Swordfish Sudoku Technique
An X-Wing across three lines instead of two, with one wrinkle that makes it far harder to see.
Also called: sword fish, three-line elimination.
What a Swordfish is
Find three rows in which a digit is confined to the same set of three columns. The digit must appear once in each row and once in each column, so all three columns are consumed.
The wrinkle: a row does not have to use all three columns. Two of the three is enough, as long as it uses no column outside the set. This is why Swordfish are missed — the pattern is often ragged rather than a neat nine-cell block.
Once the three columns are spoken for, the digit can be eliminated from those columns in every other row.
As with the X-Wing, it works identically with rows and columns exchanged.
How to spot one
- Restrict yourself to rows where the digit has two or three homes. A row with four is out.
- Take those rows three at a time and union their columns. If the union is exactly three columns, you have a Swordfish.
- Only worth hunting once X-Wings have been ruled out — an X-Wing is a strictly simpler pattern and will fire first when both exist.
Worked example
| Digit 6 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Row 1 | × | ||||||||
| Row 2 | 6 | 6 | |||||||
| Row 3 | × | × | |||||||
| Row 4 | |||||||||
| Row 5 | 6 | 6 | |||||||
| Row 6 | × | ||||||||
| Row 7 | × | × | |||||||
| Row 8 | |||||||||
| Row 9 | 6 | 6 |
6 marks a cell where the digit can still go. × marks a candidate this technique removes. Blank cells are not part of the pattern.
- Row 2 is limited to columns 1 and 4, row 5 to columns 4 and 8, row 9 to columns 1 and 8. The union is columns 1, 4 and 8 and nothing else.
- Three rows must each place a 6, and only three columns are available to receive them, so those columns are fully allocated.
- Strike 6 from columns 1, 4 and 8 in every other row — here rows 1, 3, 6 and 7.
What it eliminates
The digit, from all three columns of the pattern in every row outside the three that formed it.
When you need it
On Extreme grids and below, once the clue count is low enough that X-Wings have run out. Rarer in practice than its reputation suggests.
Difficulty here is set by how many clues are left in the grid: Easy starts from 46, Medium 40 and Hard 34, with Extreme and Insane stripped further still. Fewer clues is what makes the techniques below necessary — the fewer digits you start with, the deeper you have to reason.