Turbot Fish

Turbot Fish is a retired umbrella name for short single-digit chains. Its shapes are now classified as X-Chains — two-link forms appear as Skyscraper, 2-String Kite or Two-Node X-Chain, and longer ones as Three-Node or Four+ Node X-Chains. The construction is an open single-digit AIC: if the first endpoint is false, the chain forces the far endpoint true, so at least one endpoint is true — possibly both — and the digit can be removed from a candidate that sees both endpoints.

What is a Turbot Fish?

Write the construction as (A=B)-(C=D): A=B and C=D are strong links (XOR node pairs), while B-C is a weak inference (NAND), meaning B and C cannot both be true. It follows that A or D is true. It does not follow that A and D always have opposite truth values.

Where it lives now: the two-link shapes are the Skyscraper, 2-String Kite, Empty Rectangle and Two-Node X-Chain; longer same-digit chains are covered by the X-Chain page.

How to spot it

For one digit, find two justified strong-inference nodes and a valid weak inference between one side of each. Sharing a geometric point is not enough unless the candidate propositions are distinct and incompatible. The unconnected sides are the elimination endpoints; a target must see both.

The logic

If A is false, B is true; because B and C cannot both be true, C is false; therefore D is true. Thus A or D is true. A target that sees both endpoints would make both false if it contained the digit, contradicting the chain, so the target candidate can be removed. This is the Type 1 same-digit elimination.