Turbot Fish

Turbot Fish is the shortest X-Chain — two strong links on a single digit joined by a weak link, where at least one of the two strong links lives inside a box. It's the third member of the "three short chains" trio alongside Skyscraper (two strong links in parallel rows/columns) and Two-String Kite (one row strong link + one column strong link).

Note: This technique uses chain colouring to display candidates. Square (▢) and Diamond (◇) shapes represent the two colour partitions.

The Pattern

A Turbot Fish on digit d is a four-cell chain:

A ══ B ── C ══ D

• A–B is a strong link on d (conjugate pair in row, column, or box)
• C–D is a strong link on d (conjugate pair in row, column, or box)
• B–C is a weak link — B and C share some unit and both hold d
• At least one of the two strong links must be inside a box (otherwise you're looking at a Skyscraper or Two-String Kite, not a Turbot Fish)

The endpoints A and D both carry d on strong links — one of them must be true.

The Elimination Rule

Any cell that shares a unit with both A and D can be eliminated on d:

• If A is d, then D isn't, and the candidate can take d only via D. But the candidate sees D, so it can't be d either.
• If D is d, the symmetric argument rules out any cell sharing a unit with A.

Either way, the candidate is eliminated.

How to Spot a Turbot Fish

1. Pick a single digit with a few conjugate pairs.
2. Find a conjugate pair inside a box — this is the "fish body".
3. Look for a second strong link (anywhere — row, column, or another box) connected to the first via a shared unit.
4. Check that the two non-shared endpoints both see a common cell — that cell is the elimination target.

Example

This puzzle reaches a Turbot Fish on digit 4 after the opening singles:

R3C4 ══ R3C2 ── R8C2 ══ R7C3

• R3C4 ══ R3C2 — strong link in row 3 (conjugate pair on digit 4)
• R3C2 ── R8C2 — weak link in column 2
• R8C2 ══ R7C3 — strong link in box 7 (conjugate pair on digit 4)

Endpoints R3C4 and R7C3 both carry digit 4. Any cell that sees both is eliminated.

puzzle: .1.8.3..6.....1...4...2..7.8..2.4...2...95......6..93.97...83.41.......9.83......
mode: free
technique: Turbot Fish
settings:
  showCandidates: true

Open the puzzle, enable hints, and run the v2 engine — the Turbot Fish step appears after the opening singles clear.

Relationship to the Short-Chain Trio

The "two strong links + one weak link on a single digit" pattern decomposes into three named variants depending on the unit types involved:

They're all the same logical move under the hood — the engine separates them so that the hint title matches what most solvers learn in the literature.

Tips

1. Box conjugate pairs are key — without a box-anchored strong link, you have a Skyscraper or Two-String Kite, not a Turbot Fish.
2. Look for digits with exactly two candidates in a box — that's your starting strong link.
3. The weak link is just a shared row, column, or other box — it links the two strong-link cells you're not eliminating against.
4. Both endpoints must "see" the target — verify the elimination cell shares a unit with both before deleting.

Related Techniques

• Skyscraper — Two-strong-link variant with parallel row/column links
• Two-String Kite — Two-strong-link variant with perpendicular row + column links
• X-Chain — Longer chains following the same alternating-link mechanism
• X-Cycles — Closed-loop version
• X-Wing — Two parallel strong links forming a rectangle