Introduction
Swordfish is an advanced Sudoku technique that extends X-Wing logic to three dimensions, providing powerful eliminations for challenging puzzles. Named for the fish-like pattern it creates, Swordfish uses three rows or columns instead of two, making it more complex to identify but highly effective when found. Mastering Swordfish significantly improves your ability to solve hard and expert puzzles in Sudoku, making it an essential skill for serious solvers.
The Swordfish technique works similarly to X-Wing but operates across three rows or columns. When a candidate appears in specific patterns across three rows, aligned in three columns, it creates elimination opportunities that break through difficult puzzle positions. Understanding Swordfish opens up new solving possibilities where simpler techniques have been exhausted.
What Is the Swordfish Technique
Swordfish is an advanced Sudoku solving method that eliminates candidates based on patterns formed across three rows or three columns. When a candidate number appears in exactly two or three cells in each of three different rows, and these cells align in the same three columns, they form a Swordfish pattern. This pattern forces the candidate to occupy specific positions, allowing elimination of that candidate from all other cells in those columns.
Similarly, a column-based Swordfish occurs when a candidate appears in exactly two or three cells in each of three different columns, aligned in the same three rows. The elimination logic works the same way, removing the candidate from other cells in those rows. Swordfish is named for the fish-like pattern created when visualizing the candidate placements across the grid.
Swordfish is a type of fish pattern, extending X-Wing logic to three dimensions. It's more powerful than X-Wing because it examines relationships across more cells, creating more elimination opportunities. This makes Swordfish essential for puzzles where X-Wing and other intermediate techniques don't provide sufficient progress.
Key Points
Point 1: Swordfish Requires Three Rows or Columns
Swordfish specifically requires three rows or three columns, unlike X-Wing which uses two. The candidate must appear in two or three cells in each of the three rows, with those cells aligning in the same three columns. This three-dimensional pattern creates the elimination logic.
Point 2: Candidate Distribution Can Vary
Unlike X-Wing which requires exactly two cells per row, Swordfish allows the candidate to appear in two or three cells in each row. This flexibility makes Swordfish patterns more varied and sometimes easier to find, though the logic remains the same.
Point 3: Row-Based Swordfish Eliminates in Columns
When you find a row-based Swordfish (candidate in three rows, aligned in three columns), eliminate that candidate from all other cells in those three columns. The logic is that the candidate must appear in specific positions within those columns, making it impossible elsewhere.
Point 4: Column-Based Swordfish Eliminates in Rows
A column-based Swordfish works similarly but uses columns instead of rows. When a candidate appears in three columns, aligned in three rows, eliminate that candidate from all other cells in those rows. The elimination logic is identical, just rotated 90 degrees.
Point 5: Swordfish Often Reveals Other Opportunities
After applying Swordfish eliminations, new solving opportunities typically emerge. Removing candidates often creates naked singles, hidden singles, or reveals other advanced patterns. Swordfish frequently acts as a breakthrough technique that unlocks multiple subsequent solving steps.
How It Works (Step-by-Step)
Step 1: Scan for Candidate Distribution Across Three Rows
Choose a candidate number and scan the entire grid. Look for three rows where this candidate appears in two or three cells each. Note which columns these cells occupy. You're searching for three rows where the candidate appears in the same three columns, creating alignment.
Step 2: Identify the Swordfish Pattern
When you find three rows with the candidate appearing in the same three columns (with two or three occurrences per row), you've identified a potential Swordfish. Verify that the candidate appears in two or three cells in each row, and these cells align in the same three columns. The pattern should form a fish-like shape.
Step 3: Apply Elimination Logic
Once confirmed, eliminate the candidate from all other cells in those three columns. The logic is that the candidate must appear in specific positions within those columns, but cannot appear elsewhere. This creates clear eliminations that often reveal new solving opportunities.
Step 4: Check for Column-Based Swordfish
Repeat the process checking columns instead of rows. Look for three columns where the candidate appears in two or three cells each, aligned in the same three rows. When found, eliminate the candidate from all other cells in those rows.
Step 5: Verify and Continue Solving
After making eliminations, verify that they're correct by checking the logic. Then continue solving using other techniques. Swordfish eliminations often reveal naked singles, hidden singles, or create conditions for other advanced techniques.
Examples
Example 1: Row-Based Swordfish in a Hard Puzzle
In a hard puzzle, the number 6 appears in cells R1C2, R1C5, and R1C8 in row 1; in cells R4C2, R4C5, and R4C8 in row 4; and in cells R7C2 and R7C5 in row 7. These form a Swordfish pattern in columns 2, 5, and 8. The number 6 must appear in specific positions within these columns, eliminating 6 from all other cells in columns 2, 5, and 8. This elimination reveals that R2C5 must be 3, breaking the puzzle open.
Example 2: Column-Based Swordfish Eliminating Candidates
A column-based Swordfish appears with candidate 4 in columns 2, 5, and 8. In column 2, 4 appears in R2C2, R5C2, and R8C2. In column 5, 4 appears in R2C5 and R5C5. In column 8, 4 appears in R2C8, R5C8, and R8C8. This forms a Swordfish in rows 2, 5, and 8. Eliminate 4 from all other cells in rows 2, 5, and 8. Removing 4 from R2C3 creates a naked single, allowing placement of 7.
Example 3: Swordfish Combined with Hidden Single
After applying a Swordfish elimination that removes candidate 3 from several cells in a box, a hidden single appears. In box 6, the number 3 can now only appear in one cell, R6C9. Placing 3 there reveals more eliminations, and the puzzle progresses smoothly. This demonstrates how Swordfish often creates cascading solving opportunities.
Summary
Swordfish is a powerful advanced Sudoku technique that extends X-Wing logic to three dimensions, using three rows or columns to create logical eliminations. By recognizing when cells form Swordfish patterns, you can make eliminations that break through difficult puzzle positions. This technique is essential for solving hard and expert puzzles where simpler methods are insufficient.
Mastering Swordfish requires practice in pattern recognition and logical analysis. Start by scanning for row-based patterns, then check for column-based Swordfish. With regular practice, identifying these patterns becomes faster and more intuitive. Swordfish eliminations often reveal other solving opportunities, making this technique a cornerstone of advanced Sudoku solving.
Practice Swordfish in your next Sudoku session, then explore related techniques in X-Wing Sudoku Technique: Use Cases and Examples and 11 Advanced Sudoku Strategies and Examples. For different puzzle challenges, try Number Puzzle or Word Puzzle.
FAQ (Frequently Asked Questions)
Q1: How do I know if I've found a valid Swordfish pattern?
A valid Swordfish requires the candidate to appear in two or three cells in each of three rows or columns, with these cells aligned in the same three columns or rows. The pattern must form a fish-like shape when visualized. Verify the alignment and candidate distribution before applying eliminations.
Q2: Can Swordfish work with more than three rows or columns?
No, Swordfish specifically requires exactly three rows or three columns. If a pattern involves four rows or columns, it's a different fish pattern (Jellyfish). Swordfish is the three-dimensional extension of X-Wing, while Jellyfish extends to four dimensions.
Q3: How often do Swordfish patterns appear in puzzles?
Swordfish patterns are less common than X-Wing but appear regularly in hard and expert difficulty puzzles. In hard puzzles, you might find one Swordfish opportunity. In expert puzzles, Swordfish patterns appear more frequently, often multiple times with different candidates. Very difficult puzzles may require identifying several Swordfish to make progress.
Q4: What if I find a Swordfish but it doesn't eliminate any candidates?
If your Swordfish pattern doesn't eliminate any candidates, it means those candidates were already eliminated by other techniques, or the pattern isn't actually a Swordfish. Double-check that the candidate appears in the correct pattern across three rows or columns, and verify the alignment. Sometimes the pattern exists but doesn't provide new eliminations.
Q5: Can Swordfish be used without candidate notation?
No, candidate notation, also called pencil marks, is absolutely essential for finding Swordfish patterns. Without seeing all possible candidates in cells, identifying Swordfish patterns is nearly impossible. Proper notation makes scanning for Swordfish opportunities much more efficient and accurate.
Q6: Should I look for Swordfish before or after other advanced techniques?
Swordfish is typically looked for after X-Wing and other intermediate techniques are exhausted, but before the most complex techniques like Remote Pairs or complex chains. It's more complex than X-Wing but easier than some chain techniques. Many solvers check for Swordfish after X-Wing when puzzles require more advanced methods.
Next Steps
Ready to master the Swordfish technique? Play Sudoku now and practice identifying Swordfish patterns in challenging puzzles. For more advanced techniques, read X-Wing Sudoku Technique: Use Cases and Examples and 11 Advanced Sudoku Strategies and Examples. If you want to try different puzzle types, explore Number Puzzle or Word Puzzle.