Turbot Fish in Sudoku: Short X-Chain Explained

A Turbot Fish is a short single-digit chain.

Despite the name, it is not a Fish in the X-Wing/Swordfish base-set and cover-set framework.

The cleanest modern definition is:

a Turbot Fish is an X-Chain that is four candidates long.

The chain alternates Strong and Weak Links for one digit and starts and ends with a Strong Link. That proves that at least one endpoint must contain the chain digit.

Any outside candidate for that digit that sees both endpoints can therefore be eliminated.

Several familiar named patterns — especially Skyscraper, Two-String Kite, and certain Empty Rectangle structures — are recognizable geometric forms of this same short-chain logic.

Quick rule

For one candidate digit X:

find a Strong Link between candidates A and B;
connect B by a Weak Link to C;
connect C by a Strong Link to D;
the resulting chain is:

A =X= B -X- C =X= D

At least one of endpoints A or D must be true.

Therefore:

eliminate X from every outside cell that sees both A and D.

Why the Turbot Fish chain works

Read the chain from endpoint A.

If A is false:

Strong Link A = B forces B true;
Weak Link B - C forces C false;
Strong Link C = D forces D true.

So:

A false → D true

Read it from the other direction:

D false → A true

The endpoints cannot both be false.

At least one endpoint contains X.

A candidate T that sees both endpoints is therefore impossible:

if A is X, T cannot be X;
if D is X, T cannot be X.

T is eliminated in every valid case.

Step-by-step Turbot Fish example

Turbot Fish is an X-Chain of length four

This relationship is important because it removes much of the mystery from the name.

An X-Chain:

follows one candidate digit;
alternates Strong and Weak Links;
starts and ends Strong;
eliminates the digit from candidates that see both endpoints.

A Turbot Fish is simply the shortest useful version with four candidate nodes:

endpoint
  = strong =
node
  - weak -
node
  = strong =
endpoint

Longer chains continue as ordinary X-Chains.

So if you already understand X-Chain, Turbot Fish is not a new proof system. It is a compact, recognizable case.

What counts as a Strong Link in Turbot Fish?

For a single digit X, the most common Strong Link is a conjugate pair:

X has exactly two possible positions in one house.

If one position is false, the other must be true.

Those conjugate pairs can occur in:

a row;
a column;
a box.

The two Strong Links in a Turbot Fish do not need to use the same house type.

That flexibility is what creates several different-looking geometries.

What creates the middle Weak Link?

The middle candidates B and C must be unable to both contain X.

For ordinary candidate nodes, that means they see each other — they share a row, column, or box.

The link is weak because:

B true → C false
C true → B false

but both may be false.

Do not assume visual closeness creates a Weak Link. The two candidates must share a Sudoku house.

How Skyscraper fits the Turbot framework

A Skyscraper uses two conjugate-like pairs in parallel rows or columns.

One side of the two pairs aligns, while the two opposite candidates become the “roofs”.

Those roofs are the endpoints of the short single-digit chain.

Any target seeing both roofs can be eliminated.

The geometry is memorable enough that Skyscraper deserves its own Guide, but the underlying implication can be written as a Turbot/X-Chain.

How Two-String Kite fits the Turbot framework

A Two-String Kite connects:

one row Strong Link;
one column Strong Link;
through candidates that interact inside a box.

Again, the two outer endpoints cannot both be false.

The Kite name describes the recognizable geometry. Turbot Fish describes the short-chain family.

How Empty Rectangle relates to Turbot Fish

Some Empty Rectangle patterns can be expressed as Turbot Fish, particularly when the ER side behaves like a simple candidate node rather than a larger grouped node.

More general Empty Rectangles may be easier to describe using grouped links.

That is why the techniques overlap conceptually without being perfect synonyms.

The useful lesson is:

if a Skyscraper, Kite, or simple ER proof feels confusing as a picture, rewrite it as alternating Strong and Weak Links.

Turbot Fish vs Sudoku Fish

This naming collision causes frequent confusion.

Sudoku Fish family

X-Wing, Swordfish, Jellyfish, Finned Fish, Franken Fish, and Mutant Fish use base sets and cover sets.

Turbot Fish

Uses a four-candidate X-Chain.

The word “Fish” in Turbot Fish is historical terminology, not evidence that it uses the same general Fish-set proof.

If you want the X-Wing/Swordfish framework, use the Sudoku Fish Guide.

Turbot Fish vs X-Wing

Both focus on one digit, but their proofs differ.

X-Wing

Two base houses are covered by two cover houses, forcing the digit distribution and allowing cover eliminations.

Turbot Fish

Two Strong Links are connected by a Weak Link, forcing at least one outer endpoint true.

A candidate seeing both endpoints can be removed.

Some patterns can have alternative descriptions, but do not transfer the target rules from one framework to the other without proving them.

Turbot Fish vs X-Chain

Turbot Fish is a subset of X-Chain.

Every standard Turbot Fish can be written as a four-node X-Chain.

Not every X-Chain is a Turbot Fish because an X-Chain can contain more candidate nodes.

So the progression is:

recognizable Turbot patterns
→ four-node X-Chain
→ longer X-Chains
→ broader AIC logic

Turbot Fish vs Simple Coloring

Both use Strong-Link relationships for a single digit.

Simple Coloring usually builds a larger network of conjugate pairs and assigns two alternating colors.

Turbot Fish focuses on one short chain and one pair of endpoints.

If several conjugate pairs form a larger connected component, Coloring may be the more convenient representation.

If only two Strong Links connected by one Weak Link are needed, Turbot logic is often quicker.

How to find Turbot Fish

1. Choose a candidate digit

Scan one digit at a time.

2. Identify conjugate pairs

Look for rows, columns, or boxes where the digit has exactly two possible positions.

These are your natural Strong Links.

3. Look for a cross-connection

Try to connect one endpoint of one Strong Link to one endpoint of another through a shared house.

That is the Weak Link.

4. Identify the two unused endpoints

These become the outer endpoints of the chain.

5. Search for common peers

Any outside candidate for the same digit that sees both endpoints is a possible elimination target.

6. Verify the chain explicitly

Before deleting anything, trace:

false → true → false → true

from either endpoint.

7. Re-scan after progress

A single Turbot elimination may create a Hidden Single, Locked Candidate, or new conjugate pair.

Return to simpler logic first.

Recognizable Turbot shapes vs generic Turbot chains

Named shapes are useful because they speed up recognition.

Common short-chain geometries include:

Skyscraper;
Two-String Kite;
simple Empty Rectangle forms.

But the chain definition is broader than any one picture.

If four candidates satisfy the alternating Strong–Weak–Strong structure and the endpoints support a common-peer elimination, the logic works even if the shape does not look like your memorized example.

That is one reason learning the link proof is more durable than learning silhouettes.

Common Turbot Fish mistakes

Mistake 1: using a pair that is not Strong

A row containing three candidates for X does not give a conjugate pair between two of them.

Verify the house has exactly two legal positions for that digit.

Mistake 2: the middle nodes do not see each other

Without a valid Weak Link, the implication does not propagate.

Mistake 3: eliminating from a cell that sees only one endpoint

The target must be false whichever endpoint is true.

That requires seeing both endpoints.

Mistake 4: switching digits mid-chain

A Turbot Fish is a single-digit X-Chain. If the chain changes digits, you have moved into a different chain family.

Mistake 5: applying Fish-set eliminations because of the name

Do not use base/cover rules here. Turbot Fish is a chain.

Mistake 6: searching for Turbot after the pattern already has a simpler name

There is nothing wrong with solving a Skyscraper as a Skyscraper or a Kite as a Kite. Use the representation that lets you verify the move confidently.

FAQ

Is Turbot Fish actually a Fish technique?

Not in the X-Wing/Swordfish sense. It is normally defined as a four-candidate X-Chain.

How long is a Turbot Fish chain?

The standard Turbot Fish is four candidate nodes long, connected Strong–Weak–Strong.

Are Skyscraper and Two-String Kite Turbot Fish?

They can be represented as recognizable Turbot/X-Chain forms and are commonly grouped with this short single-digit logic.

Is Empty Rectangle a Turbot Fish?

Some simple Empty Rectangle structures can be represented as Turbot Fish. More general ERs may use grouped candidates, so the categories overlap without being identical.

What can a Turbot Fish eliminate?

The chain digit can be removed from any outside candidate that sees both outer endpoints of the chain.

Should I learn Turbot Fish before X-Chain?

It is a useful bridge. Named Turbot shapes make short chains easier to recognize, while X-Chain gives you the general rule for longer structures.

What to learn next

Compare the three common short single-digit geometries — Skyscraper, Two-String Kite, and Empty Rectangle — then continue to X-Chain to remove the four-node limit.