When a digit's places in three rows all fall inside the same three columns, the three rows fill those columns with that digit. Every other cell in those columns loses it. A row can have two places or three, and the same holds with rows and columns swapped.
How to spot it
Like an X-wing, a swordfish reads one digit at a time and looks across whole rows. The difference is the count. It takes three rows and three columns instead of two and two.
Pick a digit and note, for every row, the columns where it can still go. Keep the rows that give two or three places. Set the others aside. Then look for three of those rows whose places, taken together, use only three columns. A row does not need a place in every one of the three columns. It only must not reach a fourth.
This is why a swordfish is harder to see than an X-wing. There is no rectangle to look for. The cells of the pattern can leave gaps, and the three rows can sit anywhere on the grid.
Count the 3s row by row
Take the 3. Rows two, three and nine already have theirs. Row six leaves it six places, and rows four, five and eight leave it three each. Row one has five empty cells, and the 3 fits in only two of them: the first and the second.
Add rows that stay inside three columns
Row seven has three empty cells and two places for the 3, in columns two and four. That brings the set to three columns: one, two and four. A third row fits if every place it has is in those columns. Row five has three places, in columns one, two and four, so it fits. Rows four and eight also have three places each, but both reach column three, so they stay out.
See why each column gets a 3
Each of the three rows needs a 3, and each can only put it in column one, two or four. That is three 3s going into three columns. No column can take two of them, because a column holds one 3. So each of the three columns receives exactly one, from one of these rows. You do not need to know which row fills which column.
Clear the 3 from the rest of the three columns
Columns one, two and four each take their 3 from the pattern. No other cell in those columns can hold one. Five marks go: the 3 in row six from all three columns, and in rows four and eight of column four. The seven cells of the pattern keep their 3s.
Read what the strike left behind
In column four, the cell in row four showed only 2 and 3. Without the 3 it is a 2, a naked single. Before the strike this grid had no single of either kind anywhere, and nothing simpler than a fish removed a mark. The swordfish is what opened it.
Why two places are enough
The argument counts rows against columns. Three rows each owe the grid one 3, and all of their places lie inside three columns. Three 3s in three columns, one per column, means those columns are full. It does not matter how the places are spread. Two rows here have only two places and one has three. A row could have all three, or the rows could link in a chain, one column shared at a time.
What breaks it is a fourth column. If any of the three rows can put its 3 outside the set, that row might not fill a column at all, and the count no longer holds.
On this grid the 3 goes in the first cell of row one, the fourth cell of row five and the second cell of row seven. That is one per column, as the argument said. You can make the whole strike without knowing it.
Rows and columns can swap. If a digit's places in three columns all fall inside the same three rows, it leaves every other cell of those rows. The question at the end of this page uses a column swordfish.
Three rows, four columns
Rows two, four and nine each have exactly two places for a 2. In row two they are columns three and eight. In row four, three and four. In row nine, two and three. Column three turns up in all three rows, and at a glance it looks like a swordfish.
Now count the columns. Two, three, four and eight make four. Three rows can place their 2s across four columns and leave one of them empty, so no column is guaranteed. Drop column eight and treat the rest as a swordfish on columns two, three and four, and you would strike the 2 from the second cell of row one. On this grid that is where row one's 2 goes.
Before you strike, list the columns from every row. If the list runs to four, there is nothing to remove.
Columns one and two, then one, two and four, then two and four. Three columns in all. Each of them gets its 3 here.
Columns three and eight, then three and four, then two and three. Four columns. Nothing can be struck.
The same cells from the columns
After the strike, column one has the 3 in rows one and five, column two in rows one, five and seven, and column four in rows five and seven. Read from the columns, the same seven cells are a swordfish again. It removes nothing this time, because rows one, five and seven have no other cells with a 3. Once its strike is made, any row swordfish reads this way from its columns.
A jellyfish is the same argument with four rows and four columns. It is the next technique on the path.
Work one digit at a time. Keep the rows where it has two or three places, and look for three whose places share the same three columns. If they do, the digit leaves the rest of those columns. A fourth column anywhere and there is nothing to strike.
Where this sits on the path
A swordfish places nothing. It removes candidates and leaves the placing to the singles. On the grid above it made one naked single, in column four.
It is the second of the fish. The X-wing locks one digit into two columns using two rows. The swordfish does it with three, and the extra row lets it work when no X-wing is there. On this grid nothing smaller than a swordfish removes anything at all. The jellyfish comes next and adds a fourth row.
Columns three, five and seven each have the 6 in only two places. Column three uses rows two and four, column five rows two and nine, column seven rows four and nine. Which 6s can you strike?
List the rows the three columns use. Those are the lines the columns fill with a 6, and that is where the strike happens.
Recap
- Look for
- One digit with two or three places in each of three rows, all inside the same three columns.
- Scope
- Three rows, with the strike in their three columns. Or three columns, with the strike in their three rows.
- Result
- The digit comes out of every other cell in those three columns. The pattern's cells keep it.
- Tell-tale
- Rows with only two or three places for a digit that keep landing in the same columns.
- If it fails
- If the three rows reach a fourth column, there is no swordfish. Look for an X-wing among two of them, try columns as the base, or move to the next digit. If four rows share four columns, look for a jellyfish.