Jellyfish

The Jellyfish strategy is the crown jewel of fish patterns in Sudoku—an expert-level technique that extends the logic of X-Wing and Swordfish to a massive 4x4 grid pattern. While extraordinarily rare, Jellyfish patterns unlock eliminations in the most challenging puzzles where simpler strategies fail.

As the largest commonly recognized fish pattern, Jellyfish represents a pinnacle of pattern recognition in Sudoku solving. Understanding this technique demonstrates mastery of fish pattern logic and prepares you for the most diabolical puzzles.

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What is the Jellyfish Strategy?

The Jellyfish strategy identifies a 4x4 pattern where a specific candidate appears in exactly four rows, and all instances of that candidate in those rows are confined to the same four columns (or vice versa with rows and columns swapped).

The Fish Pattern Family

Jellyfish is part of the fish pattern progression:

• X-Wing: 2 rows × 2 columns (2x2 pattern)
• Swordfish: 3 rows × 3 columns (3x3 pattern)
• Jellyfish: 4 rows × 4 columns (4x4 pattern)

Each pattern type follows the same logical principle but increases in complexity and rarity as the size grows.

How Jellyfish Works

When you identify a Jellyfish pattern for candidate X:

1. Find exactly four rows where candidate X appears
2. Verify that all instances of X in these four rows are confined to the same four columns
3. Eliminate candidate X from all other cells in those four columns (outside the four Jellyfish rows)

The logic is powerful: if candidate X must appear exactly once in each of the four rows, and those instances can only be in four specific columns, then X must occupy exactly four cells total—one in each row and one in each column. Therefore, X cannot appear anywhere else in those four columns.

Column-Based Jellyfish

Jellyfish can also work in reverse:

1. Find exactly four columns where candidate X appears
2. Verify that all instances of X in these columns are confined to the same four rows
3. Eliminate candidate X from all other cells in those four rows (outside the four Jellyfish columns)

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Jellyfish Example

Let's examine a Jellyfish pattern for candidate 7:

Why This Works

Since candidate 7 must appear exactly once in each of rows 1, 3, 5, and 8, and those appearances can only be in columns 2, 4, 6, and 9, we know that 7 will occupy exactly four cells in those columns—one per row. Therefore, the remaining cells in columns 2, 4, 6, and 9 (the cells in rows 2, 4, 6, 7, and 9) cannot contain 7.

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Tips for Finding Jellyfish Patterns

1. Start with Smaller Fish

Always look for X-Wings and Swordfish first. Jellyfish are extremely rare, and you'll waste time searching for them if simpler patterns are available. Only look for Jellyfish when smaller fish patterns don't yield results.

2. Focus on Constrained Candidates

Look for candidates that appear in only a few cells per row or column. Jellyfish patterns are more likely to emerge when candidates are already restricted by other solving techniques.

3. Use Candidate Marking

Pencil marks are essential for Jellyfish identification. Without clear candidate markings, spotting a 4x4 pattern across multiple rows and columns is nearly impossible.

4. Look for Symmetry

While not required, Jellyfish patterns sometimes exhibit symmetry or regularity that makes them easier to spot. Look for evenly distributed candidate placements.

5. Don't Overthink It

If you're spending more than a couple minutes looking for a Jellyfish, move on to other strategies. The pattern is so rare that other techniques (like chains or coloring) are often more productive in expert-level puzzles.

6. Verify Your Pattern

Before making eliminations, double-check that:

• You have exactly four rows (or columns)
• The candidate appears in at least two cells total across those rows
• All instances are confined to exactly four columns (or rows)
• You're eliminating from the correct cells

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Common Mistakes to Avoid

Incomplete Pattern Recognition

The most common error is identifying only three rows or columns, not four. A Jellyfish requires exactly four rows AND four columns. If your pattern is smaller, it might be a Swordfish or X-Wing instead.

Incorrect Elimination Direction

Remember: if you identify rows, you eliminate from columns, and vice versa. Don't eliminate from the same direction you used to find the pattern.

Overlooking the Pattern Entirely

Jellyfish patterns can look chaotic and irregular. Don't expect perfect symmetry—the candidate might appear 2-3 times per row in some rows and only 1-2 times in others, as long as all instances fit within the four columns.

Missing Smaller Patterns First

Never jump straight to Jellyfish hunting. Always exhaust simpler strategies first, as they're far more common and efficient.

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Practice Exercises

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Frequently Asked Questions

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