The Jellyfish Technique in Sudoku

The fish family in one sentence

A fish works on a single digit. If that digit is confined to a small set of columns across the same number of rows, then in those columns the digit can be removed everywhere outside those rows. An X-Wing uses two rows and two columns, a Swordfish uses three of each, and a Jellyfish uses four of each.

What a Jellyfish looks like

Pick a digit and look at four rows. If, across those four rows, the digit can only appear in the same four columns, you have a Jellyfish. The candidates do not need to fill all sixteen intersections. Each of the four rows just has to keep the digit inside that shared set of four columns.

The elimination

1. Choose a digit that is proving stubborn and mark its candidate positions.
2. Scan for four rows whose candidates for that digit all fall within the same four columns.
3. You have a Jellyfish. The digit will occupy exactly one cell in each of those four columns, and all of them sit in your four rows.
4. Erase that digit from every other cell in those four columns.
5. Repeat with rows and columns swapped, since a Jellyfish can point either way.

A word of honesty

The Jellyfish is rare and easy to miss, and most boards that seem to need one can be cracked another way. It is worth knowing for completeness and for the hardest puzzles, but do not spend ages hunting for a Jellyfish before trying coloring or a wing. Treat it as a tool for the deep end.