Turbot Fish
A Turbot Fish is a single-digit forcing chain built from two strong links connected by a weak link. A strong link is a digit confined to exactly two cells in a house. The two strong links share a common cell or are joined by a weak link — a digit appearing in multiple cells where only one can be true. The chain runs from one end of the first strong link, through the connector, to the opposite end of the second strong link. Any candidate outside the chain that sees both ends can be eliminated, because one end must be true and the other false.
What is a Turbot Fish?
A Turbot Fish is a single-digit forcing chain that uses exactly two strong links joined by a weak link. A strong link exists when a digit can only go in two cells within a house (row, column, or box) — one of them must be true. A weak link exists when a digit appears in multiple cells in a house, but at most one can be true. The pattern works as follows: pick a digit, find two strong links on that digit in different houses, and check if they are connected — either by sharing a common cell, or by a weak link (the digit appears in both houses but not in the shared cell). The chain starts at one end of the first strong link, passes through the connector, and arrives at the opposite end of the second strong link. Because the first strong link guarantees one of its two cells is true, and the second strong link guarantees one of its two cells is true, the chain forces a specific polarity: if the starting cell is true, the ending cell must be false, and vice versa. Any cell outside the chain that sees both the start and end cells for the same digit cannot hold that digit — if it did, it would force both to be false, breaking both strong links. The Turbot Fish is the simplest non-looping single-digit chain, and it is closely related to the Skyscraper and 2-String Kite, which are specific configurations of the same underlying pattern.
How to spot it
To find a Turbot Fish, start by picking a digit and scanning for strong links — houses where that digit is confined to exactly two cells. You need two strong links in different houses (they can be in different house types: one in a row, one in a column, or one in a box, etc.). Check if the two strong links are connected: either they share a common cell, or the digit has a weak link between them (the digit appears in both houses but not in the shared cell). If the two strong links are connected, trace the chain from one end of the first link through the connector to the far end of the second link. Then look for any cell outside the chain that can see both the start and end cells — if such a cell has the target digit as a candidate, that candidate can be eliminated. The Skyscraper is a special case where both strong links are in parallel rows or columns; the 2-String Kite is a special case where one strong link is in a row and the other in a column, connected through a box. The general Turbot Fish covers all other configurations.
The logic
The Turbot Fish relies on the forcing chain created by two strong links and a connector. A strong link on digit X in a house means exactly one of two cells contains X — if one is true, the other is false. The chain starts at cell A (one end of the first strong link), passes through the connector to cell B (the far end of the second strong link). If A is true, the connector propagates the chain and forces B to be false. If A is false, the first strong link forces the other cell in that link to be true, which propagates through the connector and forces B to be true. So regardless of whether A is true or false, B has the opposite polarity. Any cell outside the chain that sees both A and B for the same digit faces a contradiction: if it contained the digit, both A and B would be false, but the strong links guarantee one of each pair must be true. Therefore that candidate can be eliminated. The logic is identical to the Skyscraper and 2-String Kite — the Turbot Fish is simply the general case that does not fit either named pattern.