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.

3 3 3 3 3 ✗3

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

  1. Find a near-fish — a fish spoiled by one or more extra candidates.
  2. Pick a target the clean part of the fish would eliminate.
  3. Chain from each stray candidate to the same elimination at the target.
  4. 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.