Jellyfish

The Jellyfish extends the X-Wing and Swordfish patterns to four rows and four columns. It's rare, difficult to spot, but essential for the hardest puzzles.

The Fish Family

Before diving into Jellyfish, understand the pattern progression:

Each pattern uses the same logic at increasing scale.

What is a Jellyfish?

A Jellyfish occurs when:

• A candidate appears in exactly 2-4 cells in each of four rows
• Those cells collectively span exactly four columns
• (Or the row/column roles reversed)

The pattern:

• Pick any 4 rows
• Find where a digit can go in each row
• If all candidates fall within the same 4 columns, that's a Jellyfish

The Logic

Consider digit 5 appearing in four rows, confined to columns A, B, C, D:

        Col A   Col B   Col C   Col D
Row 1:    5       5
Row 3:    5               5
Row 6:            5       5       5
Row 8:    5               5

Each row needs one 5. With four rows and four columns:

• Each column will get exactly one 5 from these rows
• The four 5s will occupy one cell per row AND one cell per column

Result: Columns A, B, C, D are "claimed" by these four rows.

Elimination: Remove the candidate from columns A, B, C, D in ALL OTHER rows.

Jellyfish Requirements

For a valid Jellyfish:

1. Four rows where the candidate appears
2. 2-4 candidates per row (not all rows need all four columns)
3. All candidates confined to four columns
4. Each of the four columns must have at least one candidate

The cells don't form a grid — unlike X-Wing's perfect rectangle, Jellyfish cells can be scattered across the 4×4 area.

Visual Examples

Compact Jellyfish

        Col 1   Col 3   Col 5   Col 8
Row 2:    X       X
Row 4:    X               X
Row 6:            X       X       X
Row 9:    X                       X

8 cells forming the Jellyfish. Eliminate from columns 1, 3, 5, 8 in rows 1, 3, 5, 7, 8.

Sparse Jellyfish

        Col 2   Col 4   Col 6   Col 9
Row 1:    X       X
Row 3:            X       X
Row 5:    X               X
Row 7:                    X       X

Each row has exactly 2 candidates. Still a valid Jellyfish.

Dense Jellyfish

        Col 1   Col 2   Col 5   Col 7
Row 2:    X       X       X       X
Row 4:    X       X       X       X
Row 6:    X       X       X       X
Row 8:    X       X       X       X

All 16 cells filled. Valid but you can't determine individual placements — only make eliminations.

Column-Based Jellyfish

The same pattern works with columns as the primary constraint:

• Four columns, each with 2-4 candidates for a digit
• All candidates in exactly four rows
• Eliminate from those rows in other columns

How to Find Jellyfish

Method 1: Candidate Counting

1. Pick a digit
2. For each row, count cells with that candidate
3. If a row has 2-4 candidates, note which columns they're in
4. Find four rows whose candidates span exactly four columns

Method 2: Column Inspection

1. Pick a digit
2. For each column, list which rows have the candidate
3. Look for four columns where candidates cluster in the same four rows

Method 3: Build from Swordfish

1. Find a Swordfish (3×3 pattern)
2. Check if a fourth row/column fits the pattern
3. Extend to Jellyfish if possible

Worked Example

Digit 3 candidates in the grid:

Row 1: columns 1, 4
Row 2: columns 2, 4, 7, 9
Row 3: columns 1, 4, 7
Row 4: columns 2, 5, 7
Row 5: columns 1, 2
Row 6: columns 4, 5, 9
Row 7: columns 1, 4, 5, 7
Row 8: columns 2, 9
Row 9: columns 5, 7, 9

Search for Jellyfish:

Look for rows whose candidates fit in four columns.

Try rows 1, 3, 5, 8:

• Row 1: 1, 4
• Row 3: 1, 4, 7
• Row 5: 1, 2
• Row 8: 2, 9

Combined columns: 1, 2, 4, 7, 9 — that's 5 columns, not 4. Not a Jellyfish.

Try rows 2, 4, 6, 9:

• Row 2: 2, 4, 7, 9
• Row 4: 2, 5, 7
• Row 6: 4, 5, 9
• Row 9: 5, 7, 9

Combined columns: 2, 4, 5, 7, 9 — 5 columns. Not a Jellyfish.

Try rows 1, 3, 7, X:

Looking for rows with candidates in 1, 4, 5, 7...

This process continues until you find (or don't find) a valid 4×4 pattern.

Why Jellyfish Are Rare

Combinatorial explosion:

• C(9,4) = 126 possible 4-row combinations
• Each must be checked for column confinement
• Most combinations don't produce Jellyfish

Puzzle design:

• Most puzzles are solvable without Jellyfish
• Only "diabolical" or specifically designed puzzles require them

Practical advice:

• Don't hunt for Jellyfish early
• Use simpler techniques first
• Jellyfish are a last resort for stuck puzzles

Jellyfish vs. Smaller Fish

Rule of thumb: Try smaller fish first. If they don't exist, consider Jellyfish.

Practice Exercise

Is this a Jellyfish?

Digit 7 in columns 1, 3, 6, 9:

• Column 1: rows 2, 5, 8
• Column 3: rows 2, 4, 8
• Column 6: rows 4, 5, 7
• Column 9: rows 5, 7, 8

Common Mistakes

Mistake 1: Confusing cells with positions

A Jellyfish needs candidates in 4 rows confined to 4 columns (or vice versa). Don't just count total cells.

Mistake 2: Missing a column

If candidates span 5 columns, it's not a Jellyfish. Verify all columns are accounted for.

Mistake 3: Wrong elimination direction

• Row-based Jellyfish: eliminate from the COLUMNS in OTHER rows
• Column-based Jellyfish: eliminate from the ROWS in OTHER columns

Mistake 4: Hunting too early

Jellyfish appear in very hard puzzles. Don't waste time looking in easy/medium puzzles.

Squirmbag and Beyond

The pattern extends further:

• Squirmbag: 5 rows × 5 columns
• Whale: 6 rows × 6 columns
• Leviathan: 7 rows × 7 columns

These are mostly theoretical. In practice, puzzles requiring anything beyond Jellyfish are extremely rare and usually solved with other advanced techniques instead.

Quick Reference

Jellyfish pattern:

• 4 rows (or columns) with a candidate
• All candidates in exactly 4 columns (or rows)
• 2-4 candidates per row/column

Elimination rule:

• Row-based: eliminate from the 4 columns in ALL OTHER rows
• Column-based: eliminate from the 4 rows in ALL OTHER columns

Finding it:

1. Pick a candidate
2. Find rows with 2-4 instances
3. Check if 4 rows span exactly 4 columns
4. Or vice versa for columns

When to look:

• Expert/Evil puzzles
• All simpler techniques exhausted
• The digit has many candidates but clear clustering