Swordfish (Column) is an advanced strategy that expands on the logic of the X-Wing. While an X-Wing uses a 2x2 pattern (2 columns, 2 rows), a Swordfish uses a 3x3 pattern (3 columns, 3 rows).
It eliminates candidates by proving that "since the numbers for these 3 columns MUST be in these 3 rows, no other cells in those rows can have that number."
Interactive Example
Click "Apply Logic" to see the strategy in action.
Real Example Walkthrough
In the example puzzle above, the strategy targets the number 1:
1. The Base Sets (Columns) We look at three specific columns: - Column 4 - Column 5 - Column 9
In these three columns, the candidate 1 appears only in three rows: - Row 1 - Row 4 - Row 8
2. The Pattern Let's map out where 1 can go in our base columns: - Col 4: Locked to Rows 1, 4 - Col 5: Locked to Rows 1, 8 - Col 9: Locked to Rows 4, 8
Notice that across all three columns, the candidates are restricted entirely to Rows 1, 4, and 8.
3. The Logic - We need to place three 1s—one for Column 4, one for Column 5, and one for Column 9. - We have exactly three rows available for them (Row 1, 4, 8). - Therefore, these three rows must contain the 1s for our three columns. - Consequently, no other cell in Row 1, Row 4, or Row 8 can contain a 1.
4. The Elimination We can eliminate 1 from any cell in the cover rows (1, 4, 8) that is NOT part of our Swordfish pattern. - Eliminate 1 from R1C7 inside Row 1. - Eliminate 1 from R4C6 inside Row 4.
How to Spot a Swordfish
Finding a Swordfish is difficult because the pattern can be incomplete (not every intersection needs a candidate).
- Pick a Candidate: Focus on one number at a time (e.g., all the 1s).
- Count Candidates in Columns: Look for columns where the candidate appears 2 or 3 times.
- Find the Match: Look for three such columns where the candidates perfectly align into just three rows.
- It's okay if a column completely misses one of the rows (like Col 4 having candidates only in Rows 1 and 4, missing Row 8).
- As long as the total set of rows across all 3 columns is exactly 3 rows, it works.
Visual Guide
Here is a simplified view of a perfect Swordfish interaction:
C1 C2 C3
R1 X . X <- Row 1 (Cover Set)
R2 . X X <- Row 2 (Cover Set)
R3 X X . <- Row 3 (Cover Set)
^ ^ ^
| | |
Col Col Col
1 2 3
(Base Sets)
- Each Base Column has candidates restricted to Rows 1, 2, 3.
- Therefore, Rows 1, 2, 3 must contain the solutions for these columns.
- Any other X in Rows 1, 2, 3 (not in these columns) can be eliminated.
Common Mistakes
- Confusing Base and Cover Sets: Remember, if you start with Columns (Base), you eliminate from Rows (Cover). If you start with Rows, you eliminate from Columns.
- Counting Too Many Rows: If your three columns span across 4 rows, it's not a Swordfish. It must be exactly 3 rows.
- Eliminating from Base Sets: You never eliminate from the columns you used to build the pattern. You eliminate horizontally from the rows crossing through them.
Tips for Beginners
- Use Candidate Highlighting: Most solvers verify highlighting. Select a number to see all its positions. This makes patterns like Swordfish jump out visually.
- Look for "Almost" X-Wings: Often a Swordfish looks like a messy X-Wing with an extra column attached.
- Check Bi-Value Cells: Cells with only 2 options are often key parts of these patterns.
Comparison Table
| Strategy | Pattern Size | Base Sets | Cover Sets | Logic |
|---|---|---|---|---|
| X-Wing | 2x2 | 2 Columns | 2 Rows | Locked 2x2 box |
| Swordfish | 3x3 | 3 Columns | 3 Rows | Locked 3x3 grid |
| Jellyfish | 4x4 | 4 Columns | 4 Rows | Locked 4x4 grid |
Related Strategies
- X-Wing (Column): The simpler 2x2 version of this strategy.
- Jellyfish (Column): The expanded 4x4 version.
- Finned Swordfish: A Swordfish that's "almost" perfect but has a few extra candidates.