Finned Swordfish
The Finned Swordfish strategy extends the finned fish concept to 3x3 patterns, creating one of the most sophisticated fish techniques in standard Sudoku solving. While a regular Swordfish demands a perfect 3x3 formation, the Finned Swordfish accommodates imperfect patterns with extra candidates, applying conditional logic to unlock eliminations that would otherwise be impossible.
This expert-level technique represents a significant step up in complexity from the Finned X-Wing, requiring sharp pattern recognition across nine boxes and careful analysis of fin relationships. Mastering Finned Swordfish marks your transition into truly advanced Sudoku solving.
What is a Finned Swordfish?
A Finned Swordfish occurs when you have an almost-perfect Swordfish pattern (3 rows and 3 columns) with extra candidates in one of the boxes that intersect the pattern. These extra candidates—the "fin"—prevent the pattern from being a perfect Swordfish but don't invalidate the elimination logic.
The Structure of a Finned Swordfish
A Finned Swordfish for candidate X consists of:
- The Body: Three rows (or columns) where candidate X appears, mostly confined to the same three columns (or rows), forming the core Swordfish pattern
- The Fin: One or more extra candidates of X in a box that intersects the Swordfish pattern, breaking the perfect 3x3 formation
- Elimination Zone: Cells that can "see" both the normal Swordfish elimination zone AND all fin cells
The Conditional Logic
The power of Finned Swordfish comes from either-or reasoning:
- Case 1: If the fin is FALSE (candidate is not in any fin cell), the remaining pattern forms a perfect Swordfish with normal elimination rules
- Case 2: If the fin is TRUE (candidate IS in a fin cell), then the candidate cannot appear in other cells in the same box as the fin
- Conclusion: Any cell eliminated in BOTH cases can be safely removed
The intersection of these two scenarios typically limits eliminations to the box containing the fin—specifically, cells that would be eliminated by the perfect Swordfish AND share box/row/column visibility with the fin.
Identification Process
- Look for candidate X appearing in exactly three rows (or columns)
- Check if these instances are mostly confined to three columns (or rows)
- Identify extra candidates that break the perfect pattern—these are fins
- Verify all fins are in the same box
- Find cells that see both the Swordfish elimination zone and all fins
- Eliminate candidate X from those cells
Finned Swordfish Example
Let's examine a Finned Swordfish pattern for candidate 3:
Setup:
- Row 1: Candidate 3 appears in R1C2, R1C5, R1C8
- Row 4: Candidate 3 appears in R4C2, R4C5
- Row 7: Candidate 3 appears in R7C2, R7C5, R7C8, R7C9 (fin)
Analysis:
This almost forms a perfect Swordfish in rows 1, 4, and 7, columns 2, 5, and 8. However, R7C9 is an extra candidate in Box 9 that breaks the perfect pattern. This is the fin.
The Normal Swordfish Pattern:
If R7C9 didn't exist, we'd have a perfect Swordfish and could eliminate 3 from all other cells in columns 2, 5, and 8 (outside rows 1, 4, and 7).
Conditional Reasoning:
- If R7C9 = 3 (fin is true): Then 3 cannot be in any other cell in Box 9, including R8C8 and R9C8
- If R7C9 ≠ 3 (fin is false): The pattern becomes a perfect Swordfish, eliminating 3 from column 8 outside rows 1, 4, 7—including R8C8 and R9C8
Valid Eliminations:
In BOTH scenarios, we can eliminate candidate 3 from R8C8 and R9C8 because:
- They're in column 8 (Swordfish elimination zone)
- They're outside rows 1, 4, and 7
- They're in Box 9 (same box as the fin)
- They can "see" the fin at R7C9
Invalid Eliminations:
We CANNOT eliminate 3 from R2C8, R3C8, R5C8, or R6C8 (other column 8 cells) because these cells are not in Box 9 and cannot "see" the fin in R7C9.
Understanding "Seeing" in Finned Patterns
A cell "sees" a fin if they share:
- The same row, OR
- The same column, OR
- The same box
For Finned Swordfish, eliminations typically occur within the fin's box because that's where the seeing relationship is strongest.
Tips for Finding Finned Swordfish
1. Build on Swordfish Experience
Only search for Finned Swordfish after you're comfortable finding regular Swordfish patterns. Understanding the perfect 3x3 pattern makes identifying imperfect versions much easier.
2. Start with Row/Column Analysis
Pick a candidate and scan for three rows where it appears. Check if those instances are mostly confined to three columns, with just 1-3 extra cells breaking the pattern.
3. Locate the Fin Box Early
Quickly identify which box contains the fins. This box is where your eliminations will likely occur, so focusing on it saves time.
4. Use Systematic Candidate Marking
Finned Swordfish patterns are nearly impossible to spot without pencil marks. Maintain clear, consistent candidate notations in all cells.
5. Look for Compressed Patterns
Finned Swordfish often appear when a candidate is already constrained by other techniques. If you see a candidate with limited placements, it's worth checking for finned fish.
6. Check Both Orientations
Always examine both row-based and column-based patterns. A finned fish that's hard to see in rows might be obvious in columns, and vice versa.
7. Verify Before Eliminating
Due to the complexity, double-check your pattern:
- Exactly three rows and three columns?
- Fins all in one box?
- Elimination targets see all fins?
- Targets are in the Swordfish elimination zone?
Common Mistakes to Avoid
Over-Eliminating Across the Grid
The most common error is treating a Finned Swordfish like a perfect Swordfish and eliminating from entire columns or rows. Remember: eliminations are typically restricted to cells that see the fin, usually within one box.
Miscounting the Pattern Size
Ensure you have exactly three rows AND three columns. Four rows with three columns is a different pattern (possibly Finned Jellyfish or invalid), and two rows with three columns might be a different technique entirely.
Missing Multi-Cell Fins
A Finned Swordfish can have 2-3 fin cells in the same box. Don't assume there's only one fin—look for all extra candidates in the fin box.
Ignoring "Seeing" Relationships
Not all cells in the Swordfish elimination zone can be eliminated. Always verify that target cells can see ALL fin cells before removing candidates.
Giving Up on Imperfect Patterns
When you find an "almost Swordfish," don't immediately move on. Check if it's a Finned Swordfish—these imperfect patterns are actually more common than perfect ones.
Practice Exercises
Exercise 1: Identifying the Fin
Candidate 7 appears in the following cells:
- Row 2: R2C1, R2C4, R2C7
- Row 5: R5C1, R5C4, R5C6, R5C7
- Row 8: R8C1, R8C7
Question: Is this a Finned Swordfish? If so, identify the fin(s).
Show Answer
Answer: Yes, this is a Finned Swordfish! Rows 2, 5, and 8 form a Swordfish in columns 1, 4, and 7, with R5C6 as the fin (the extra candidate in Box 5 that breaks the perfect pattern).
Exercise 2: Finding Eliminations
You've identified a Finned Swordfish for candidate 5 in columns 3, 6, and 9, confined to rows 1, 4, and 7, with a fin at R2C9 (in Box 3). Candidate 5 also appears in R2C6 and R3C6.
Question: Which cells allow eliminations?
Show Answer
Answer: You can eliminate candidate 5 from R2C6 and R3C6. These cells are in row 2 and 3 (within the Swordfish elimination zone for column 6) AND are in Box 2 and Box 3, which can see the fin at R2C9. Actually, R2C6 can see the fin directly (same row), and R3C6 can see it through Box 3.
Exercise 3: Pattern Recognition Challenge
Candidate 9 appears in:
- Row 3: R3C2, R3C5, R3C8
- Row 6: R6C2, R6C5, R6C8
- Row 9: R9C2, R9C5, R9C8
Question: Is this a Finned Swordfish or a regular Swordfish?
Show Answer
Answer: This is a perfect Swordfish (not finned)! There are exactly 9 candidates in a perfect 3x3 formation across rows 3, 6, 9 and columns 2, 5, 8. No extra candidates means no fin. You can eliminate candidate 9 from all other cells in columns 2, 5, and 8.
Frequently Asked Questions
What is a Finned Swordfish in Sudoku?
A Finned Swordfish is an expert-level variation of the Swordfish pattern where a 3x3 fish formation has extra candidates (fins) that break the perfect pattern. The fin creates conditional logic allowing eliminations from cells that see both the Swordfish elimination zone and all fin cells, typically within the box containing the fins.
How does a Finned Swordfish differ from a regular Swordfish?
A regular Swordfish has 2-6 candidates distributed across exactly 3 rows and 3 columns in a perfect pattern, allowing eliminations across entire columns or rows. A Finned Swordfish includes extra candidates (fins) in one box that break this perfect formation, limiting eliminations to only cells that can see both the normal Swordfish zone and the fins.
Is Finned Swordfish harder to spot than Finned X-Wing?
Yes, Finned Swordfish is significantly more challenging to identify than Finned X-Wing because it involves a 3x3 pattern instead of 2x2, with more cells to track and more complex fin relationships. The larger pattern size makes visual recognition more difficult and requires careful candidate analysis.
Can a Finned Swordfish have multiple fins?
Yes, a Finned Swordfish can have multiple fin cells, as long as they're all located in the same box. The elimination logic remains the same: you can only eliminate from cells that see ALL fin cells and are in the Swordfish elimination zone.
How common are Finned Swordfish patterns in Sudoku?
Finned Swordfish patterns are rare and typically appear only in expert-level or diabolical puzzles. They're more common than regular Swordfish (due to relaxed pattern requirements) but still uncommon enough that many solvers may only encounter them occasionally in very difficult puzzles.