Platon Sudoku · Sudoku Study

Turbot Fish · Step-by-step example

Two strong links for one digit connect through a weak link; the shape may resemble a skyscraper, a kite, or an empty rectangle. Remove the digit from any candidate that sees both outer endpoints.

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Recognize the pattern

Two strong links for one digit connect through a weak link; the shape may resemble a skyscraper, a kite, or an empty rectangle.

How to find it

Trace two strong links and their weak connection. Identify the two outer endpoints before looking for a shared target.

What it allows

Remove the digit from any candidate that sees both outer endpoints.

Avoid the mix-up

Two highlighted pairs are not enough without a valid weak connection. A candidate seeing only one outer end cannot be removed.

Step-by-step example · Skyscraper

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · See the shared four-candidate chain

Turbot Fish is the umbrella name for a four-candidate X-Chain. Skyscraper, Two-String Kite, and a two-candidate Empty Rectangle are named layouts of this same chain. Follow the four circles for 3.

Step 2 · Two places in row 3

In row 3, 3 can only go in R3C1 or R3C5. One of them must be 3.

Step 3 · Two places in row 8

In row 8, 3 can only go in R8C2 or R8C5. One of them must be 3.

Step 4 · Connect the two strong links

R3C5 and R8C5 see each other in column 5. They form the weak link: they cannot both be 3. This layout is Skyscraper; here we are viewing its shared Turbot Fish chain.

Step 5 · Try an assumption

What if R7C1 were 3? Numbers marked ? are part of this assumption, not confirmed answers. R3C1 shares column 1 with R7C1, so it cannot also be 3. R8C2 shares box 7 with R7C1, so it cannot also be 3.

Step 6 · Two identical digits in one region

R3C1 cannot be 3, so row 3 has only R3C5 left. Under this assumption, it must be 3. R8C2 cannot be 3, so row 8 forces R8C5 to be 3. But R3C5 and R8C5 share column 5: that would put 3 there twice!

Step 7 · The assumption cannot be right

For each target, assuming 3 repeats that digit in column 5. Remove candidate 3 from R7C1; all temporary assumptions are withdrawn.

What it allows

For each target, assuming 3 repeats that digit in column 5. Remove candidate 3 from R7C1; all temporary assumptions are withdrawn.

Turbot Fish · Remove the digit from any candidate that sees both outer endpoints.

Step-by-step example · Two-string kite

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · See the shared four-candidate chain

Turbot Fish is the umbrella name for a four-candidate X-Chain. Skyscraper, Two-String Kite, and a two-candidate Empty Rectangle are named layouts of this same chain. Follow the four circles for 4.

Step 2 · Two places in row 1

In row 1, 4 can only go in R1C5 or R1C2. One of them must be 4.

Step 3 · Two places in column 3

In column 3, 4 can only go in R4C3 or R2C3. One of them must be 4.

Step 4 · Connect the two strong links

R1C2 and R2C3 see each other in box 1. They form the weak link: they cannot both be 4. This layout is Two-String Kite; here we are viewing its shared Turbot Fish chain.

Step 5 · Try an assumption

What if R4C5 were 4? Numbers marked ? are part of this assumption, not confirmed answers. R1C5 shares column 5 with R4C5, so it cannot also be 4. R4C3 shares row 4 with R4C5, so it cannot also be 4.

Step 6 · Two identical digits in one region

R1C5 cannot be 4, so row 1 has only R1C2 left. Under this assumption, it must be 4. R4C3 cannot be 4, so column 3 forces R2C3 to be 4. But R1C2 and R2C3 share box 1: that would put 4 there twice!

Step 7 · The assumption cannot be right

For each target, assuming 4 repeats that digit in box 1. Remove candidate 4 from R4C5; all temporary assumptions are withdrawn.

What it allows

For each target, assuming 4 repeats that digit in box 1. Remove candidate 4 from R4C5; all temporary assumptions are withdrawn.

Step-by-step example · Empty rectangle

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · See the shared four-candidate chain

Turbot Fish is the umbrella name for a four-candidate X-Chain. Skyscraper, Two-String Kite, and a two-candidate Empty Rectangle are named layouts of this same chain. Follow the four circles for 1.

Step 2 · Two places in box 3

In box 3, 1 can only go in R3C7 or R1C8. One of them must be 1.

Step 3 · Two places in column 4

In column 4, 1 can only go in R9C4 or R1C4. One of them must be 1.

Step 4 · Connect the two strong links

R1C8 and R1C4 see each other in row 1. They form the weak link: they cannot both be 1. This layout is Empty Rectangle; here we are viewing its shared Turbot Fish chain.

Step 5 · Try an assumption

What if R9C7 were 1? Numbers marked ? are part of this assumption, not confirmed answers. R3C7 shares column 7 with R9C7, so it cannot also be 1. R9C4 shares row 9 with R9C7, so it cannot also be 1.

Step 6 · Two identical digits in one region

R3C7 cannot be 1, so box 3 has only R1C8 left. Under this assumption, it must be 1. R9C4 cannot be 1, so column 4 forces R1C4 to be 1. But R1C8 and R1C4 share row 1: that would put 1 there twice!