Solving Tips

Sudoku Jellyfish Technique: The 4x4 Advanced Elimination Method

2025-06-11 · 10 min read

Jellyfish is an advanced Sudoku technique and an extension of X-Wing (2 rows × 2 columns) and Swordfish (3 rows × 3 columns). The name comes from the jellyfish's tentacle-like form — the complex 4×4 pattern spreads like jellyfish tentacles. The core principle: When a candidate appears in four rows only within four columns, it can be eliminated from other cells in those four columns.

         Core Principle:

        If a digit appears in four rows where the candidate positions in each row are limited to the same group of four columns (can be any 2-4 of these columns), then this digit must occupy four positions among these four columns in these four rows. Therefore, cells in these four columns that don't belong to these four rows cannot contain this digit.

Jellyfish Rule

If a candidate appears in four rows where each row's candidate positions are limited to the same group of four columns,
then that candidate can be deleted from other rows in these four columns (not in the Jellyfish rows).

Before reading this article, it's recommended to first master X-Wing and Swordfish — they form the foundation for understanding Jellyfish.

Jellyfish Principle: Candidate in 4 rows appears only in 4 columns, eliminate from other cells in these 4 columns

Example Analysis: Row-based Jellyfish

Let's examine a Jellyfish example involving candidate 3 in rows 1, 2, 4, 9.

Figure: Candidate 3 forms Jellyfish pattern in rows 1, 2, 4, 9

Open this example in calculator

Analyzing the Distribution of Candidate 3

First, let's observe the distribution of candidate 3 in each row:

Row 1: Candidate 3 appears in

R1C3: Candidates {3, 5}
R1C6: Candidates {1, 3, 4, 8}

→ The 3 in Row 1 can only be in Column 3 or Column 6

Row 2: Candidate 3 appears in

R2C3: Candidates {1, 3, 6}
R2C6: Candidates {1, 3, 6}
R2C9: Candidates {1, 3}

→ The 3 in Row 2 can only be in Column 3, Column 6, or Column 9

Row 4: Candidate 3 appears in

R4C1: Candidates {3, 8}
R4C6: Candidates {3, 8}

→ The 3 in Row 4 can only be in Column 1 or Column 6

Row 9: Candidate 3 appears in

R9C1: Candidates {3, 6, 8}
R9C3: Candidates {2, 3, 8}
R9C6: Candidates {2, 3, 6}
R9C9: Candidates {1, 3, 8}

→ The 3 in Row 9 can only be in Column 1, Column 3, Column 6, or Column 9

Discovering the Jellyfish Pattern

1 Summarize distribution: Distribution of candidate 3 in these four rows:

Row 1: Columns 3, 6 (2 positions)
Row 2: Columns 3, 6, 9 (3 positions)
Row 4: Columns 1, 6 (2 positions)
Row 9: Columns 1, 3, 6, 9 (4 positions)

2 Confirm Jellyfish: In these four rows, all positions of candidate 3 appear only in columns 1, 3, 6, 9. Although the number of positions per row differs (2-4), they're all limited to the same group of four columns — this forms a Jellyfish pattern.

3 Understand the logic: Since:

The 3 in Row 1 must be in Column 3 or 6
The 3 in Row 2 must be in Column 3, 6, or 9
The 3 in Row 4 must be in Column 1 or 6
The 3 in Row 9 must be in Column 1, 3, 6, or 9

Therefore, the four 3s in these four rows must occupy 4 positions in columns 1, 3, 6, 9. This means the digit 3 in columns 1, 3, 6, 9 is occupied by these four rows.

4 Execute elimination: Therefore, cells in columns 1, 3, 6, 9 that don't belong to rows 1, 2, 4, 9 cannot contain 3:

R3C3: Delete candidate 3
R7C3: Delete candidate 3
R3C6: Delete candidate 3
R7C6: Delete candidate 3
R3C9: Delete candidate 3
R7C9: Delete candidate 3
R6C1: Delete candidate 3
R8C1: Delete candidate 3

Conclusion:
Jellyfish: Digit 3 in rows 1, 2, 4, 9 appears only in columns 1, 3, 6, 9.
Action: Delete candidate 3 from R3C3, R7C3, R3C6, R7C6, R3C9, R7C9, R6C1, R8C1.

Two Forms of Jellyfish

Like X-Wing and Swordfish, Jellyfish has two symmetric forms:

1. Row-based Jellyfish

This is the case shown above:

Observation target: Four rows
Pattern feature: A candidate appears in these four rows with each row's positions limited to the same group of four columns
Elimination target: Delete this candidate from other rows in these four columns

2. Column-based Jellyfish

Opposite form with the same principle:

Observation target: Four columns
Pattern feature: A candidate appears in these four columns with each column's positions limited to the same group of four rows
Elimination target: Delete this candidate from other columns in these four rows

         Memory Tip:

        Row-based Jellyfish eliminates from columns, column-based Jellyfish eliminates from rows.

        This is consistent with X-Wing and Swordfish rules: Observe rows → eliminate from columns; observe columns → eliminate from rows.

Fish Technique Family Comparison

Jellyfish is a member of the Fish technique family, forming a complete system with X-Wing and Swordfish:

Technique	Rows/Columns	Recognition Difficulty	Practical Frequency
X-Wing	2 rows × 2 columns	Relatively Easy	Common
Swordfish	3 rows × 3 columns	Medium	Occasional
Jellyfish	4 rows × 4 columns	Relatively Difficult	Rare

About Larger Fish:
Theoretically, there are 5×5 Squirmbag, 6×6 Whale, and other larger Fish patterns, but they're extremely rare in actual Sudoku puzzles. A 9×9 Sudoku can have at most 9 rows × 9 columns, and Fish involving 5+ rows almost never appear in normal puzzles. Therefore, mastering up to Jellyfish (4×4) is sufficient for most difficult puzzles.

How to Find Jellyfish?

Finding Jellyfish requires systematic observation and is more complex than X-Wing and Swordfish:

1 Choose a candidate: Focus on one candidate (1-9) and analyze individually.

2 Record row distribution: Record the column numbers where this candidate appears in each row. Skip already-filled rows and rows with too many positions.

3 Find four-row combination: Find 4 rows where all their candidate column numbers combined give exactly 4 different columns.

4 Confirm Jellyfish pattern: If you find such four rows, they form a Jellyfish pattern.

5 Execute elimination: Delete this candidate from other rows in these four columns (not in the Jellyfish rows).

Important Notes:

Jellyfish requires exactly four rows, and candidate positions in these four rows span only four columns total
Each row can have 2, 3, or 4 candidate positions, but all must be within the same group of four columns
If four rows span 5 or more columns, no Jellyfish can be formed
Jellyfish is a cross-row/column technique without box concepts
Due to recognition difficulty, it's recommended to try after X-Wing and Swordfish fail

Technique Summary

Key points for Jellyfish technique:

Pattern size: 4 rows × 4 columns, the largest commonly used pattern in the Fish family
Recognition condition: A candidate in four rows occupies only four columns total
Flexibility: Each row can have 2-4 candidate positions, doesn't need to fill all four columns
Elimination rule: Row-based Jellyfish eliminates from columns, column-based Jellyfish eliminates from rows
Application scenario: Last resort when X-Wing and Swordfish can't break through
Practical tip: Due to complexity, using candidate marking for analysis is recommended

         Practical Advice:

        Jellyfish is very rare in practice but may be the only breakthrough in some expert puzzles. Recommendations:
        First exhaust all intermediate techniques and X-Wing, Swordfish
Choose candidates with fewer positions for analysis
Use candidate marking and organize per-row distribution on paper or mentally
If manual analysis is too complex, use a solver to assist learning

    

Practice Recommendations

To master Jellyfish technique:

Master X-Wing and Swordfish first — they're the foundation for Jellyfish
Understand the common principle of the Fish family: The elimination logic of N rows × N columns pattern
Consciously check for Jellyfish when facing expert puzzles
Use solvers to find Jellyfish examples and verify your understanding

Practice Now:
Start an expert-level Sudoku game and try to find and apply Fish techniques!

Swordfish X-Wing Techniques Index