Swordfish in Sudoku, Explained
A swordfish is an x-wing with three lines instead of two. If a digit's candidates in three rows all fall within the same three columns, those three rows will fill that digit into those three columns. You can then remove the digit from every other cell in those columns.
It's rarer than an x-wing and harder to see, but the logic is identical. If x-wings make sense to you, swordfish will too.
The pattern
Pick a digit, say 5, and suppose:
- In row 1, 5 can only go in columns 2 or 7.
- In row 4, 5 can only go in columns 2, 5 or 7.
- In row 8, 5 can only go in columns 5 or 7.
Three rows, and between them their candidates use only three columns: 2, 5 and 7. Each row needs one 5, and no two rows can put it in the same column. So rows 1, 4 and 8 will use up columns 2, 5 and 7 for the digit 5, one each.
That means columns 2, 5 and 7 get their 5s from rows 1, 4 and 8. Erase 5 from every other cell in columns 2, 5 and 7.
Notice that no row needs all three columns. Each row can have two or three candidates, as long as the three rows together stay within the same three columns.
Rows or columns
Like the x-wing, it works in both directions. If a digit is confined to three rows within three columns, remove it from the rest of those three rows. The lines you search in are the ones where the digit is confined; the lines they cross are the ones you clean.
How to find one
- Work one digit at a time. Select a placed copy of it so its notes light up.
- List the rows with only two or three candidates for that digit, and which columns they use.
- Look for three rows whose columns combine to exactly three.
- Check the crossing columns for something to remove. If there's nothing, move to the next digit.
If you find two rows that already share the same two columns, that's an x-wing. Use it first; it's simpler.
Bigger fish
The same idea extends to four lines (a jellyfish) and beyond. They exist, but they almost never matter in practice. Puzzles that need them are rare outside of puzzle collections built to show them off.
Practice
Try the Swordfish lesson, then the Technique Journey Capstone, which brings everything together. Then pick an Expert puzzle on the play page.
FAQ
Does each row in a swordfish need three candidates?
No. Each row can have two or three. What matters is that the three rows together only use three columns.
Is a swordfish harder than an x-wing?
It uses the same logic, but it's harder to spot because you have to track three lines at once.
How often do I need a swordfish?
Not often. Most hard puzzles fall to singles, intersections, pairs and x-wings. A swordfish is what you reach for when those run out.