Proven Sudoku
Complex Fish (rank framework)
Also called Generalized fish, Franken and Mutant fish.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
The fish idea, but boxes are allowed to join the rows and columns. That covers a family of patterns with names like Franken and Mutant. The counting rule stays the same, only the shapes get stranger.
The exact rule, for stronger players
The rule, stated exactly: Generalize the fish by allowing base and cover sets to be any houses, not only lines of one orientation, and by allowing base candidates outside the covers (fins). Rank is the number of cover sets minus base sets. At rank zero with no fins, all non-base cover cells are eliminated; with fins, eliminations are restricted to cells that also see every fin.
What it removes: Remove d from cover cells outside the base sets that also see every fin. With no fins, the fin condition is vacuous.
Why it works: The counting argument is unchanged: n base sets place n copies of d, and if the covers can absorb only n, they are saturated. A fin is a base candidate escaping the covers, so the conclusion holds only when the fin is false, which restricts eliminations to cells that see the fin.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
- Basic Fish (base and cover formulation)Pick some rows where a digit has only a few spots left.
- Locked Candidates (general form)Sometimes all the spots for a digit inside one group also sit inside a second group.
Related complex fish
- Endo-FinA spare square that sits inside two parts of the pattern at the same time.
- Finned FishA fish pattern with one extra square hanging off it.
- Franken FishA fish where a box is allowed to join in with the rows and columns.
- Kraken FishA fish that does not quite work.
- Mutant FishA fish where rows, columns and boxes can be mixed freely on both sides.
How often does it come up?
Our rough estimate: umbrella page for Tier 9. Finned and Sashimi variants are reasonably common; Franken and Mutant are rare outside hard puzzle collections.