Swordfish and Jellyfish

If the X-wing is new to you, read our X-wing guide first. These patterns need full notes; see pencil marks if you don't use them yet.

The idea

Take one digit. Find three rows where that digit's candidates all fall within the same three columns. Each of those rows needs its digit somewhere in those columns, and each column can hold the digit only once. So the three rows use up the digit in all three columns between them. No other square in those three columns can hold it.

That's a swordfish. Four rows confined to four columns is a jellyfish. Two rows in two columns is the X-wing. As always, rows and columns can swap places.

The detail that trips people up: a row doesn't need a candidate in all three columns. It can have two, as long as every candidate it has is within the three. What matters is that, taken together, the rows only reach into three columns.

A real swordfish

Here is one from a puzzle with exactly one solution, at a point where every simpler technique, including X-wings, had been used up.

Highlighted: 7 the pattern · struck through: 7 removed

Look at the digit 4: in row 3, only columns 2 and 8; in row 8, only columns 2, 5 and 8; in row 9, only columns 2 and 5. Those three rows only reach into columns 2, 5 and 8. Some rows have only two spots, which is fine. So the three 4s of those rows fill columns 2, 5 and 8 between them, one in each.

That removes 4 from every other square in columns 2, 5 and 8: row 1, column 2, row 2, column 2 and row 2, column 8. After that, the next step our solver found was an XY-wing.

To check one of these by hand, suppose row 1, column 2 were the 4. That column would then be closed to 4 everywhere else, so the three base rows would have only the other two columns for their three 4s. Two columns can hold only two 4s, so one row would be left with nowhere for its 4. The assumption fails, and the candidate can go. The same counting argument works for any fish: n lines need n copies of the digit, and they only have n crossing lines to put them in.

A real jellyfish

Jellyfish are rare. This one was the simplest step available in its puzzle.

Highlighted: 7 the pattern · struck through: 7 removed

The digit is 8: in row 1, only columns 1, 2, 4 and 8; in row 2, only columns 1, 2, 4 and 8; in row 4, only columns 4 and 8; in row 5, only columns 1 and 2. Four rows, and between them they only reach columns 1, 2, 4 and 8. Those four rows need four 8s, and the four columns can take exactly four. So the 8s of columns 1, 2, 4 and 8 are all accounted for by these rows.

That removes 8 from row 3, column 1, row 3, column 2, row 3, column 4, row 6, column 8 and row 7, column 8. After that, a naked single appears: row 6, column 8 is 5.

How rare are they?

While writing these guides our solver worked through 1,076 newly generated puzzles, always using the simplest technique available. An X-wing was needed in 30 of them, a swordfish in 6, and a jellyfish in 1. So learn the X-wing well, keep the swordfish in mind for tough puzzles, and treat a jellyfish as a lucky find.

How to look for them

1. Pick a digit that still has a lot of candidates.
2. List, for each row, the columns where it can go. Ignore rows where it's already placed or where it has more than three (for a swordfish) or four (for a jellyfish) spots.
3. Look for three rows whose columns combine to only three columns. Writing the column numbers down helps. In the example above, the rows' columns were 2 and 8; 2, 5 and 8; 2 and 5, which combine to just 2, 5 and 8.
4. Then do the same for columns.
5. Check for something to remove in the cleared lines. Many swordfish exist but clear nothing.

Mistakes to avoid

• Clearing the base lines. If the pattern is three rows, clear the columns, not the rows.
• A fourth column sneaking in. One stray candidate in a fourth column breaks a swordfish. Check every candidate of the digit in each base row.
• Stopping at the first fish. After an elimination, scan the same digit again. Removing candidates can create another pattern, or a single.

Practise

Our expert puzzles are the place to look. For a pattern of a different kind, built from squares with two candidates, see the XY-wing. The techniques page lists every technique in the order you will need them.