Fish & Wings
Turbot Fish
A Turbot Fish removes one digit using two strong links — rows, columns or boxes where the digit has exactly two places — joined by two of their ends that see each other. Those two ends cannot both hold the digit, so at least one of the two free ends must, and any cell that sees both free ends loses it. Skyscraper and 2-String Kite are its best-known shapes; the general form also uses boxes.
What you need to see on the grid
Reach for a Turbot Fish when a digit has strong links but no Skyscraper or kite: the app tries those two shapes first, then the general one. Four terms carry the method:
- Strong link
- A row, column or box where the digit has exactly two places: one of them must hold it. A box counts just like a line.
- Weak link
- Two cells that see each other — same row, column or box — and both list the digit. At most one of them holds it.
- Free ends
- The end of each strong link that is not part of the weak link. Strong – weak – strong means at least one of them holds the digit.
- Skyscraper and kite
- Two parallel lines joined across is a Skyscraper; a row and a column joined in a box is a 2-String Kite. Everything else — here, a row and a box — is the general Turbot Fish.
How to apply it, step by step
One example runs through all four steps: the digit 1, in a hard puzzle from the app, at the exact point where its hint needs a Turbot Fish. Every diagram shows the whole grid. The cells a step needs are filled in; the others are left blank and hatched, so you know you can ignore them. A digit missing from a drawn cell is already placed in its row, column or box, drawn or not.
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Step 1Find two rows, columns or boxes where the digit has two places
Pick a digit and look for its strong links: units where it has exactly two places. Boxes count as well as rows and columns.
For 1, row 9 leaves only R9C5 and R9C9, and box 2 only R1C5 and R3C4. One cell of each pair holds the 1.
Row 9 and box 2. 1 has two places in each: R9C5 and R9C9, R1C5 and R3C4. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 9 R2 R3 4 5 R4 R5 R6 R7 R8 R9 6 9 5 4 3 - Digit already on the grid
- Unit where 1 has exactly two places
- A place for 1 in a link
- Candidate 1, the digit studied
- Not needed for this step
Filled in: row 9; box 2. The other 63 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 2Join them through two ends that see each other
Look for one end of the first link that sees one end of the second. R9C5 and R1C5 are both in column 5, so they cannot both be 1: that is the weak link between the two strong ones.
The chain now reads strong, weak, strong: R9C9 – R9C5 in row 9, R9C5 – R1C5 in column 5, R1C5 – R3C4 in box 2. Its two outer cells, R9C9 and R3C4, are the free ends. Column 5 has other 1s; they do not matter, because the weak link only says "not both".
Column 5 joins the links: R9C5 and R1C5 see each other. Numbered in order: free end R9C9, R9C5, R1C5, free end R3C4. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 9 R2 R3 4 5 R4 9 R5 R6 5 R7 R8 R9 6 9 5 4 3 - Digit already on the grid
- Unit where 1 has exactly two places
- A place for 1 in a link
- Chain cell, numbered in order
- Candidate 1, the digit studied
- Not needed for this step
Filled in: row 9; column 5; box 2. The other 58 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 3Remove the digit from every cell that sees both free ends
If R9C5 is not 1, row 9 puts the 1 on R9C9; if R1C5 is not 1, box 2 puts it on R3C4. The weak link guarantees that one of R9C5 and R1C5 is not 1 — so at least one free end is.
R3C9 shares row 3 with R3C4 and column 9 with R9C9: it sees both free ends and loses 1. The only other cell seeing both, R9C4, already holds 5.
Technique: Turbot Fish
The two links and R3C9, which sees the free ends R3C4 (row 3) and R9C9 (column 9). 1 leaves R3C9. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 9 R2 R3 4 5 R4 R5 R6 R7 R8 R9 6 9 5 4 3 - Digit already on the grid
- Unit where 1 has exactly two places
- A place for 1 in a link
- Chain cell, numbered in order
- Candidate 1, the digit studied
- Candidate removed
- Not needed for this step
Filled in: row 9; box 2; cell R3C9. The other 62 cells are left blank: they are not needed for this step. Removed: 1 from R3C9.
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Step 4Collect what the elimination unlocks
A Turbot Fish never places a digit by itself, so look at the cell it just cleared. R3C9 had two candidates, 1 and 2. With 1 gone, only 2 is left: a Naked Single, and the app's next hint in this puzzle.
Technique: Naked Single
Row 3 after the Turbot Fish. R3C9 has only 2 left. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 R3 9 7 6 4 5 3 2 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- The cell that must be 2
- Candidate 2, the digit studied
- Digit placed
- Not needed for this step
Filled in: row 3. The other 72 cells are left blank: they are not needed for this step. Placed: R3C9 = 2.
Common mistakes
Mixing up the middle link and the outer links
The middle link only has to say "not both": any two cells that see each other will do, however many other places the digit has in that unit. What must have exactly two places are the two outer links. Mixing the roles up is the usual way to clear a cell wrongly.
Forgetting that boxes make links too
Players who scan only rows and columns never see this example: its second link is box 2. When a digit has two places in a box, that box is a strong link just like a line.
Clearing cells that see only one free end
The chain proves that one free end holds the digit, never which one. A cell such as R3C8 sees R3C4 but not R9C9; if R9C9 is the 1, nothing stops R3C8 from being 1 too.
Recent daily puzzles that needed this technique
Keep going
- SkyscraperTwo two-place columns that share a base row: one roof holds the digit, so cells seeing both roofs lose it.
- 2-String KiteA two-place row and a two-place column meeting in one box: the cell where their far ends cross loses the digit.
Learn the move, not just the digit
In a real game, when a Turbot Fish is what opens the next cell, the hint in the app names it and shows the cell it unlocks — the same move as step 4 above.