Swordfish Technique: Advanced Sudoku Strategy

The Swordfish is an advanced sudoku technique that extends the X-Wing pattern from two rows to three. When a candidate number appears in only two or three cells in each of three different rows, and all of those cells fall within the same three columns, you can eliminate that candidate from every other cell in those three columns. The Swordfish is one of the most powerful elimination techniques in sudoku and is typically required only in puzzles rated hard or expert. Understanding it requires comfort with X-Wings, pencil marks, and candidate elimination logic.

From X-Wing to Swordfish: The Logical Extension

The X-Wing works because when a candidate appears in exactly two cells in each of two rows (aligned in the same columns), the candidate must occupy one cell in each column. The Swordfish applies the same logic to three rows.

Here is the key principle: if a candidate number is confined to at most three columns across three rows, then within those three columns, the candidate must appear once per row. This "locks" three instances of the candidate into those three columns, allowing you to eliminate the candidate from all other cells in those columns.

The naming convention comes from the fish family of techniques in sudoku. An X-Wing is a "2-fish" (two rows, two columns). A Swordfish is a "3-fish" (three rows, three columns). The Jellyfish is a "4-fish" (four rows, four columns). Each level gets progressively rarer and harder to spot.

The Swordfish Pattern Defined

A Swordfish requires the following conditions:

1. Choose a candidate number.
2. Find three rows where that candidate appears in only two or three cells each.
3. All candidate positions across these three rows must fall within the same three columns.

Importantly, each row does not need to have candidates in all three columns. A row might have the candidate in only two of the three columns. The requirement is that the union of all candidate positions spans exactly three columns.

When these conditions are met, you can eliminate the candidate from every other cell in those three columns — specifically, from cells in the six rows that are not part of the Swordfish.

Visual Example: Step by Step

Let us trace through a Swordfish example with candidate 6. After filling in pencil marks, you discover:

• Row 1: candidate 6 appears only in Column 2 and Column 5.
• Row 5: candidate 6 appears only in Column 2 and Column 8.
• Row 9: candidate 6 appears only in Column 5 and Column 8.

Let us check: the union of columns across all three rows is {2, 5, 8} — exactly three columns. The Swordfish conditions are met.

Here is a simplified view of the grid for candidate 6 in those three columns:

         Col 2    Col 5    Col 8
Row 1:   [6]      [6]      .        ← Swordfish row
Row 2:   6?       6?       6?       ← eliminate all
Row 3:   6?       .        6?       ← eliminate from C2, C8
Row 4:   .        6?       .        ← eliminate from C5
Row 5:   [6]      .        [6]      ← Swordfish row
Row 6:   6?       6?       .        ← eliminate from C2, C5
Row 7:   .        .        6?       ← eliminate from C8
Row 8:   6?       6?       6?       ← eliminate all
Row 9:   .        [6]      [6]      ← Swordfish row

Every cell marked "6?" has candidate 6 eliminated. Why? Because the three instances of 6 in rows 1, 5, and 9 must occupy three of the six [6] cells — one per row. No matter which arrangement occurs, each of columns 2, 5, and 8 gets exactly one 6 from these three rows. So no other cell in those columns can contain 6.

Verifying with the Possible Arrangements

Let us confirm by listing all possible arrangements:

• Arrangement 1: R1C2=6, R5C8=6, R9C5=6. Each column gets one 6. Valid.
• Arrangement 2: R1C5=6, R5C2=6, R9C8=6. Each column gets one 6. Valid.

In this case, there are only two valid arrangements (because each row has only two candidates). Both arrangements place exactly one 6 in each column, confirming that all eliminations are correct.

Column-Based Swordfish

Like the X-Wing, the Swordfish works symmetrically. Instead of starting with rows and eliminating from columns, you can start with columns and eliminate from rows.

If a candidate appears in only two or three cells in each of three columns, and all those cells fall within the same three rows, you can eliminate the candidate from all other cells in those three rows.

The logic is identical — just rotated. In practice, you should check for both orientations, though most solvers find one orientation more natural to scan for than the other.

How to Search for Swordfish Patterns

Finding a Swordfish is significantly harder than finding an X-Wing because you are looking for a three-way alignment instead of a two-way alignment. Here is a systematic approach:

Step 1: Complete Pencil Marks

Swordfish detection requires complete, accurate pencil marks. Any missing or incorrect candidates will cause you to miss patterns or find false ones. Ensure you have applied all simpler techniques (singles, pairs, pointing pairs, X-Wings) before looking for a Swordfish.

Step 2: Identify Candidate-Sparse Rows

For each candidate number, scan each row and note how many cells contain that candidate. You are looking for rows with exactly two or three instances. Rows with four or more instances are not useful for Swordfish (though they might be part of a Jellyfish).

Step 3: Check Column Alignment

For each candidate with three qualifying rows, check whether their combined column positions span exactly three columns. This is the most tedious part. You are checking combinations of three rows out of potentially many qualifying rows.

A practical shortcut: start with the candidate that has the fewest total appearances on the grid. Fewer appearances mean fewer rows to check and a higher chance of finding a Swordfish.

Step 4: Eliminate and Cascade

Once confirmed, eliminate the candidate from all other cells in the three target columns (or rows, for column-based Swordfish). Then re-scan for hidden singles and other patterns created by the eliminations.

Why Swordfish Patterns Are Rare

Swordfish patterns are less common than X-Wings for mathematical reasons. The three-row, three-column alignment constraint is much harder to satisfy than the two-row, two-column constraint of the X-Wing. In practice, you might encounter a Swordfish in perhaps 10 to 15 percent of hard puzzles, compared to X-Wings appearing in 30 to 40 percent.

Additionally, Swordfish are only useful when they produce eliminations — that is, when there are other candidates in the target columns to eliminate. Even when the pattern exists, it sometimes does not help because the target columns are already clean.

Common Mistakes

Miscounting Column Coverage

The most common error is thinking you have a Swordfish when the candidate positions actually span four columns instead of three. Always carefully verify that the union of column positions across all three rows is exactly three columns. If it is four, the pattern is not a Swordfish (it might be a Jellyfish).

Incomplete Pencil Marks

If a row actually has the candidate in three cells but your pencil marks only show two, you might incorrectly identify a Swordfish or miss one entirely. Always ensure pencil marks are up to date before searching for fish patterns.

Confusing the Direction of Elimination

For a row-based Swordfish, you eliminate from other cells in the target columns, not the target rows. The defining rows are where the candidates are locked — the columns are where eliminations happen. Mixing this up will corrupt your solve.

Swordfish in Competitive Play

In competitive settings like Sudoku Royale, the ability to quickly recognize a Swordfish gives you a significant edge on hard puzzles. Most competitors never learn fish patterns beyond the X-Wing, so finding a Swordfish can be the move that breaks a puzzle open while your opponents are still stuck.

That said, in speed-solving contexts, some players prefer strategic bifurcation (trying one of two candidates in a constrained cell) over searching for complex patterns. The time spent finding a Swordfish might exceed the time spent on a quick trial-and-error approach. The right choice depends on your pattern recognition speed and the specific puzzle. For more on speed-solving trade-offs, see our speed solving guide.

For an overview of all advanced techniques including those beyond the Swordfish, see our advanced strategies guide.