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Swordfish: The Three-Line Fish Pattern

Extend X-Wing to three rows or columns for even more powerful eliminations.

9 min read

If X-Wing is impressive, Swordfish is spectacular! This technique extends the X-Wing pattern from two lines to three, creating even more powerful eliminations.

What is a Swordfish?

A Swordfish is like an X-Wing, but uses three rows or three columns instead of two. It's a rectangular pattern where a candidate appears 2-3 times in each of three parallel lines, all aligned within the same three perpendicular lines.

The Pattern

Row A:  X _ X _ _ _ _ _ _
Row D:  _ _ X _ _ X _ _ _
Row G:  X _ _ _ _ X _ _ _
        ↓   ↓     ↓
      Col1 Col3 Col6

The candidate appears in 3 rows, confined to 3 columns → Eliminate from those 3 columns

How Swordfish Works

If a candidate appears 2-3 times in each of three rows, and all instances are confined to the same three columns, then:

The candidate must be placed three times within this 3x3 grid of possibilities
One placement per row, one per column
You can eliminate the candidate from all other cells in those three columns

Row-Based Swordfish

Pattern: Candidate appears in 3 rows, confined to same 3 columns

Requirements:

Each row has 2 or 3 instances of the candidate
All instances across the 3 rows fit within 3 columns
Each column must have at least one instance

Elimination: Remove from those 3 columns (except the 3 Swordfish rows)

Column-Based Swordfish

Pattern: Candidate appears in 3 columns, confined to same 3 rows

Elimination: Remove from those 3 rows (except the 3 Swordfish columns)

The Logic Behind It

Within the 3x3 grid formed by the three rows and three columns:

Exactly 3 cells will contain the candidate
One per row, one per column (like mini-Sudoku rules)
Therefore, those columns/rows are "occupied" by the Swordfish

Flexibility: The 2-3 Rule

Unlike X-Wing (which requires exactly 2), Swordfish allows:

2 or 3 instances per line
As long as all instances fit within 3 perpendicular lines

This makes Swordfish more flexible but harder to spot!

How to Find Swordfish

Choose a candidate number
Find 3 rows with 2-3 instances of that candidate
Check if all instances fit in 3 columns
Verify each column has at least one instance
If yes: Eliminate from those columns (except Swordfish rows)
Repeat for columns to find column-based Swordfish

Common Mistakes

Expecting perfect symmetry: Not all 9 intersection cells need the candidate
Forgetting the "at least one per column" rule: Each perpendicular line must have at least one instance
Requiring exactly 3 in each row: 2 or 3 is fine!
Missing column-based patterns: Always check both orientations
Eliminating from the wrong lines: Remove from perpendicular lines only