Mutant Fish

A Mutant Fish is the most general fish of all. Where a Franken Fish lets a box join a base or cover set of rows and columns, a Mutant Fish lets both sets mix rows, columns and boxes in any combination at once. It is the outer limit of fish logic — powerful, rare, and worth understanding as the family's grand unification.

The idea

The engine is unchanged from the humble X-Wing. Pick base units in which a digit is confined, and cover units that catch all of those candidates, with the two sets the same size. Any cover cell that is not also a base cell can lose the digit. What makes a fish "mutant" is only the freedom of the units: a base might be a row, a column and a box together, and the cover another mix entirely. That flexibility catches eliminations no straighter fish can express, at the cost of being much harder to spot.

A worked example

Imagine the digit 6 confined, across a row, a column and a box, to a set of cells that a different row, column and box between them fully cover. The first trio is the base, the second the cover; both hold the same number of units. Every 6 in a cover unit that lies outside the base can be struck. Because the units cross in three directions, the cells cleared may sit far from any single line of the base — the signature reach of a mutant fish.

Step by step

1. Choose a digit and chart all its remaining candidates.
2. Assemble base units — any mix of rows, columns and boxes confining the digit.
3. Assemble equal cover units that catch every base candidate.
4. Eliminate the digit from cover cells outside the base.

Common mistakes

• Overlap errors. Cells shared between mixed units are easy to miscount; a single slip invalidates the fish.
• Unequal sets. Base and cover must match in size — the whole argument depends on it.
• Using it too soon. Almost every mutant fish has a simpler equivalent; treat it as a last resort, not a first look.

Which Sudoku types is this best for?

The same logic applies across variants, but it pays off more in some than others.