Turbot Fish
A Turbot Fish is a single-digit chain that spans just four cells. It links two strong links — pairs where a digit can go in only two places — with a single weak link in between. It is one of the most useful intermediate patterns because three techniques you may already know are all special cases of it: the skyscraper, the two-string kite and the empty rectangle.
The idea
Pick one digit — say 7. Find two units (rows, columns or boxes) where 7 is limited to exactly two cells each: those are your strong links. If one end of the first link can see one end of the second link, those two ends are joined by a weak link. The chain now alternates strong–weak–strong. The logic runs like this: if the first strong link's far end is not 7, then its near end is; that near end knocks out the weak-link partner; which forces the second strong link's far end to be 7. Either way, one of the two far ends is a 7. So any cell that can see both far ends cannot be 7 — remove it.
A worked example
Take the digit 7. Suppose column 1 has 7 only in rows 2 and 8, and column 5 has 7 only in rows 2 and 9 — two strong links. The near ends, r2c1 and r2c5, share row 2, so they form the weak link. The chain reads r8c1 = r2c1 − r2c5 = r9c5, and its free ends are r8c1 and r9c5: one of them must be 7. Any cell that sees both — r8c5 (row 8 and column 5) and r9c1 (column 1 and row 9) — therefore cannot be 7. Those two eliminations are exactly what a skyscraper would give, because a skyscraper is a Turbot Fish.
Two strong links on 7 (solid) joined by a weak link (dashed). One free end must be 7, so the red cells — seeing both ends — lose their 7.
Step by step
- Choose a digit and mark every cell where it is still a candidate.
- Find two strong links — units where the digit sits in only two cells.
- Join them with a weak link — one end of each link must see the other.
- Eliminate the digit from any cell that sees both free ends of the chain.
Common mistakes
- Weak where you need strong. The two outer links must be strong (exactly two spots); only the middle link is weak.
- Eliminating on the wrong cell. The removal happens where a cell sees both free ends, not the ends themselves.
- Forgetting boxes count. A strong link can live in a box, not just a row or column — that is what makes the empty rectangle a Turbot Fish.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.