Franken and Mutant Jellyfish
Short answer: a Jellyfish counts four lines against four lines. Drop the rule that they have to be lines: let a 3×3 box stand in on either side, and the count still works. Four units that share no copy of the shape hold four copies between them, so four units that cover all of those candidates hold one each — and the shape leaves every other cell of the covering units.
What a Franken Jellyfish looks like
Every fish is one piece of arithmetic. Four units each need the shape once; no two of them can share a copy; so between them they hold exactly four copies. If four other units contain every candidate those four units have, each of the four must spend its single copy on one of them — and no candidate elsewhere in them can survive. Nothing in that argument says "row" or "column". A Franken fish puts a box on one side or the other; a Mutant fish goes further and mixes rows with columns inside the same side.
The base sets here are two rows and two columns at once, which a plain fish never allows — that is the Mutant half. The cover sets are one row and three boxes, which is the Franken half. Both appear in one position more often than either name suggests, because a box is simply another unit that holds one of each shape.
How to use a Franken or Mutant Jellyfish
- Start where a plain fish failed. Pick a shape with roughly eight to fourteen homes left. Run the ordinary row-and-column search first: if a plain or finned Jellyfish is there, take it. This is what you reach for when that search comes up empty and the shape still looks over-constrained.
- Pick four base units that share nothing. Any four units — rows, columns or boxes — with two or more homes for the shape each, and with no single cell holding the shape in two of them. Four rows are disjoint automatically; a row and a box that overlap are only disjoint if the shape cannot go in the cells they share. Check it, because the whole count depends on it.
- Cover every candidate with four more units. List every cell in the base that can still hold the shape, and try to blanket them with four other units. Boxes are usually what makes it fit: a base line spilling across two boxes is often covered by those two boxes when no column will do it.
- Strike the cover, not the base. Remove the shape from every cell of the four covering units that is not inside one of the four base units. Cells in both are pattern cells and stay. If the cover contains a unit with no base candidate in it at all, the pattern is wrong — throw it out and re-cover.
The same generalisation applies at every size: a Franken X-Wing is two units against two, a Franken Swordfish three against three. Four is where it earns its keep, because that is where the row-and-column version has usually already failed. If the base almost fits but one stray cell spoils it, and that cell sits in a single box, you are looking at the finned version of the same idea — the finned Jellyfish page has the argument in its simplest form.
Franken and Mutant vs a plain Jellyfish
A plain Jellyfish is easier to find and easier to trust: four rows, four columns, and the geometry does the bookkeeping for you. The moment boxes join in you lose that safety net, and the two mistakes that follow are always the same — base units that quietly share a candidate, and a cover unit that contains no base candidate at all. Both make the elimination invalid rather than merely useless. Check those two things every time, and prefer the plain fish whenever one exists: it strikes the same marks with a quarter of the work.
Find Franken and Mutant Jellyfish in your own grid
Paste a puzzle and this page will look for Franken and Mutant Jellyfish in it — the same pattern shown above, in your grid instead of ours. Nothing is uploaded; it runs in your browser.
Frequently asked questions
What is the difference between a Franken fish and a Mutant fish?
A Franken fish allows boxes but keeps each side to lines running one way — base sets are rows and boxes, cover sets columns and boxes, say. A Mutant fish drops that too and lets rows and columns mix on the same side. Mutant is the larger family and contains every Franken; the deduction is identical, so most solvers hunt for both at once and only name them afterwards.
Why must the base sets share no candidate?
Because the count is the whole argument. Four units each hold the shape exactly once, and if no cell is in two of them, those are four different cells. Let two base units overlap on a cell that can hold the shape and they might be using the same copy, leaving only three to place — and four cover units are then no longer full, so nothing can be struck.
Can a unit be both a base set and a cover set?
No. A unit on both sides would be counted twice and the arithmetic collapses. The same goes for a cover unit that contains none of the base candidates: it cannot receive one of the four copies, which means the other three cover units would have to take four between them. If your cover has a spare unit in it, you have not found a fish.
Is this worth hunting for by hand?
Rarely, and only after everything else. Box-based fish are hard to see because the boxes cut across the lines you are reading, and most positions that hold one also hold something simpler. Learn the shape of the argument rather than the search: it is the same counting that X-Wing uses, and recognising it is what lets you read a solver's explanation instead of taking its word.