Swordfish Strategy in Sudoku: The Three-Row Pattern Explained
The Swordfish is a 3-row or 3-column extension of the X-Wing pattern. This advanced Sudoku technique occurs when a candidate digit appears in only three rows and is confined to only three columns, allowing you to eliminate that candidate from the rest of those columns. It's a powerful pattern that tackles puzzles where simpler methods like [Pointing Pairs](/techniques/pointing-pairs) have been exhausted. Mastering the Swordfish is a key step in solving expert-level puzzles, sitting between the 2x2 [X-Wing](/techniques/x-wing) and the larger 4x4 Jellyfish in the 'Fish' family of strategies.
Understanding the Swordfish Pattern
A Swordfish pattern is defined by a single candidate number. The classic form, a 3x3 Swordfish, exists in two orientations: Rows or Columns. In the Row Swordfish, you find three rows where the candidate appears in only three shared columns. The positions in these rows and columns can form any arrangement, not necessarily a perfect rectangle, as long as every one of the three rows contains the candidate in two or three of the three columns, and every one of the three columns contains the candidate in two or three of the three rows. The logic then allows you to eliminate that candidate from all other cells in those three columns.
Swordfish vs. X-Wing vs. Jellyfish: A Pattern Comparison
The 'Fish' techniques are a family of patterns based on the same core logic of locked candidate alignment across rows and columns. Here is a side-by-side comparison of the key members.
How to Spot and Apply a Swordfish
To find a Swordfish, systematically scan candidate numbers (1 through 9). Look for a number that, in three specific rows, appears only in cells belonging to three specific columns. The candidate does not need to be present in every cell of the implied 3x3 grid; it just needs to be confined to those three columns within your chosen three rows. Once identified, you can confidently remove that candidate number from all other cells in those three target columns. This elimination often creates new Naked Pairs or singles, breaking the puzzle open.
- **Scan by Candidate:** Don't look at the whole grid. Pick one number (e.g., all the 5s) and examine its positions.
- **Check Confinement:** For three rows, ask: 'Is this number only found in three columns across these rows?'
- **Verify Both Ways:** A true Swordfish also means that, within the three columns, the number is only found in your chosen three rows.
Example: Identifying a Row-Based Swordfish
Consider candidate 7. You notice that in rows 2, 5, and 8, the digit 7 appears only in columns 3, 4, and 7. In row 2, it's in columns 3 and 7. In row 5, it's in columns 4 and 7. In row 8, it's in columns 3 and 4. This forms a Swordfish on 7 in rows 2,5,8 and columns 3,4,7. The logical conclusion is that the 7s for these three columns must be placed somewhere within these three rows. Therefore, you can eliminate candidate 7 from any other cell in columns 3, 4, and 7 that is not in rows 2, 5, or 8.
The Finned Swordfish Variant
A Finned Swordfish is a common variant where the perfect 3x3 pattern is broken by one extra candidate, called a 'fin,' in one of the rows. Specifically, you have a base Swordfish pattern confined to three rows and three columns, but one of the rows has an extra candidate for the number in a fourth column. Crucially, this fin cell must lie in the same 3x3 box as one of the Swordfish cells from that row. The elimination rule changes: you can only eliminate the candidate from cells that see both the fin and the relevant Swordfish cells. This means the target elimination cell must be in the same box as the fin and also in one of the Swordfish columns for that row.
Key Facts
- ▪A Swordfish is an advanced Sudoku pattern involving a single candidate digit arranged across three rows and three columns.
- ▪The logic states that if a candidate is confined to three rows and three columns, it can be eliminated from all other cells in those columns (or rows).
- ▪Swordfish is a direct extension of the X-Wing pattern, which uses two rows and two columns.
- ▪The pattern works in two orientations: a 'Row Swordfish' eliminates candidates in columns, and a 'Column Swordfish' eliminates candidates in rows.
- ▪Positions in a Swordfish do not need to form a perfect 3x3 rectangle; they can be in any arrangement as long as the confinement rule is met.
- ▪A Finned Swordfish occurs when an extra candidate (the fin) breaks the pure pattern, allowing eliminations only in cells that see both the fin and the Swordfish body.
- ▪Mastering Swordfish is essential for solving hard and expert-level Sudoku puzzles where simpler techniques are insufficient.
- ▪Swordfish is part of a family of 'Fish' patterns, which also includes X-Wing (2x2) and Jellyfish (4x4).
Frequently Asked Questions
How is a Swordfish different from an X-Wing?
An X-Wing uses two rows and two columns. A Swordfish uses three rows and three columns, applying the same confinement and elimination logic on a larger scale. It's the next step for harder puzzles.
Do the cells in a Swordfish have to be filled in?
No. The candidate does not need to be in all nine cells of the 3x3 grid. It must simply be confined to only three columns within three chosen rows (or vice-versa), with at least two appearances per row/column.
What is a Finned Swordfish?
It's a Swordfish pattern with one extra candidate (the fin) in one row. Eliminations are only possible in cells that share a box with the fin and align with the Swordfish's columns, seeing both the fin and the pattern.
Should I look for Swordfish or X-Wing first?
Look for X-Wings first as they are simpler and more common. If you cannot find one, then scan for the larger Swordfish pattern. Our hint engine often suggests this progression.
Can a Swordfish pattern exist in columns instead of rows?
Yes. A Column Swordfish has a candidate confined to three columns and three rows. You then eliminate that candidate from the rest of those three rows. The logic is perfectly symmetrical.