Turbot Fish

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A Turbot Fish is a two-strong-link chain, a type of AIC (alternating inference chain). One strong link comes from a conjugate pair in a box, while the other comes from a conjugate pair in a row or column. The two strong links have no particularly obvious geometric relationship.

How to spot it

• For each candidate x from 1 to 9, examine its conjugate-pair strong links.
• Find one conjugate pair in a box and another in a row (or column).
• If one cell from each conjugate pair lies in the same column (or row), candidate x can be eliminated from any cell that sees both of the other two cells.

How it works

• Let the two conjugate-pair strong links for candidate x be [A]━[B] and [C]━[D]. If B and C share a row (or column), they see each other and form the weak link [B]┉[C], producing the two-strong-link chain [A]━[B]┉[C]━[D]. By the rules of an AIC, the end nodes A and D also have a strong relationship: at least one of them must be true.
• If A does not contain x, then B must contain x. This prevents C from containing x, which in turn forces D to contain x. The same reasoning works in reverse: if D does not contain x, then A must contain x.
• Therefore, candidate x can be eliminated from any cell that sees both A and D.

Examples

On the board above, candidate 3 forms one conjugate pair in row R3 and another in box 7. It occurs only in R3C2 and R3C9 within the row, and only in R8C3 and R9C2 within the box, producing two strong links. Cells R3C2 and R9C2 share a column and form a weak link, giving a two-strong-link chain with end nodes [R3C9:3] and [R8C3:3]. At least one end node must be true, so candidate 3 can be eliminated from R8C9, which sees both end nodes.

The characteristic feature of a Turbot Fish is the conjugate pair clustered inside a box, resembling the two close-set eyes of a turbot, a type of flatfish.

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Here are some other forms of the Turbot Fish.