Jellyfish Sudoku Technique

The Jellyfish is the four-by-four member of the fish family: one digit, four base lines, four cover lines. It works exactly like an X-Wing, only wider, and it is the last fish size worth searching in a 9x9 grid.

What the pattern is

Pick a digit and four rows. If, inside those four rows, every remaining candidate for that digit sits in the same four columns, you have a Jellyfish. Four rows need four copies of the digit, and those four copies have only four columns to use, so each of those columns is fully spoken for. The digit can then be removed from those four columns in every other row.

The pattern also runs the other way round: four columns whose candidates for a digit are confined to four rows eliminate the digit from those rows elsewhere.

A base line does not need all four columns. Two or three positions are fine, as long as they fall inside the chosen four columns and the four lines together use all four.

When to look for it

Hunt a Jellyfish only after Swordfish has failed, and only for digits that are already scarce. If a digit still appears seven or eight times per row, the search is hopeless. The good targets are digits with two or three places in most rows.

There is no point going bigger. In a 9x9 grid, a five-line fish always has a matching four-line fish among the remaining lines, so anything above a Jellyfish is wasted effort.

How to apply it, step by step

1. Choose a digit and list, for every row, the columns where it is still a candidate.
2. Keep only the rows with two, three, or four positions.
3. Look for four of those rows whose combined column set has exactly four columns.
4. Confirm the count: four rows, four columns, no fifth column anywhere.
5. Remove the digit from those four columns in the other five rows.
6. Repeat with columns as the base lines.

A worked example

Digit 6, with only these positions left in four rows:

digit 6, remaining positions

r2:  c1 c3
r4:  c3 c5
r6:  c5 c7
r8:  c7 c1

four rows -> exactly four columns {c1, c3, c5, c7}
=> 6 leaves c1, c3, c5 and c7 in rows 1, 3, 5, 7 and 9

Rows 2, 4, 6 and 8 each contain one 6, and all four of them must land in columns 1, 3, 5 and 7. Those four columns can hold only four 6s in total, so all four are used up by these rows and no other row may place a 6 there.

This particular Jellyfish is a closed loop of shared columns, so it does not break down into two X-Wings. That is the type worth the search.

Common mistakes

• Counting a fifth column. One stray candidate in a base line kills the pattern outright, so re-check every base row before eliminating anything.
• Using a base line with only one position. That is a hidden single; place it and re-scan instead.
• Eliminating inside the base lines. The four base rows keep their candidates; only the other five rows lose them.
• Mixing digits. A fish is single-digit logic from start to finish.
• Searching for a Jellyfish before checking subsets. Naked and hidden quads are far more common and much easier to see.

Where you meet it

The Jellyfish is a diabolical-tier pattern. It first becomes necessary in Expert puzzles, and it turns up again in harder grids where a digit stays stubbornly spread across the board. On Easy through Hard puzzles, a smaller fish or a subset will always get there first.