Jellyfish

The Rare 4×4 Fish Pattern

By Minimal Sudoku Team•Last updated: January 28, 2025

The Jellyfish is the 4×4 extension of the Fish family. With only about 1 in 443,687 puzzles requiring this technique, it's the "hole-in-one" of Sudoku — rare, but incredibly powerful when found.

Quick Summary

What: A candidate confined to 4 columns across 4 rows (or vice versa)
Pattern: 8–16 cells forming a 4×4 grid alignment
Result: Eliminate that candidate from other cells in the aligned rows or columns
Difficulty: Expert — rare and hard to spot

The Concept

A Jellyfish follows the same logic as X-Wing and Swordfish, but at a larger scale. When a candidate appears in at most 4 positions in each of 4 different rows (or columns), and all those positions align within the same 4 columns (or rows), you have a Jellyfish.

Unlike smaller fish patterns, a Jellyfish can have anywhere from 8 to 16 cells — not all positions in the 4×4 grid need to be filled.

Row-Based Jellyfish

Find 4 rows where a candidate appears in only 2–4 cells each, all within the same 4 columns.

→ Eliminate from those columns

Column-Based Jellyfish

Find 4 columns where a candidate appears in only 2–4 cells each, all within the same 4 rows.

→ Eliminate from those rows

The Golden Rule

🪼 Jellyfish Rule

When a candidate is confined to the same 4 columns across 4 rows (with 2–4 occurrences per row), eliminate that candidate from all other cells in those 4 columns. The same applies with rows and columns swapped.

How to Find a Jellyfish

Find rows with limited candidates

Look for rows (or columns) where a specific candidate appears in only 2–4 cells. For example, digit 5 appears only in columns 1 and 9 in row 1.

Find three more matching rows

Look for three additional rows where the same candidate also appears in 2–4 cells — and those cells must fall within the same 4 columns as the first row.

Verify the alignment

Confirm all candidate positions across the 4 rows are confined to exactly 4 columns. Each column should have the candidate in at least 2 of the 4 rows.

Eliminate candidates

Remove the candidate from all other cells in those 4 columns (for row-based) or 4 rows (for column-based Jellyfish).

Practical Example

Jellyfish on Digit 5

Jellyfish pattern example showing digit 5 in rows 1, 3, 4, and 7

In this example, we've found a row-based Jellyfish for the digit 5:

Row 1: Digit 5 appears only in columns 1, 9
Row 3: Digit 5 appears only in columns 1, 5, 9
Row 4: Digit 5 appears only in columns 2, 9
Row 7: Digit 5 appears only in columns 1, 2, 5

All four rows have their 5 candidates confined to the same four columns: 1, 2, 5, and 9. This means columns 1, 2, 5, and 9 will each contain exactly one 5 from these rows.

Elimination

Remove 5 as a candidate from all other cells in columns 1, 2, 5, and 9 (outside rows 1, 3, 4, and 7).

Why It Works

The logic extends directly from X-Wing and Swordfish. In each of the 4 columns, the candidate must appear somewhere. Since it can only go in cells within rows 1, 3, 4, or 7, those four rows will "absorb" all four 5s — one per column.

We don't need to know exactly which cell in each column gets the 5. We just know that between them, rows 1, 3, 4, and 7 will claim all four 5s from these columns. Therefore, no other cell in those columns can contain a 5.

Visual representation:

Rows 1, 3, 4, and 7 align with columns 1, 2, 5, and 9 — a Jellyfish on 5.

→ Eliminate 5 from other cells in columns 1, 2, 5, and 9.

Not All 16 Positions Required

A valid Jellyfish doesn't need all 16 cells filled. As long as each row has the candidate in 2–4 of the defining columns (and vice versa), the pattern works. Eight cells is the minimum.

Fish Family Comparison

Pattern	Size	Difficulty
X-Wing	2 rows × 2 columns	🟡 Medium
Swordfish	3 rows × 3 columns	🟠 Hard
Jellyfish	4 rows × 4 columns	🔴 Expert

Each fish pattern uses the same core logic — candidates are "locked" across multiple lines. Larger fish are rarer but eliminate more candidates when found.

Why Stop at 4?

Theoretically, you could have a 5×5 "Squirmbag" or larger, but these are extremely rare in human-solvable puzzles. Most solvers never encounter anything larger than Jellyfish.

How Rare Is It?

Just how rare is a Jellyfish? Analysis shows that only about 0.0002% of Sudoku puzzles require this technique — roughly 1 in 443,687. This is the "needle in a haystack" of the Sudoku world.

To put that in perspective:

Event	Odds	vs Jellyfish
Hole-in-one (amateur golfer)	1 in 12,500	35× more likely
Four-leaf clover (first try)	1 in 10,000	44× more likely
Royal Flush (Texas Hold'em)	1 in 649,740	Slightly rarer
Jellyfish required	1 in 443,687	—

So you're about 35 times more likely to hit a hole-in-one than to need a Jellyfish. On the other hand, you're slightly more likely to encounter a Jellyfish than to be dealt a Royal Flush — but both are firmly in "don't hold your breath" territory.

Lottery Comparison

While you have a much better chance of finding a Jellyfish than winning the Powerball jackpot (1 in 292 million), encountering one is roughly as likely as winning a decent scratch-off prize ($100–$500 range).

Detection Tips

Start with X-Wings

If you find an X-Wing but it doesn't produce useful eliminations, check if it could be part of a larger Swordfish or Jellyfish pattern.

Use Software Assist

Jellyfish are notoriously hard to spot manually. If you're stuck on an expert puzzle, consider using a solver to check for fish patterns you might have missed.

Column-First Can Be Easier

Sometimes scanning columns for the pattern is easier than rows. Try both orientations when searching.

Rare in Practice

With odds of 1 in 443,687, most expert puzzles don't require Jellyfish at all. If you're spending too long looking for one, other techniques (like chains) might be more productive.

Master the smaller fish patterns first — Jellyfish builds directly on their logic: