In a Swordfish, a number confined to the same three columns in three rows leaves the rest of those columns. It is the idea of the X-Wing with one more row.
The three rows must each receive the number once. Since, in those rows, the number can only go in those three columns, each column must also receive it once. So the number is removed from all the other cells in those columns.
The name places it in a family of patterns known as fish. It also works with rows and columns swapped. And there is one difference from the X-Wing: the cells do not form a complete rectangle, because each row may have the number in only two of the three columns.
An example
There are no singles, locked candidates, subsets, X-Wings or Y-Wings in this grid. Let's look at the 5. In row 2 it can only go in columns 3 and 7: the empty cell in column 6 does not have the 5 in its notes. In row 4, in columns 1 and 3. In row 8, in columns 1, 3 and 7.
Only three columns appear across the three rows: 1, 3 and 7. Each row does not need to have all of them: rows 2 and 4 have only two.
Each row receives a 5, and no two of them can be in the same column. That is three numbers for three columns: however they are arranged, each column receives its 5 in one of these rows.
A column has only one 5. So the 5 is removed from the notes of the other cells in the three columns: rows 1, 3 and 9 in column 1; rows 1 and 9 in column 3; and rows 1, 3 and 9 in column 7.
The cell in row 9, column 7 only had the 5 and the 9. It keeps the 9: a naked single. From here, the Easy techniques solve the puzzle to the end.
In this grid you can also get there from the other side: in columns 2, 4 and 8, the 5 only fits in rows 1, 3 and 9, and the result is the same. Finding either one is enough.
What is not a Swordfish
Three rows that, together, use four columns. If, in row 2, the 5 could also go in column 6, the three rows would have four possible columns. There would no longer be a closed set of three columns, and this pattern would not remove any candidate.
An X-Wing with an extra row. If two of the rows only use the same two columns, they already form an X-Wing between them. That is the pattern to apply.
A row where the number has only one place. That is a hidden single: place the number, and the pattern is no longer needed.
How to search
One number at a time. Go through the rows and mark those where the number has only two or three possible cells. Colours help you keep track.
Look for three that, together, only use three columns. Start with two rows that share a column and look for a third that, together with them, does not go beyond three columns.
Do the same with the columns, looking for three where the number only fits in the same three rows.
Check whether it removes anything. The Swordfish only allows a removal if the number is still in the notes of other cells in the three columns (or the three rows).
After removing, look for singles, especially in the cells that lost a candidate.
Your turn
Find a Swordfish and strike out the candidates removed from the other cells of its three columns (or its three rows). Tap each cell, choose the number and, when you finish, press "Check".
With four rows: the Jellyfish
With four rows and four columns, the same idea is called a Jellyfish. It is rare and hard to see. It is often just the other side of a smaller pattern, with rows and columns swapped.
In a 9×9 grid, a pattern of five rows and five columns always has an equivalent in the rows and columns left over, at most four of each. So there is no need to look for larger patterns.
Let's look at the 5. In row 2 it can only go in columns 4 and 9. In row 5, in columns 5 and 9: the cell in column 1 does not have the 5 in its notes. In row 7, in columns 4 and 8. In row 8, in columns 5 and 8. Only four columns appear across the four rows: 4, 5, 8 and 9.
That is four numbers for four columns: each column receives its 5 in one of these rows. Only column 5 has the 5 in another cell, the one in row 4, which loses it and keeps the 2 and the 8.
Find a Jellyfish and strike out the candidates removed from the other cells of its four columns (or its four rows). Tap each cell, choose the number and, when you finish, press "Check".