Sudoku technique
Swordfish
The X-Wing stretched to three rows and three columns: a digit can only occupy those three columns across those three rows, whatever the exact split. It gets eliminated everywhere else on those three columns.
A puzzle that requires it
Level Extreme — the puzzle is shown twice: right below, and again in the demo that follows.
| 1 | 2 | 3 | ||||||
| 7 | 9 | 2 | 4 | |||||
| 3 | 5 | |||||||
| 4 | 5 | 7 | ||||||
| 6 | 5 | |||||||
| 1 | 8 | 2 | ||||||
| 1 | 3 | |||||||
| 7 | 3 | 6 | 9 | |||||
| 3 | 9 | 8 |
Demonstration
State of the grid right when the technique applies, after 13 earlier deductions.
Demo — watch first, you'll play right after.
- Technique's pattern
- Candidates removed
- Solved earlier
- Given (clue)
| 8 | 1 | 7 | 9 | 2 | 3 | |||
| 7 | 9 | 6 | 3 | 2 | 4 | |||
| 8 | 3 | 5 | 9 | |||||
| 4 | 3 | 5 | 7 | |||||
| 6 | 4 | 3 | 5 | |||||
| 1 | 8 | 6 | 3 | 4 | 2 | |||
| 8 | 1 | 3 | 8 | |||||
| 7 | 3 | 4 | 6 | 9 | ||||
| 3 | 9 | 6 | 8 |
Swordfish
Le 8 n'occupe que 3 lignes sur ces 3 colonnes, et elles s'alignent. Quelle que soit la répartition, ces 3 lignes ont déjà leur 8 à l'intérieur du motif : il disparaît partout ailleurs sur elles.
Candidates removed:
- the 8 from cell L1C1
- the 8 from cell L3C1
- the 8 from cell L7C1
- the 8 from cell L7C9
The Swordfish extends the X-Wing to three rows. When a digit is possible in only two or three cells on each of three rows, and all those cells fall in the same three columns, that digit is eliminated from the rest of those three columns.
The principle
Choose a digit, say 4. Find three rows where 4 is possible in only two or three cells, and where all those cells are in the same three columns, say columns 2, 5 and 8. It is the X-Wing pattern, stretched by one row and one column. The rows do not need to have the 4 in all three columns: one row may have it only in columns 2 and 5, another only in columns 5 and 8.
Why does it work? Each of the three rows must contain a 4, and that 4 can only be in one of the three columns. That makes three 4s to place. A column holds only one 4: those three 4s therefore fill three different columns, that is columns 2, 5 and 8, once each.
You do not know which row takes which column, but you know those three columns already have their 4 inside the pattern. You can therefore remove the 4 from every other cell of those three columns.
How to spot it
You need candidate notes. Take one digit at a time and find the rows where it appears only two or three times. Look for three of those rows whose cells together occupy exactly three columns. If they occupy four, it is not a Swordfish.
Then run the same search with rows and columns swapped: three columns whose cells for the digit fall in the same three rows give a Swordfish that cleans those three rows. The X-Wing is quicker to look for: start with it.
A worked example
For the 4, row 2 allows it only in columns 2 and 5, row 5 only in columns 5 and 8, row 8 only in columns 2 and 8. Together, those three rows use only columns 2, 5 and 8: it is a Swordfish, although no row has the 4 in all three columns.
Each row puts its 4 in one of those columns, and each column receives only one. In column 5, the cell in row 6 has candidates 4 and 9. Remove the 4, 9 remains, and you can place that 9. Do the same in columns 2 and 8 for the cells of rows 1, 3, 4, 6, 7 and 9 that still hold the 4. The cells of rows 2, 5 and 8 do not change.
Common mistakes
The most common mistake is to eliminate in the wrong place. When the pattern is formed by three rows, you clean the columns, never the other cells of those three rows: that is where the 4 will end up.
Another trap is to accept three rows whose cells occupy four columns, or a row where the digit is possible in four cells. The three rows must fit together in three columns, not one more. Conversely, do not reject a pattern because one row has only two cells: that is allowed.
When to use it
The Swordfish is expected at the Extreme level, along with the XY-Wing, the XYZ-Wing and the Jellyfish. It is a rare pattern, kept for the highest levels of the site. The Jellyfish takes the same reasoning to four rows.
- Extreme sudoku
- Technique: the Jellyfish
- Technique: the X-Wing
- How to solve a sudoku
- Learn the techniques
Frequently asked questions
Why does the Swordfish eliminate the digit in the columns?
Because each of the three rows of the pattern must have that digit, and their possible places are in the same three columns. Each of those columns gets its digit inside the pattern: it can no longer appear elsewhere in those columns.
Must every row have the digit in all three columns?
No. A row may have the digit in only two of the three columns. What matters is that all the cells of the three rows fit in the same three columns.
Can a Swordfish also be built with columns?
Yes. If the digit is possible in only two or three cells on each of three columns, and those cells fall in the same three rows, remove it from the other cells of those three rows.
Does a Swordfish place a digit?
No, it removes candidates. Those eliminations can then leave a Naked or Hidden Single, which lets you place a digit.
Practice
Every technique helps remove candidates ; once a cell has only one left, you place it.
Three puzzles where Swordfish is the key move, served right before the step, with a coach.
Puzzle 1
Extreme
The technique is used once in this puzzle
Puzzle 2
Extreme
The technique is used once in this puzzle
Puzzle 3
Extreme
The technique is used twice in this puzzle
Puzzles change every day.