Jellyfish
The four-row, four-column generalisation of swordfish. A digit confined to the same four columns across four rows lets you eliminate it elsewhere in those columns.
A jellyfish is the four-row generalisation of swordfish, which is itself the three-row generalisation of X-wing. The fish family scales by row count: X-wing fits in two rows × two columns; swordfish in three × three; jellyfish in four × four. Each step up adds one row and one column, and the underlying argument is the same in all of them.
The pattern
Pick a digit. Find four rows where the digit's only candidate cells fall within the same four columns. The digit must occupy four cells out of the sixteen in that 4×4 grid — exactly one per row and one per column — but every cell that holds the digit lives in those four columns. So the digit can be eliminated from every other cell of those four columns, outside the four rows.
The same logic works rotated 90°. Four columns whose only candidate cells fall within four rows produces a column-based jellyfish; the eliminations happen in the four rows.
The argument is identical to X-wing's and swordfish's; only the count grows. Whichever way the digit distributes itself among the rows of a jellyfish, it stays inside the four columns.
Why it's harder to spot than swordfish
Jellyfish are mathematically common but visually subtle. Four rows is a lot to scan; four columns is a lot to keep in working memory; sixteen cells is enough that a quick visual sweep can miss the pattern. The candidate cells often have other candidates listed, so the jellyfish doesn't visually announce itself. You have to be scanning a single digit at a time across the whole grid.
A spotting habit: after exhausting X-wing and swordfish on a stuck digit, write down the digit's candidate cells row by row. If three rows already share columns and a fourth row has candidates only in those same columns plus possibly nowhere else, jellyfish is alive. Most jellyfish are found by enumeration, not pattern recognition.
A note on five-row fish
The fish family stops being practically useful at jellyfish. A five-row fish — a squirmbag — is mathematically valid but never produces eliminations the four-row fish doesn't. Mathematicians sometimes catalog further variants for completeness; solvers stop at jellyfish.
See also
- X-wing— When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.
- Swordfish— The X-wing's three-row counterpart. When a digit's possible cells across three rows fall in the same three columns, that digit can be eliminated from those columns elsewhere.
- Finned X-wing— An X-wing where one of the four corners has an extra candidate cell — a fin — in its row or column. The eliminations restrict to cells that see both the X-wing and the fin.
- Candidate— A digit (1–9) a cell could still legally hold — one not yet ruled out by anything in its row, column, or 3×3 box. Every empty cell has between one and nine.
Read more
- Why the X-wing keeps tripping people up
The X-wing is a famous Sudoku technique that almost everyone knows and almost no one spots in time. Here's the perceptual problem behind it.