Proven Sudoku

Techniques / Complex fish

Complex fish: finned, sashimi, franken and mutant

Fish that almost work, plus a precise account of the exceptions.

8 techniques in this family, introduced at tier 9. How to read a sudoku grid explains the notation used below.

What these have in common

Every member is a basic fish with something wrong with it, and a rule for salvaging the eliminations that survive the defect.

Why the logic holds

A fish needs the digit's spots in the base sets to sit wholly inside the cover sets. When a few spare candidates spoil that, they are called fins. The fish argument still holds everywhere except where a fin could be true. So the moves that survive are the ones that also see every fin. Franken and Mutant fish bend a different rule. They let boxes act as base or cover sets, not just rows and columns.

When to reach for it

Realistically, when a solver is doing the searching. A finned X-Wing is findable by hand and worth knowing. A Mutant Jellyfish is not something people spot at a kitchen table.

How the members differ

Finned fish carry spare candidates in a base set. Sashimi fish are finned fish where cutting the fin would leave a corner bare, so the shape is broken but the move still works. Endo-fins sit where two base sets overlap. Franken fish mix lines and boxes. Mutant fish mix them freely in both roles. Kraken fish hang a chain off the fin. Cannibalism is the odd case where a candidate sits in a base set and a cover set at once, and ends up cutting itself.

The mistake to avoid

Dropping the fin rule on even one move. A move taken from a finned shape as though it were clean is simply wrong. And because the rest of the shape is sound, it can ride a long way into a solve before anything contradicts it.

Start with Finned Fish. A fish pattern with one extra square hanging off it.

Every technique in this family