Jellyfish in Sudoku: The Four-Row Fish, Explained Simply

A jellyfish is a fish pattern on four rows and four columns. If a digit's candidates in four rows all fall inside the same four columns, those four rows take that digit in each of the four columns, so the digit can be removed from every other cell in those columns (and the same with rows and columns swapped).

To spot one, pick a digit, write down the columns it can use in each row, and look for four rows whose columns add up to just four. It is the big sibling of the X-Wing (two lines) and the Swordfish (three lines), and it is rare.

How the jellyfish works

Here is the position, from a real puzzle in our library, looking only at the digit 1:

• Row 1: 1 can go in columns 3 or 4.
• Row 3: columns 3, 4 or 6.
• Row 4: columns 6 or 9.
• Row 7: columns 4 or 9.

Those four rows each need a 1, and together they only use columns 3, 4, 6 and 9. Four different 1s in four different rows must also be in four different columns, so each of those columns gets its 1 from one of these rows. No row has to be decided for this to hold.

That fills the 1 of columns 3, 4, 6 and 9. No other cell in those columns can be 1. Columns 3 and 9 have no other 1s, but columns 4 and 6 do:

• Column 4 loses the 1 from R5C4, R8C4 and R9C4.
• Column 6 loses the 1 from R5C6, R6C6, R8C6 and R9C6.

Seven eliminations from one pattern. Before it, box 8 had six cells that could hold a 1. After it, only R7C4 and R9C5 are left.

Puzzle 201388 from the Sudoku Royale library. Givens (row by row, dots are blanks): .....2.8...8.7.19.2...6..7...539..6..3....4.7...4...5.567.8....9.................. The candidates shown are what is left after singles, pointing and claiming, naked and hidden pairs, triples and quads, X-Wing and Swordfish, with nothing else applied.

The fish family: X-Wing, Swordfish, Jellyfish

All basic fish use the same logic with a different number of lines:

A base row does not need a candidate in every cover column. In the example, row 1 uses only two of the four columns and row 4 only two. What matters is that the union of the columns is exactly four.

Fish larger than four lines are never needed. For every fish on N rows there is a matching fish on the columns that are left over, and for a digit with nine open lines one of the two is always four lines or fewer. The example shows this: the same seven 1s can also be removed with a jellyfish on columns 1, 2, 5 and 8, whose 1s all sit in rows 5, 6, 8 and 9.

How to spot a jellyfish

1. Check smaller fish first. X-Wings and Swordfish are much more common and easier to confirm. A true jellyfish is only worth hunting when those come up empty.
2. Pick one digit and list its columns per row. Skip rows where it has five or more candidates, since those rows cannot be part of a four-column fish.
3. Look for four rows that share four columns. Rows with only two or three candidates are the best starting points.
4. Eliminate in the cover columns. Remove the digit from every cell of those columns outside the four base rows. Then try the same with columns as the base.

Jellyfish are rare. Of roughly 300 library puzzles we scanned after the basic techniques ran out, only one had a jellyfish that no X-Wing or Swordfish could replace. The hint in Sudoku Royale knows the pattern, so if one does turn up in your game, a hint can point it out.

For where fish sit among the other techniques, see our list of sudoku techniques in learning order or the overview of advanced sudoku strategies. The finned X-Wing shows how fish still work when one extra candidate spoils the pattern.