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.

Great fit Classic Sudoku A staple single-digit chain on hard Classic grids, unifying skyscrapers, kites and empty rectangles. → Works Killer Sudoku Works once candidates settle, though cage logic usually resolves Killer sooner. → Works Sudoku X The diagonals add strong links, giving the chain extra ways to form. → Limited Samurai Sudoku Single-grid chains matter less than juggling the five overlapping grids. →

Where to practise this

This technique starts paying off at Expert, which is where puzzles first stop yielding to anything simpler. Reading about a pattern and spotting it on a live grid are different skills - the second one only comes from playing.

Play Expert Sudoku About Expert Sudoku

Related techniques

Skyscraper Sudoku Technique Explained Two rows where a digit sits in only two cells, sharing one column; the digit is cleared from cells that see both far ends. X-Cycles - Single-Digit Loop Sudoku Technique A loop of alternating strong and weak links on one digit; continuous loops eliminate around the ring, a broken loop forces the digit at the discontinuity. X-Wing Sudoku Technique Explained One digit confined to the same two columns across two rows (or vice versa) - eliminate it from the rest of those lines. XY-Wing Sudoku Technique (Y-Wing) Explained A pivot cell with two candidates links two pincer cells; the digit they share is removed from any cell both pincers see.