Franken Fish

What Does "Franken" Mean in Sudoku?

A Franken fish mixes different house types (rows, columns, and blocks) into a single fish pattern. Basic fish use only rows vs. columns. Franken fish add blocks to the base or cover sets, dramatically expanding the patterns available.

How Basic Fish Differ from Franken Fish

Basic fish: base houses all one type, cover houses the complementary type. Franken fish: base includes at least one block, with non-block houses all the same type. Cover is drawn from complementary types.

The Generalized Fish Principle

The pigeonhole principle: N base houses place N instances of a digit. If all candidates fall within N cover houses, extra candidates in cover houses outside base houses can be eliminated. Validity requires: every base cell must be covered, and every cover house must contain at least one base cell.

Franken X-Wing (N=2)

2 base houses (at least one block), 2 cover houses. Level 10 (Master). Significantly harder than basic X-Wing because mixed house types are less visually obvious.

Franken Swordfish (N=3) and Franken Jellyfish (N=4)

Franken Swordfish: 3 base, 3 cover. Level 10 (Master). Franken Jellyfish: 4 base, 4 cover. Level 11 (Extreme). One of the rarest techniques.

Why Franken Fish Are Hard to Find

The search space is vastly larger than basic fish. Base sets are drawn from all 27 houses. The intersection geometry of blocks with lines is hard to visualize. Rarely found by hand.

Relationship to Other Fish Variants

Basic Fish: rows vs. columns only. Level 4-9. Finned/Sashimi Fish: allow fins. Level 7-9. Franken Fish: allow blocks in base/cover. Level 10-11. Mutant Fish: allow any house combination. Most general but extremely rare.

Summary

Franken fish allow blocks in the base and cover sets, unlocking eliminations no basic fish can find. The pigeonhole logic is identical. The trade-off is complexity: Level 10-11, realistically found only with solver aid.