Turbot Fish

The Turbot Fish is a generalized pattern that unifies several techniques you may already know. It's built from two strong links connected by a weak link, forming a chain that forces eliminations.

What is a Turbot Fish?

A Turbot Fish occurs when:

• You have two strong links for the same candidate
• These strong links are connected by a weak link
• The endpoints that aren't connected can eliminate candidates they both see

Strong link: A unit (row, column, or box) where the candidate appears in exactly 2 cells. If one cell doesn't have the digit, the other MUST.

Weak link: Two cells that see each other. If one has the digit, the other CANNOT.

Understanding Links

Strong Links

In a strong link, one cell must be true:

Row 5: [only 2 cells have candidate 7]

    Cell A ══════ Cell B
           strong

If A ≠ 7, then B = 7
If B ≠ 7, then A = 7

Sources of strong links:

• Row with exactly 2 candidates
• Column with exactly 2 candidates
• Box with exactly 2 candidates

Weak Links

In a weak link, at least one cell must be false:

Cell A ─────── Cell B
        weak

If A = 7, then B ≠ 7
(But if A ≠ 7, B could be anything)

Sources of weak links:

• Any two cells in the same row
• Any two cells in the same column
• Any two cells in the same box

The Turbot Fish Structure

    A ════════ B        Strong link 1
               │
               │ weak link
               │
    D ════════ C        Strong link 2

Cells A-B form a strong link. Cells C-D form a strong link. Cells B-C share a unit (weak link).

The Logic

Follow the chain:

1. If A = true: Then B = false (strong link)
2. If B = false: C might or might not be true (weak link alone doesn't force)

Let's try the other direction:

1. If A = false: Then B = true (strong link)
2. If B = true: Then C = false (weak link, they see each other)
3. If C = false: Then D = true (strong link)

Key insight:

• Either A is true
• Or D is true
• (Or both could be true in some configurations)

Elimination: Any cell that sees BOTH A and D will always see a true cell. Eliminate the candidate from such cells.

The Four Turbot Fish Types

Depending on what creates each link, we get different patterns:

Type 1: Skyscraper

• Strong link 1: Row
• Strong link 2: Row
• Weak link: Column (same column)

This is exactly the Skyscraper pattern!

Type 2: 2-String Kite

• Strong link 1: Row
• Strong link 2: Column
• Weak link: Box (same box)

This is exactly the 2-String Kite pattern!

Type 3: Turbot Fish (Box/Line)

• Strong link 1: Box
• Strong link 2: Row or Column
• Weak link: Row or Column

Uses a box-based strong link.

Type 4: Turbot Fish (Box/Box)

• Strong link 1: Box
• Strong link 2: Box
• Weak link: Row or Column

Both strong links come from boxes.

Worked Example

Consider digit 6:

Strong link 1 (Row 2):

• R2C3 and R2C7 are the only cells with 6 in row 2

Strong link 2 (Box 9):

• R8C8 and R9C7 are the only cells with 6 in box 9

Weak link:

• R2C7 and R9C7 are in the same column 7

The chain:

R2C3 ══════ R2C7
              │
              │ (column 7)
              │
R8C8 ══════ R9C7
     (box 9)

Logic:

• Either R2C3 = 6
• Or R8C8 = 6

Elimination: Cells that see both R2C3 and R8C8:

• R2C8: same row as R2C3, same column as R8C8
• R8C3: same column as R2C3, same row as R8C8

Eliminate 6 from these cells if present.

How to Find Turbot Fish

Method 1: Start with Strong Links

1. For a candidate, list all strong links:

   • Rows with exactly 2 cells
   • Columns with exactly 2 cells
   • Boxes with exactly 2 cells

2. For each pair of strong links:

   • Check if one endpoint of each shares a unit
   • If yes, you have a potential Turbot Fish

3. Verify and find eliminations from the other endpoints.

Method 2: Chain Building

1. Start at any cell in a strong link (call it A)
2. Note the other cell in that link (B)
3. Look for cells that B sees (weak links)
4. If any of those cells (C) is in another strong link (to D)
5. You've found A ═ B ─ C ═ D

Method 3: Pattern Recognition

With practice, certain configurations become visually recognizable:

• Two "parallel" strong links with a perpendicular connection
• A cell that bridges two independent strong links

Turbot Fish vs. Specialized Patterns

The Turbot Fish framework explains why other patterns work:

Understanding Turbot Fish means you understand them all!

Extended Turbot Fish

The concept extends to longer chains:

A ═══ B ─── C ═══ D ─── E ═══ F

If the chain has an ODD number of strong links:

• A and F act like Turbot Fish endpoints
• Cells seeing both can have the candidate eliminated

This leads into more advanced chain techniques.

Practice Exercise

Find the Turbot Fish and elimination:

Digit 3:

• Box 1 (top-left): 3 only in R1C1 and R3C2
• Column 2: 3 only in R3C2 and R7C2
• Box 7 (bottom-left): 3 only in R7C2 and R9C1

Common Mistakes

Mistake 1: Confusing strong and weak links

• Strong: exactly 2 candidates in a unit (one MUST be true)
• Weak: just sharing a unit (one at most can be true)

Mistake 2: Wrong chain direction

The logic only works with alternating strong-weak-strong. Weak-strong-weak doesn't force eliminations.

Mistake 3: Missing strong links in boxes

Don't forget to check boxes! Many Turbot Fish use box-based strong links.

Mistake 4: Incomplete elimination search

Both endpoints can eliminate. Check all cells seeing both.

Quick Reference

Turbot Fish structure:

• 2 strong links
• Connected by 1 weak link
• 4 cells total, 2 endpoints

Elimination rule:

• Endpoints: cells NOT at the weak link connection
• Eliminate from cells that see BOTH endpoints

Finding it:

1. Find all strong links for a digit
2. Look for pairs connected by a weak link
3. Identify endpoints and find elimination targets

Pattern variations:

• Row-Row connection: Skyscraper
• Row-Column via box: 2-String Kite
• Box involved: Turbot Fish proper

When to look:

• After simpler patterns fail
• Digits with few remaining placements
• Strong links are visible in different units