Swordfish

The X-wing with three rows and three columns: when a digit is confined to three columns across three rows, clear it from the rest of those columns.

A real example from a sudoku.ie puzzle. Look at the 5s in rows 1, 6 and 7. In those three rows, the 5 can only go in columns 5, 6 or 7. So those rows must place their 5s in columns 5, 6 and 7, one each, which leaves no room for another 5 anywhere else in columns 5, 6 and 7. Remove 5 from row 8, column 5 and row 9, column 7. Yellow cells make the pattern. Red marks show what you can cross out.

What it is

The swordfish is the X-wing stretched to three rows and three columns.

Pick a digit. Find three rows where that digit can only go in two or three cells each. If all of those cells, taken together, fall in just three columns, you have a swordfish. Those three rows need three copies of the digit, and they can only put them in those three columns, one per column. So each of the three columns gets its copy from one of these three rows. That means no other cell in those three columns can hold the digit.

As with the X-wing, it works the other way round too. Three columns where the digit is confined to the same three rows let you clear it from the rest of those rows.

How to spot it

Focus on a single digit. Go through each row and count how many cells it could go in. Note every row where the answer is two or three, and write down which columns they are.

Then look for three of those rows whose columns, put together, make only three columns. Each row does not have to use all three columns. A row with candidates in just two of the three columns is fine.

Repeat the same check with columns, looking for three columns whose candidates fall in just three rows.

On paper, it helps to lightly circle every candidate for your chosen digit, so the pattern stands out.

A worked example

Take the digit 8. Looking along the rows, you find:

In row 1, 8 can only go in column 2 or column 8.
In row 5, 8 can only go in column 2 or column 4.
In row 9, 8 can only go in column 4 or column 8.

Together, these use only columns 2, 4 and 8. That is a swordfish.

Think it through. Row 1’s 8 is in column 2 or 8. Row 5’s 8 is in column 2 or 4. Row 9’s 8 is in column 4 or 8. They must all be in different columns. Try it: if row 1 takes column 2, row 5 must take column 4, and row 9 must take column 8. If row 1 takes column 8, row 9 must take column 4, and row 5 must take column 2. Either way, columns 2, 4 and 8 each get their 8 from rows 1, 5 and 9.

So no other cell in column 2, 4 or 8 can be 8. Say row 3, column 4 has candidates 3, 6 and 8. Remove the 8. Say row 7, column 2 has 1 and 8. Remove the 8 and place the 1.

Why it works

Three rows each need one 8. Their possible cells lie in only three columns. Three rows into three columns, one each: every column’s 8 is used up by these rows, so nothing else in those columns can be 8.

A common mistake

The most common mistake is clearing the digit from the wrong lines. If you found the swordfish by looking at rows, you remove from the columns, and the other way round. A useful rule: you remove from the lines you did not count.

Another mistake is including a row where the digit has a candidate outside the three columns. If row 5 could also hold 8 in column 6, the three rows now cover four columns and nothing can be removed. Check every candidate in each row.

When you will need it

The swordfish is one of the Expert techniques on sudoku.ie, along with the XY-wing and XYZ-wing. It is the hardest technique any of our daily puzzles require, and you will need it on some Saturdays. If you enjoy it, the jellyfish takes the same idea one step further.