Jellyfish

A Jellyfish is the size-4 Basic Fish in Sudoku.

It follows one candidate digit across:

• four base rows and four cover columns;
• or four base columns and four cover rows.

For a row-based Jellyfish, select four rows such that every candidate for the Fish digit in those rows lies within the same four columns.

The four base rows each require one placement of that digit.

Those four required placements must therefore occupy the four cover columns.

So candidate copies of the Fish digit can be removed from the cover columns everywhere outside the four base rows.

The core relationship is:

4 base sets require 4 placements, covered by 4 cover sets.

Jellyfish is not a new proof after X-Wing or Swordfish.

It is the same Basic Fish counting argument at size 4.

Quick rule

For a row-based Jellyfish:

1. choose one candidate digit X;
2. select four rows whose complete candidate-X positions are all contained in the same four columns;
3. treat the four rows as base sets;
4. treat the four columns as cover sets;
5. remove X from those cover columns outside the four base rows.

The candidate distribution can be irregular.

The Fish does not need to look like a complete 4×4 rectangle.

Jellyfish is the size-4 Basic Fish

The Basic Fish family scales by the number of bases and covers:

X-Wing   → 2 bases / 2 covers
Swordfish → 3 bases / 3 covers
Jellyfish → 4 bases / 4 covers

Larger Basic Fish can be defined in the same way, but size 4 is already difficult to identify manually because the number of candidate combinations grows quickly.

That is why understanding the abstract base/cover model matters more than memorizing a Jellyfish silhouette.

The candidate-position union test

Suppose candidate 6 appears in four rows as:

r1 → c2/c8
r3 → c2/c5/c9
r6 → c5/c8
r9 → c2/c8/c9

The union of all source columns is:

{c2,c5,c8,c9}

There are:

• four base rows;
• four distinct cover columns.

If those are the complete candidate-6 positions in the selected rows, the structure can form a Jellyfish.

Candidate 6 can then be eliminated from c2/c5/c8/c9 outside r1/r3/r6/r9.

Why Jellyfish works

Each base row must contain the Fish digit exactly once.

Four base rows therefore require four placements.

Every legal source position for those placements lies in only four cover columns.

Each cover column can also contain the digit only once.

So the four placements required by the bases consume the available capacity of the four covers.

There is no room for another copy of the digit in those cover columns outside the base rows.

Those outside cover candidates can be eliminated.

The proof is exactly the same as an X-Wing or Swordfish:

N base sets → N required placements → all covered by N cover sets.

Step-by-step board example

A Jellyfish does not require a full 4×4 candidate grid

A common visual misconception is to expect sixteen source candidates at every intersection of four rows and four columns.

That is unnecessary.

A valid Jellyfish may have base-row candidate counts such as:

2 / 3 / 2 / 3

or another sparse distribution.

Some intersections may contain no Fish candidate at all.

What matters is that:

• every selected base has legitimate source candidates;
• every source candidate lies within the four covers;
• all four covers genuinely participate in the Fish.

Every base and cover must genuinely participate

If four proposed base rows use only three cover columns, you do not need a size-4 Fish.

There may be:

• a Swordfish;
• a simpler single-digit restriction;
• or a Hidden Single that should be solved first.

Likewise, if the complete source-position union needs five columns, the four rows do not form a Basic Jellyfish.

The clean structural test is:

four selected bases → complete Fish-digit position union contained in exactly four covers.

Column-based Jellyfish

Transpose the pattern.

If four columns contain all candidate X positions within only four rows, then:

• columns are the base sets;
• rows are the cover sets.

The four base columns need four placements of X.

Those placements must consume the four cover rows.

So X can be removed from the cover rows outside the four base columns.

Jellyfish vs Swordfish

Both are Basic Fish.

Swordfish

3 base sets → 3 cover sets.

Jellyfish

4 base sets → 4 cover sets.

The logical proof is unchanged.

The practical difficulty increases because:

• there are more base combinations to inspect;
• the source pattern can be more irregular;
• smaller Fish may be embedded in the same candidate map;
• a single overlooked source candidate can invalidate the whole pattern.

Jellyfish vs X-Wing

X-Wing is often taught as a rectangle.

Jellyfish makes it obvious why Fish should not be understood as rectangle tricks.

The reusable idea is:

• choose bases;
• collect complete candidate positions;
• identify an equal number of covers;
• eliminate outside cover candidates.

Once that model is clear, X-Wing, Swordfish, and Jellyfish are simply sizes 2, 3, and 4.

Basic Jellyfish vs Finned Jellyfish

A Basic Jellyfish requires all selected base candidates to lie inside the four cover sets.

If one or more source candidates sit outside those covers, the Basic Fish proof fails.

Some such structures can form Finned or Sashimi Jellyfish, but the elimination rule becomes stricter: a target must be compatible with the Fish elimination and also see all relevant fins.

Do not use Basic Jellyfish eliminations when an uncovered source candidate remains.

The same principle is introduced more accessibly with Finned X-Wing.

A candidate with one position in a base is simpler logic

Suppose one proposed base row has only one legal position for the Fish digit.

That is already a Hidden Single in the row.

Place it first.

After the candidate map updates, the larger Fish may disappear or simplify into a smaller pattern.

Advanced pattern hunting should not skip forced placements.

How to find Jellyfish efficiently

Searching arbitrary sets of four rows or columns is expensive for a human solver.

Use candidate sparsity.

1. Choose one digit

Fish are single-digit patterns.

2. Prefer sparse candidate maps

A digit with only a few positions in several rows or columns is easier to analyze.

3. Record candidate positions by base unit

For example:

r1 → c2/c8
r3 → c2/c5/c9
r6 → c5/c8
r9 → c2/c8/c9

4. Merge four promising bases

Count the distinct opposite units in the position union.

5. Check for smaller Fish first

If three of the bases already form a Swordfish, use the simpler Fish.

6. Confirm there are no source candidates outside the covers

One missed candidate invalidates the Basic Fish.

7. Look for outside cover candidates

A productive Jellyfish needs at least one candidate X in a cover unit outside the selected bases.

What Jellyfish usually unlocks

Jellyfish is an elimination technique.

A typical progression is:

Jellyfish
↓
remove candidate X from a cover unit
↓
Hidden Single or Locked Candidate appears
↓
placement/elimination updates peers
↓
return to simple scanning

After making the Fish elimination, restart with cheaper logic rather than continuing to search for another large Fish immediately.

Common mistakes

Requiring identical candidate positions in all four bases

Not required. The complete position union is what matters.

Requiring sixteen source candidates

A Jellyfish can be sparse and irregular.

Accepting five cover units

Four base units spread across five covers do not form a size-4 Basic Fish.

Ignoring an extra source candidate outside the covers

That breaks the Basic Fish proof and may indicate a finned structure instead.

Eliminating inside the base sets

For a row-based Fish, eliminate from the cover columns outside the selected base rows.

Mixing digits

A Fish follows one candidate digit only.

Missing a smaller X-Wing or Swordfish

Prefer the smaller valid Fish when it already produces the elimination.

Recognition drill

With candidate 8 filtered, suppose:

r2 → c1/c6
r4 → c1/c4/c9
r7 → c4/c6
r9 → c1/c6/c9

Ask:

1. Are these four complete base-row candidate maps for digit 8?
2. How many distinct cover columns appear in their union?
3. Do all four cover columns genuinely participate?
4. Are there candidate 8s in those columns outside the four base rows?

If the complete union is exactly four cover columns and outside cover candidates exist, you have a productive row-based Jellyfish.

FAQ

Is Jellyfish just a larger Swordfish?

Yes. It uses the same Basic Fish proof with four base and four cover sets instead of three.

Does a Jellyfish need four candidates in every base row?

No. Sparse distributions with two or three candidates in a base are common.

Must all sixteen base/cover intersections contain the Fish digit?

No. Empty intersections are normal.

Can Jellyfish be column-based?

Yes. Swap rows and columns and the proof is unchanged.

What if four rows use only three columns?

Look for a smaller Fish, usually Swordfish, or a simpler deduction.

What if one candidate lies outside the four covers?

Then the pattern is not a Basic Jellyfish. It may belong to the finned/sashimi Fish family, but you need the stricter fin logic before making eliminations.

Is Jellyfish common in normal Sudoku solving?

It is much less common and harder to recognize manually than X-Wing or Swordfish. Its main value is both practical in some advanced puzzles and conceptual: it completes the standard size progression of Basic Fish.

What to learn next

Study Finned X-Wing to learn what changes when a promising Fish has an extra source candidate outside its cover sets. It introduces the fin logic at the smallest useful Fish size before larger finned patterns.