Solving Tips
Sudoku Swordfish Technique: 3x3 Extension of X-Wing
Swordfish is an advanced extension of the X-Wing technique, representing a more complex and powerful method in advanced Sudoku solving. Named after the swordfish's shape, this technique involves three rows and three columns, forming a larger pattern than X-Wing. The core principle is: when a candidate appears in at most three columns across three rows, with exactly three columns total, you can eliminate that candidate from other cells in those three columns.
Core Principle:
If a number appears only in certain positions within columns X, Y, and Z across rows A, B, and C (each row having this candidate in at most two or three of these columns), then this number in these three rows must occupy certain positions in columns X, Y, and Z. Therefore, other cells in columns X, Y, and Z (not in these three rows) cannot contain this number.
If a number appears only in certain positions within columns X, Y, and Z across rows A, B, and C (each row having this candidate in at most two or three of these columns), then this number in these three rows must occupy certain positions in columns X, Y, and Z. Therefore, other cells in columns X, Y, and Z (not in these three rows) cannot contain this number.
Before reading this article, we recommend mastering the X-Wing technique, as Swordfish is a direct extension of X-Wing.
Example Analysis: Row-based Swordfish
Let's examine a Swordfish example involving candidate 3 in rows 3, 5, and 7.
Figure: Candidate 3 in rows 3, 5, 7 forms a Swordfish pattern
Analysis Process
1
Observe Row 3: In row 3, candidate 3 appears only in two positions: A3 and I3.
2
Observe Row 5: In row 5, candidate 3 also appears only in two positions: A5 and D5.
3
Observe Row 7: In row 7, candidate 3 appears only in two positions: D7 and I7.
4
Discover Swordfish Pattern: Candidate 3 in rows 3, 5, and 7 appears only in columns A, D, and I:
- Row 3: column A ✓, column I ✓ (two columns)
- Row 5: column A ✓, column D ✓ (two columns)
- Row 7: column D ✓, column I ✓ (two columns)
Although each row appears in only two of these columns, the three rows combined involve only columns A, D, and I, forming a Swordfish pattern.
Swordfish Pattern Diagram
Six 3s distributed across 3 rows and 3 columns, orange lines show connections, red arrows indicate elimination direction
5
Understand the Logic: Because candidate 3 in rows 3, 5, and 7 can only be distributed in columns A, D, and I, these three 3's must occupy certain positions in these columns within these rows. Regardless of the specific distribution, candidate 3 in columns A, D, and I is occupied by rows 3, 5, and 7.
6
Execute Elimination: Therefore, cells in columns A, D, and I outside of rows 3, 5, and 7 cannot contain 3. Specifically:
- Column A: eliminate candidate 3 from A1, A2, A4, A6, A8, A9
- Column D: eliminate candidate 3 from D1, D2, D3, D4, D6, D8, D9
- Column I: eliminate candidate 3 from I1, I2, I4, I5, I6, I8, I9
Conclusion:
Rows 3, 5, and 7 form a Swordfish pattern in columns A, D, and I. Therefore, candidate 3 in other positions (rows 1, 2, 4, 6, 8, 9) of columns A, D, and I must be eliminated.
Rows 3, 5, and 7 form a Swordfish pattern in columns A, D, and I. Therefore, candidate 3 in other positions (rows 1, 2, 4, 6, 8, 9) of columns A, D, and I must be eliminated.
Key Features of Swordfish
1. Each Row Need Not Appear in All Three Columns
This is an important distinction between Swordfish and X-Wing:
- X-Wing: In two rows, each row's candidate appears exactly in the same two columns
- Swordfish: In three rows, each row's candidate can appear in 2 or 3 of these columns, as long as they combine to exactly three columns
Important Understanding:
In the example above, row 3 has candidate 3 only in columns A and I, row 5 only in A and D, and row 7 only in D and I. Although no single row has the candidate in all three columns, the three rows combined cover columns A, D, and I, which is sufficient to form a Swordfish.
In the example above, row 3 has candidate 3 only in columns A and I, row 5 only in A and D, and row 7 only in D and I. Although no single row has the candidate in all three columns, the three rows combined cover columns A, D, and I, which is sufficient to form a Swordfish.
2. Number of Columns Must Equal Number of Rows
Swordfish requires three rows corresponding to three columns (or three columns corresponding to three rows):
- If a candidate in three rows involves only two columns, it's an incomplete pattern and cannot use Swordfish
- If a candidate in three rows involves four columns, it also cannot form a Swordfish
- It must be exactly a three-row, three-column correspondence
Two Forms of Swordfish
Like X-Wing, Swordfish also has two symmetrical forms:
1. Row-based Swordfish
This is the case shown in the example above:
- Observation target: Three rows
- Pattern characteristic: A candidate appears in these three rows only in the same three columns (or two of them)
- Elimination target: Remove this candidate from other rows in these three columns
2. Column-based Swordfish
The form is reversed but the principle is the same:
- Observation target: Three columns
- Pattern characteristic: A candidate appears in these three columns only in the same three rows (or two of them)
- Elimination target: Remove this candidate from other columns in these three rows
Memory Tip:
Row-based Swordfish eliminates columns, column-based Swordfish eliminates rows.
This is completely consistent with X-Wing rules, just extended from 2×2 to 3×3.
Row-based Swordfish eliminates columns, column-based Swordfish eliminates rows.
This is completely consistent with X-Wing rules, just extended from 2×2 to 3×3.
How to Find Swordfish?
Finding Swordfish is more difficult than X-Wing and requires more systematic analysis:
1
Select a candidate: Focus on one candidate (one of 1-9), preferably a number with fewer candidate positions.
2
Find rows (or columns) with few candidates: Identify rows (or columns) where the candidate appears in only 2-3 cells.
3
Find three-row combinations: Check if there are three rows whose candidates combined involve only three columns (each row can have 2 or 3 of these columns).
4
Confirm Swordfish pattern: If such a three-row, three-column combination is found, a Swordfish pattern is formed.
5
Execute elimination: Remove the candidate from other cells in the corresponding columns (or rows).
Important Notes:
- Swordfish requires exactly three rows (or three columns) involving exactly three columns (or three rows)
- Each row can have the candidate in 2 or 3 columns, but the three rows combined cannot exceed three columns
- If a row has the candidate in 4 or more positions, it's usually not suitable for forming a Swordfish
- Swordfish is very rare and doesn't appear in most Sudoku puzzles
- Finding Swordfish is time-consuming; it's recommended to try all other techniques first
Relationship with Other Techniques
X-Wing vs Swordfish
| Comparison | X-Wing | Swordfish |
|---|---|---|
| Number of Rows | 2 rows (or 2 columns) | 3 rows (or 3 columns) |
| Number of Columns | 2 columns (or 2 rows) | 3 columns (or 3 rows) |
| Pattern Feature | Each row must have candidate in exactly two columns | Each row can have candidate in 2-3 columns |
| Recognition Difficulty | Difficult | Very Difficult |
| Frequency | Occasional | Rare |
Advanced Extensions
Swordfish can be further extended:
- Jellyfish: Four-row, four-column extension
- Squirmbag: Five-row, five-column extension (extremely rare, almost never encountered)
These techniques follow the same principle as Swordfish, but involve more rows and columns, with recognition difficulty increasing exponentially.
Technique Summary
Key points for applying the Swordfish technique:
- Essence: X-Wing extended from 2×2 to 3×3 pattern
- Recognition condition: A candidate in three rows (or three columns) combined involves only three columns (or three rows)
- Flexibility: Each row need not have the candidate in all three columns, as long as the three rows combined cover these three columns
- Elimination rule: Row-based Swordfish eliminates columns, column-based Swordfish eliminates rows
- Application scenario: Last resort when X-Wing and all other intermediate and basic advanced techniques fail
- Recognition difficulty: Requires systematic analysis of candidate distribution across multiple rows and columns, very time-consuming
- Frequency: Very rare, most difficult puzzles don't require it
Practical Advice:
Swordfish is extremely rare in practice, appearing only occasionally in the most difficult expert-level puzzles. Recommendations:
Swordfish is extremely rare in practice, appearing only occasionally in the most difficult expert-level puzzles. Recommendations:
- Use all intermediate techniques and X-Wing first
- Choose the candidate with the fewest positions for analysis (e.g., numbers with only 6-9 candidate positions remaining)
- Use paper and pen to record each number's distribution across rows and columns to help discover three-row, three-column combinations
- Some Sudoku software provides Swordfish hint features that can help with learning
- If you can't find it after 30 minutes, the puzzle may not require Swordfish; check if you missed simpler techniques
Practice Now
Practice Suggestions:
Start an expert-level Sudoku game and try using the Swordfish technique! Suggestions:
Start an expert-level Sudoku game and try using the Swordfish technique! Suggestions:
- Choose the highest difficulty, as only expert-level puzzles may require Swordfish
- Make sure you've mastered the X-Wing technique first
- Systematically analyze each candidate, looking for three-row, three-column patterns
- Be patient, Swordfish is very rare and difficult to spot