Lesson:Jellyfish

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Jellyfish is the four-row extension of the Swordfish.

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About This Lesson

Jellyfish is the four-row (or four-column) extension of the X-Wing and Swordfish patterns. It is one of the rarest and most powerful fish-based elimination techniques in Sudoku solving. While X-Wing uses two rows and two columns, and Swordfish uses three rows and three columns, Jellyfish extends this logic to four rows and four columns — forming a 4×4 fish pattern that enables mass candidate elimination.

Like its simpler counterparts, Jellyfish works on a single candidate digit at a time. The defining characteristic is that a chosen digit appears in exactly 2, 3, or 4 columns across exactly four rows — and the columns used across all four rows are the same set of four columns. When this condition is met, the digit cannot appear anywhere else in those four columns. This allows you to eliminate it from every non-base cell in those four columns.

Jellyfish is extremely rare in typical Sudoku puzzles — most well-constructed puzzles are designed to be solvable without it. However, it occasionally appears in computer-generated extreme puzzles, and understanding it deepens your grasp of fish patterns and helps you recognize why they work. The logical reasoning behind Jellyfish is exactly the same as for X-Wing and Swordfish, just scaled up.

How It Works — Step by Step

Step 1 — Choose a digit and identify rows with 2–4 candidates

Select a candidate digit. Scan all rows and find every row where that digit appears in exactly 2, 3, or 4 columns (no more). These rows are your candidate base rows. Rows where the digit appears in 5 or more columns cannot participate in a Jellyfish.

Step 2 — Find four rows whose columns form a set of exactly four

From your candidate base rows, try to select four rows such that the union of columns where the digit appears across all four rows is exactly four columns. In other words, all candidate cells for the digit in those four rows are confined to the same four columns.

Step 3 — Verify the pattern

Confirm that: (a) you have exactly four base rows, (b) the candidate digit appears in 2–4 of those four columns in each base row, and (c) the union of all those columns is exactly four. If all three conditions hold, you have confirmed a Jellyfish.

Step 4 — Eliminate from non-base cells in the four columns

In the four identified cover columns, eliminate the candidate digit from every cell that is NOT in one of the four base rows. These cells cannot hold the digit because the Jellyfish guarantees the digit will be placed within the four base rows for each of the four columns.

When to Use This Technique

Jellyfish is a technique of last resort in most practical solving. Use it only after X-Wing, Swordfish, Coloring, and XY-Wing have all been exhausted for a given digit. Because it is so rare, many solvers never encounter a genuine Jellyfish in standard puzzles. It is most useful when analyzing computer-generated extreme puzzles or studying the theoretical completeness of fish-based logic.

Worked Examples

Consider digit 3. After scanning, you find: Row 1 has 3s only in Columns {2, 5}. Row 3 has 3s only in Columns {2, 7, 9}. Row 6 has 3s only in Columns {5, 7}. Row 8 has 3s only in Columns {2, 9}. The union of columns is {2, 5, 7, 9} — exactly four columns. This is a Jellyfish with base rows {1, 3, 6, 8} and cover columns {2, 5, 7, 9}. Eliminate digit 3 from every cell in columns 2, 5, 7, and 9 that is NOT in rows 1, 3, 6, or 8.

Because Jellyfish is a generalization of X-Wing (two rows, two columns), all X-Wings are degenerate Jellyfish. The practical difference is that Jellyfish affects four columns rather than two, so the potential scope of elimination is larger. In a very constrained board, this can unlock a significant number of candidate reductions at once.

Frequently Asked Questions

How is Jellyfish different from Swordfish?

Swordfish uses three rows and three columns. Jellyfish uses four rows and four columns. The logical structure is identical — fish techniques always use N rows and N columns for any N ≥ 2. Jellyfish (N=4) is simply rarer and affects more cells.

Can Jellyfish be applied using columns as the base instead of rows?

Yes. A column-based Jellyfish uses four columns as the base and four rows as the cover. The elimination then applies to non-base cells in the four cover rows. Both orientations are valid — whichever you find first is the one to apply.

Why is Jellyfish so rare?

Well-crafted Sudoku puzzles are typically designed with a minimum-clue philosophy that gives them a unique solution achievable by a defined set of techniques. Puzzle constructors can usually achieve this without needing Jellyfish. Computer-generated extreme puzzles with lower clue counts are more likely to require it.

Is there anything beyond Jellyfish in the fish family?

Theoretically, yes — Squirmbag (N=5), Whale (N=6), Leviathan (N=7), and so on. In practice, all N≥5 fish are equivalent to a simpler technique somewhere else on the board. Most solving software does not bother implementing anything beyond Jellyfish.

Ready to test your knowledge? Try applying this technique in our Evil Sudoku puzzles, Expert level course or explore Swordfish technique guide. Keep training to improve your solve times and master the grid!

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