The Swordfish: an X-Wing with three lines

What a Swordfish is

Choose one digit. Find three rows in which that digit has only two or three possible cells, and where all of those cells fall inside the same three columns. Those three rows and three columns make a Swordfish. The digit can then be removed from every other cell in those three columns.

As with the X-Wing, rows and columns can swap roles: three columns whose candidates for a digit all fall inside the same three rows let you clear that digit from the rest of those rows. The three lines you start from are called the base; the three lines you eliminate from are the cover.

Why it works

Each of the three base rows needs its digit somewhere, and in every base row all remaining positions lie in the three cover columns. So the three base rows place three copies of the digit, all inside those three columns. No two of them can share a column, because a column holds each digit once.

Three copies in three columns, one per column, means each cover column already gets its digit from one of the base rows. Every other cell in the cover columns is therefore not that digit. As with the X-Wing, you never have to work out which cell holds which copy; every possible arrangement gives the same eliminations.

How to find a Swordfish

With full pencil marks, pick a digit and list every row where it has two or three candidates, writing down the columns for each. You are looking for three of these rows whose column numbers, taken together, use only three different columns.

The shape can be irregular. A row may have three candidates, or only two, and not every row needs to touch every column. A classic “2-2-2” Swordfish has exactly two candidates in each row, with the pairs chaining around three columns, and it is the version players most often overlook.

Then repeat the search using columns as the base. Digits that are close to finished, with only a few open positions left, are the best place to start, because they produce short lists that are easy to compare.

A worked example

On the example board, look at digit 6. In row 3 it can only go in R3C2 (row 3, column 2), with candidates 6 and 8, or in R3C4, with candidates 4 and 6. In row 5 it can go in R5C2 or R5C5, both with candidates 6 and 8. In row 8 it can go in R8C4 or R8C5, both with candidates 5 and 6. The six highlighted cells use only columns 2, 4 and 5.

No two rows share the same pair of columns, so this is not an X-Wing. But taken together the three rows are confined to three columns: a 2-2-2 Swordfish. Columns 2, 4 and 5 each receive their 6 from these rows, so 6 comes out of R1C4 (candidates 6 and 9), R2C4 (candidates 4, 5, 6 and 9) and R2C5 (candidates 5, 6 and 8).

After the eliminations, R1C4 has a single candidate left: it is 9, shown in gold. In this position nothing simpler applied. There were no singles, locked candidates, pairs, triples or X-Wings, so the Swordfish is the step that moves the puzzle forward.

Common mistakes

Thinking every row needs three candidates. Many players only look for rows with exactly three positions, and so miss Swordfish patterns built from pairs, like the one above. Two or three candidates per base line are both fine; what matters is the total of three columns.

Counting four columns. If the base rows between them touch a fourth column, the pattern is broken: one of the digits could sit in that fourth column, and a cover column might be left without its copy. Check the column list carefully before eliminating.

Eliminating from the base. The digit is removed from the cover lines, never from other cells of the base rows. The base rows are already restricted to the pattern. If you find nothing to remove in the cover columns, the Swordfish is valid but simply does not help yet.

Where the Swordfish fits

The Swordfish is the three-line member of the fish family: two lines give an X-Wing, three lines give a Swordfish. A useful habit is to scan for both at once while looking at a single digit. If you know the Skyscraper, it can also be seen as a relative of the X-Wing that handles misaligned pairs.

On Quietdoku, Swordfish is one of the techniques that Expert puzzles may require, together with X-Wing and XY-Wing. Every puzzle has exactly one solution and can be solved by logic alone, and a hint shows the next step and names the technique if you get stuck.