Jellyfish

The four-line version of the X-wing and swordfish. Rare and tricky, but the logic is the same: a digit locked into four rows and four columns.

What it is

The jellyfish is the next step up from the swordfish. Where the X-wing uses two rows and two columns, and the swordfish uses three, the jellyfish uses four.

Pick a digit. Find four rows where that digit can only go in two, three or four cells each. If all of those cells, taken together, fall in just four columns, you have a jellyfish. The four rows need four copies of the digit, and they can only place them in those four columns, one each. So every one of those columns gets its copy from these four rows, and no other cell in those four columns can hold the digit.

It works with rows and columns swapped, too.

The jellyfish is included here for completeness and for the curious. It is very rare in practice.

How to spot it

It is hard to spot by eye, so be methodical:

1. Choose one digit.
2. For each row, list the columns where it can go. Ignore rows where it is already placed.
3. Keep the rows with two, three or four candidate cells.
4. Look for four of those rows whose columns, put together, make only four columns.

Then do the same for columns.

A useful fact: every jellyfish has a matching pattern the other way round that makes exactly the same removals. If the digit still has to be placed in seven rows, a jellyfish in the rows always comes with a swordfish in the columns. If it still has to be placed in six rows, it comes with an X-wing. So if the jellyfish feels hard to see, check whether a smaller pattern does the same job.

A worked example

Take the digit 2. Looking along the rows, you find:

• In row 1, 2 can only go in column 1 or column 4.
• In row 3, 2 can only go in column 4, column 7 or column 9.
• In row 6, 2 can only go in column 1 or column 9.
• In row 8, 2 can only go in column 7 or column 9.

Together, these rows use only columns 1, 4, 7 and 9. That is a jellyfish.

Each of the four rows must place its 2 in a different column, and only four columns are available. So columns 1, 4, 7 and 9 each get their 2 from rows 1, 3, 6 and 8.

That means no other cell in those four columns can be 2. Say row 4, column 7 has candidates 2 and 5. Remove the 2 and place the 5. Say row 9, column 1 has 2, 3 and 6. Remove the 2, leaving 3 and 6.

Why it works

Four rows each need one 2. Their possible cells lie in only four columns. Four rows into four columns, one each, so every column’s 2 is spoken for. Nothing else in those columns can be 2.

A common mistake

As with the swordfish, the classic error is removing the digit from the wrong lines. If you counted rows, remove from columns. If you counted columns, remove from rows.

The other mistake is missing a stray candidate. With four rows to check, it is easy to overlook one cell where the digit could go outside the four columns. One stray candidate breaks the whole pattern. Check each row twice.

When you will need it

Our Expert puzzles are graded so that the hardest technique needed is the swordfish, together with the XY-wing and XYZ-wing. So you should not need a jellyfish for any daily puzzle on sudoku.ie. It is still worth understanding, because it shows that the X-wing, swordfish and jellyfish are really one idea at three sizes. If you can see that, the swordfish becomes much easier to spot.