Swordfish
The X-wing's three-row counterpart. When a digit's possible cells across three rows fall in the same three columns, that digit can be eliminated from those columns elsewhere.
The swordfish is the three-row generalisation of the X-wing. Where an X-wing locks a digit into two columns across two rows, a swordfish locks a digit into three columns across three rows. The same elimination logic fires, just one dimension wider.
The shape
Pick a digit. Find three rows where the digit's only possible cells fall within the same three columns — though not every row needs the digit in every column. The constraint is that the union of the three rows' candidate columns is exactly three columns, and each row has at least two candidates within that union.
Because the digit must end up in each of those three rows, and every candidate cell across all three rows sits in the same three columns, the three columns must collectively absorb all three placements (one per column, one per row). So every other cell of those three columns outside the three rows can have the digit ruled out.
Worked example: digit 5 has candidates only in columns {2, 4, 7} for row 1 (specifically at (1, 2) and (1, 7)), only in columns {2, 4, 7} for row 5 (at (5, 4) and (5, 7)), and only in columns {2, 4, 7} for row 8 (at (8, 2), (8, 4), and (8, 7)). The three rows and three columns form a 3×3 grid of candidate cells; the 5s in rows 1, 5, and 8 must sit in three of those nine cells, one per row and one per column. Every other cell in columns 2, 4, and 7 can have 5 ruled out.
Why "swordfish"
The pattern's diagram, when sketched, looks vaguely like a fish skeleton — three vertical lines crossing three horizontal lines. The naming convention extends to the (rarer) four-line shape, called a jellyfish. The X-wing, swordfish, jellyfish family is collectively known as the "fish" techniques.
When you'll see it
Swordfish are uncommon — they require a specific candidate alignment across three rows that simpler techniques would usually have already broken. On expert puzzles they show up occasionally; on standard hard puzzles, almost never. The technique earns its place in the encyclopedia rather than its place in everyday solving.
For a survey of which technique to reach for in different stuck states, see Which technique is this puzzle asking for.
See also
- X-wing— When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.
- Y-wing (XY-wing)— Three bivalue cells where the pivot shares one candidate with each wing — eliminating the third candidate from any cell that sees both wings.
- Candidate— A digit (1–9) a cell could still legally hold — one not yet ruled out by anything in its row, column, or 3×3 box. Every empty cell has between one and nine.
Read more
- Which technique is this puzzle asking for
How to read a fresh hard Sudoku and predict which intermediate technique will break it open before you've placed a single digit.