Finned X-Wing

The Finned X-Wing strategy is an elegant extension of the classic X-Wing pattern that handles imperfect formations. While a regular X-Wing requires a pristine 2x2 pattern, real-world puzzles often present "almost X-Wings" with extra candidates that break the perfect symmetry. These extra candidates—called "fins"—don't invalidate the pattern; they create conditional logic that still allows eliminations.

Mastering Finned X-Wings dramatically increases your fish pattern recognition, as these formations appear far more frequently than their perfect counterparts. This technique bridges the gap between basic fish patterns and advanced chaining logic.

What is a Finned X-Wing?

A Finned X-Wing occurs when you have an almost-perfect X-Wing pattern with extra candidate(s) in one of the boxes. These extra candidates are the "fin" of the fish—they stick out from the main body of the pattern.

Anatomy of a Finned X-Wing

A Finned X-Wing for candidate X consists of:

  • The Body: Two rows (or columns) where candidate X appears in mostly the same two columns (or rows), forming the core X-Wing pattern
  • The Fin: Extra candidate(s) of X in one of the boxes that shares space with the X-Wing pattern, breaking the perfect 2x2 formation

The Logic Behind Finned X-Wings

The conditional logic works as follows:

  1. Scenario A: If the fin is FALSE (the candidate is not in the fin cell), then the remaining pattern forms a perfect X-Wing, and normal X-Wing eliminations apply
  2. Scenario B: If the fin is TRUE (the candidate IS in the fin cell), then the candidate cannot appear in other cells in that same box
  3. Conclusion: Any cell that would be eliminated in BOTH scenarios can be safely eliminated

The key insight: you can eliminate candidate X from cells that "see" both the X-Wing elimination zone AND all fin cells. Typically, this means eliminations are confined to the box containing the fin.

How to Identify a Finned X-Wing

  1. Look for an almost-perfect X-Wing pattern (2 rows, 2 columns)
  2. Identify extra candidates in one of the four boxes formed by the pattern
  3. These extra candidates are the fin
  4. Check which cells can see both the normal X-Wing elimination zone and the fin
  5. Eliminate the candidate from those cells

Finned X-Wing Example

Let's examine a Finned X-Wing pattern for candidate 6:

Setup:

  • Row 2: Candidate 6 appears in R2C3, R2C7
  • Row 5: Candidate 6 appears in R5C3, R5C7, R5C8 (fin)

Analysis:

This almost forms a perfect X-Wing in rows 2 and 5, columns 3 and 7. However, R5C8 is an extra candidate—the fin—that breaks the perfect pattern. The fin is located in Box 6 (the box containing R5C7-R5C9).

Conditional Logic:

  • If R5C8 = 6 (fin is true): Then 6 cannot be in any other cell in Box 6, including R4C7 and R6C7
  • If R5C8 ≠ 6 (fin is false): Then the pattern becomes a perfect X-Wing, and we can eliminate 6 from all other cells in column 7 outside rows 2 and 5, including R4C7 and R6C7

Eliminations:

In BOTH scenarios, candidate 6 can be eliminated from R4C7 and R6C7, because these cells:

  • Are in the X-Wing elimination zone (column 7, outside rows 2 and 5)
  • Are in the same box as the fin (Box 6)
  • Can "see" the fin cell R5C8

Note that we cannot eliminate 6 from other cells in column 7 (like R1C7, R8C7, R9C7) because those cells cannot see the fin in Box 6.

Visualizing "Seeing" the Fin

A cell "sees" the fin if:

  • It's in the same row as a fin cell, OR
  • It's in the same column as a fin cell, OR
  • It's in the same box as a fin cell

For eliminations, the cell must see ALL fin cells (if there are multiple) AND be in the normal X-Wing elimination zone.

Tips for Finding Finned X-Wings

1. Start with Regular X-Wing Hunting

Look for almost-perfect X-Wing patterns first. When you spot a candidate appearing in two rows and mostly confined to two columns (but with 1-2 extra cells), you might have a Finned X-Wing.

2. Identify the Fin Box

The fin must be in one of the four boxes that intersect the X-Wing pattern. Quickly identify which box contains the extra candidates.

3. Check for "Seeing" Relationships

Draw lines from the fin to other candidates in the elimination zone. If a candidate in the X-Wing elimination zone is in the same box, row, or column as the fin, it can be eliminated.

4. Look for Multiple Fins

A Finned X-Wing can have multiple fin cells, as long as they're all in the same box. The logic remains the same: eliminate from cells that see ALL fins.

5. Don't Forget Column-Based Patterns

Finned X-Wings work in both directions. If you find a pattern in columns, look for eliminations in the corresponding rows.

6. Use Candidate Highlighting

In digital solvers or with colored pencil marks, highlight the X-Wing body in one color and the fin in another. This makes the pattern much easier to visualize.

Common Mistakes to Avoid

Over-Eliminating Beyond the Fin Box

The most common error is eliminating candidates from the entire column or row (as you would with a regular X-Wing). Remember: with a Finned X-Wing, eliminations are typically limited to cells that can see the fin, which usually means staying within the fin's box.

Misidentifying the Fin

Make sure the extra candidates are actually "extra" and not part of the core X-Wing pattern. The fin must break the perfect 2x2 formation and must be in one of the four boxes at the X-Wing intersections.

Forgetting to Check "Seeing" Relationships

Not every cell in the X-Wing elimination zone can be eliminated in a Finned X-Wing. Always verify that the target cell can see the fin through box, row, or column relationships.

Missing Finned Patterns Entirely

Many solvers give up when they find an "almost X-Wing" with extra candidates. Don't discard these patterns—check if they're Finned X-Wings instead!

Practice Exercises

Exercise 1: Identifying the Fin

Candidate 4 appears in the following cells:

  • Row 3: R3C2, R3C5, R3C6
  • Row 7: R7C2, R7C5

Question: Is this a Finned X-Wing? If so, which cell is the fin?

Show Answer

Answer: Yes, this is a Finned X-Wing! Rows 3 and 7 form an X-Wing in columns 2 and 5, with R3C6 as the fin (it's the extra candidate breaking the perfect pattern). The fin is in Box 2.

Exercise 2: Finding Eliminations

You've identified a Finned X-Wing for candidate 8 in rows 4 and 8, columns 1 and 9, with a fin at R8C3 (in Box 7). Column 9 also contains candidate 8 in cells R2C9, R3C9, R5C9, and R7C9.

Question: From which cells can you eliminate candidate 8?

Show Answer

Answer: You can eliminate candidate 8 from R7C9 only. This cell is in column 9 (the X-Wing elimination zone) AND in Box 9, which shares row 7-9 with the fin's box (Box 7). The other candidates (R2C9, R3C9, R5C9) cannot see the fin in Box 7, so they cannot be eliminated.

Exercise 3: Perfect vs. Finned

Candidate 9 appears in:

  • Row 1: R1C4, R1C8
  • Row 6: R6C4, R6C8

Question: Is this a regular X-Wing or a Finned X-Wing?

Show Answer

Answer: This is a perfect X-Wing (not finned) because there are exactly 4 candidates in a perfect 2x2 formation across rows 1 and 6, columns 4 and 8. There are no extra candidates, so no fin. You can eliminate candidate 9 from all other cells in columns 4 and 8.

Frequently Asked Questions

What is a Finned X-Wing in Sudoku?

A Finned X-Wing is a variation of the classic X-Wing pattern where the formation has extra candidates (called "fins") that would normally disqualify it as a regular X-Wing. The fin creates a conditional logic: if the fin is false, the X-Wing works normally; if the fin is true, it directly eliminates candidates in cells that see the fin.

How does a Finned X-Wing differ from a regular X-Wing?

A regular X-Wing has exactly 2-4 candidates in a perfect 2x2 formation across two rows and columns. A Finned X-Wing has additional candidates (fins) in one of the boxes that break the perfect pattern. While a regular X-Wing allows eliminations across entire columns or rows, a Finned X-Wing only allows eliminations in cells that see both the X-Wing pattern and the fin.

Where can I make eliminations with a Finned X-Wing?

With a Finned X-Wing, you can only eliminate candidates from cells that can "see" both the regular X-Wing elimination zone AND the fin cells. This typically means eliminations are confined to the box containing the fin, specifically in cells that would be eliminated by the normal X-Wing logic and are in the same box as the fin.

Are Finned X-Wings common in Sudoku puzzles?

Finned X-Wings appear more frequently than regular X-Wings because the pattern requirements are more relaxed (the fin allows for imperfect formations). They typically appear in expert-level puzzles and are an important technique for solving difficult Sudokus without advanced chaining methods.

Can Finned X-Wings work with columns instead of rows?

Yes, Finned X-Wings work bidirectionally. You can have a column-based Finned X-Wing where the pattern appears in two columns with a fin, allowing eliminations in rows. The logic remains the same regardless of whether you start with rows or columns.

Practice Finned X-Wing

Feeling stuck? Sometimes even experts need Trial & Error.

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