outside of these rows in these columns can be erased.

⁹Now let's turn to an example from an actual puzzle.

¹⁰We see the Swordfish pattern for candidate 7 in rows 3, 6, and 7: two or three 7's in each row, and all of them restricted to the three columns A, G, and I.

¹¹So, we can go ahead and erase all 7's from those columns (other than on rows 3, 6, and 7.)