Kraken Fish
A Kraken Fish is what you reach for when a fish almost works. An ordinary finned fish restricts its eliminations to cells near the fin; a Kraken Fish goes further, running a chain from each troublesome candidate to prove a common elimination the fish alone cannot reach.
The idea
Start from a fish whose base candidates are not all cleanly covered — there is an extra candidate, as with a finned fish. Instead of accepting the fin's narrow eliminations, pick a target cell and show that every possibility forces that target to lose a digit. The fish's clean part handles most cases; for each leftover candidate, you build a chain leading to the same conclusion at the target. If the fish and all the chains agree, the target candidate is impossible. In effect the Kraken Fish is a forcing argument that borrows the fish for most of its branches and chains for the rest.
A worked example
Following the digit 3, a near X-Wing on rows 2 and 8 across columns 3 and 7 covers all but one stray 3 — the would-be fin at r8c5. Choose a target cell that the clean X-Wing already threatens, say r5c3. In the ordinary case (the fin is not the 3) the X-Wing removes 3 from r5c3. For the other case, you must chain on 3 from the fin r8c5 and show it, too, forbids 3 at r5c3. If both routes reach the same place, the target's 3 is eliminated even though no plain fish or single chain could prove it alone.
A near X-Wing on 3 (blue, rows 2/8 × columns 3/7) with a stray fin at r8c5 (orange). The clean X-Wing already removes 3 from the target r5c3; for the fin case a chain on 3 (purple, schematic) must reach the same square. When both branches agree, r5c3 loses its 3.
Step by step
- Find a near-fish — a fish spoiled by one or more extra candidates.
- Pick a target the clean part of the fish would eliminate.
- Chain from each stray candidate to the same elimination at the target.
- Eliminate only if the fish and every chain agree.
Common mistakes
- Missing a branch. Every uncovered candidate must lead to the target; skip one and the proof is incomplete.
- Chains that wander. Each branch must genuinely reach the same target elimination, not merely a related one.
- Reaching too soon. Kraken logic is intricate — exhaust ordinary fish, chains and ALS moves first.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.