Franken Fish
A Franken Fish stretches the ordinary fish by letting a box stand in for a row or column. A plain swordfish or X-Wing builds its base and cover sets only from rows and columns. A Franken Fish allows at least one box among them, and that small change reaches eliminations the classic fish cannot.
The idea
Every fish rests on the same balance: choose a set of base units in which a digit lives, and a set of cover units that catch all those candidates. If the cover units account for every base candidate, the digit can be removed from any cover cell that is not also a base cell. In a Franken Fish one of those units — base or cover — is a 3×3 box. Because a box overlaps three rows and three columns at once, it can bridge candidates that no straight line would connect, opening eliminations elsewhere in the covering units.
A worked example
Take the digit 4. In box 1 it appears only in column 2 — at r1c2 and r2c2. In row 6 it appears at r6c2 and r6c8. Make box 1 and row 6 the two base units; columns 2 and 8 are the cover, and together they catch every one of those 4s. Base and cover both have size two, so the fish balances — each base unit must place one true 4, and both land inside the cover columns. Now any 4 sitting in column 2 or column 8 but outside box 1 and row 6 must go: for example r8c2. The box acting as a base unit is exactly what a row-and-column fish could not express.
Base units: box 1 (green) whose 4s sit in column 2, and row 6 (4s at r6c2, r6c8). Cover: columns 2 and 8. Balanced 2×2, so r8c2 — a cover cell outside both base units — loses its 4.
Step by step
- Pick a digit and map every cell where it still lives.
- Build base and cover sets, allowing a box in place of a line.
- Check the balance — the cover units must catch all base candidates.
- Eliminate the digit from cover cells that are not base cells.
Common mistakes
- Double-counting a cell. A cell where a base line and the base box overlap must be counted once — mismatched counts break the fish.
- Forgetting the balance. Base and cover must have equal size; an unbalanced set proves nothing.
- Skipping simpler tools. Franken fish are advanced — reach for chains, ordinary fish 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.