Sudoku X-Wing and Swordfish Explained: How to Spot Them and Which Candidates You Can Remove

What is an X-Wing?

The X-Wing is a technique that focuses on just one digit. When, in two columns, that digit's candidates appear only in the same two rows, the four candidate cells form the corners of a rectangle. You can then remove that digit from every other cell in those two rows. In Japan it is called "igeta riron", because the pattern looks like the crossing points of the character 井. The transposed version (the candidates in two rows appear only in the same two columns) works the same way.

A real example

Below are the candidates for 8 in columns 5 and 9 only, taken partway through an advanced puzzle. In both columns, 8 can only go in rows 3 and 7.

The 8s in columns 5 and 9 use up one place each in rows 3 and 7. That means you can remove 8 from the other cells in row 7 that had it as a candidate: R7C1, R7C3 and R7C8 (row 3 had no other candidates for 8). In the final solution, R3C9 and R7C5 were 8, which are indeed the two diagonal corners.

How to find an X-Wing

1. 1

   Write all candidates in every empty cell correctly

   An X-Wing compares the positions of candidates, so if even one candidate is missing you will either miss it or remove something by mistake. Make sure your candidates reflect every elimination so far.

2. 2

   Pick one digit and look for columns (rows) where it has exactly two candidates

   Go through 1–9 one at a time. Digits that already appear 5–6 times on the grid have fewer candidates and form patterns more easily, so check them first.

3. 3

   Look for a pair with the same two positions

   If two or more columns have exactly two candidates, compare their row numbers. If they match, such as "rows 3 and 7", you have an X-Wing.

4. 4

   Check whether anything can be removed

   Even if you find an X-Wing, it removes nothing unless the same digit is a candidate elsewhere in those two rows (columns). It only matters when there is something to remove.

If you can't find one in the columns, do the same with the rows. The key point is that the direction you search in (columns or rows with two candidates) is the opposite of the direction you remove from (rows or columns).

Swordfish: extending the X-Wing to 3 rows and 3 columns

The Swordfish extends the X-Wing to three rows (columns). If, in three rows, a digit's candidates appear in 2–3 places each and all of them together fit in the same three columns, you can remove that digit from the other cells in those three columns. Each row doesn't need three candidates; two each is fine.

This is the pattern from a real position. In rows 2, 5 and 8, 4 can only go somewhere in columns 2, 3 and 8. The three rows' 4s use up one place in each of the three columns, so all the candidates for 4 in the other rows of columns 2, 3 and 8 (7 cells in this position) could be removed at once.

Common X-Wing mistakes

The X-Wing is powerful once you can see the shape, but getting even one condition wrong makes you remove candidates you shouldn't. A wrongly removed candidate shows up many moves later as "a cell with no possible digit", and tracking down the cause is painful. Check these points before removing anything.

When solving on paper, circling only the candidates of the digit you're looking at in a coloured pen makes the four-cell rectangle stand out, so it's easier to find and you make fewer mistakes. In Sudoku Next-Move Hints, turning on Show candidates fills in every empty cell's candidates automatically, so you can practise spotting the shape without worrying about missed or stale notes. When a hint shows an X-Wing, the four cells forming the pattern are highlighted and the cells with removable candidates are marked in red.

How often will you need it?

When we created 40 Advanced puzzles with Sudoku Next-Move Hints and solved them to the end, the X-Wing was used in 12 out of about 2,400 steps in total. You need it roughly once every few puzzles, and almost all steps are Hidden Singles. Even across 40 puzzles hard enough to require guessing, the Swordfish appeared only once.

• First make sure you haven't missed any basic techniques or Naked Pairs and Naked Triples
• If you are still stuck, do one lap of 1–9 looking for an X-Wing
• If there is no X-Wing or Swordfish, the puzzle may need a trial placement

FAQ

Is "igeta riron" the same as the X-Wing?

Yes, it is the same technique. In Japan it is called igeta riron because the candidates look like the character 井, and in English it is called the X-Wing.

I found an X-Wing but no digit gets placed.

The X-Wing removes candidates, so it often doesn't place a digit right away. After removing them, check whether any new Hidden Singles or Naked Singles have appeared in the affected rows, columns and boxes.

Does a Swordfish need three candidates in each row?

No. It works as long as each of the three rows has 2–3 candidates and all of them together fit in three columns. Three rows with two candidates each also form a Swordfish.

Should I look for X-Wings in rows or in columns?

Both. There is the pattern "find two columns with two candidates each and remove from rows" and the pattern "find two rows with two candidates each and remove from columns". If you can't find one in one direction, search in the other too.

How can I tell whether a puzzle needs an X-Wing?

You can't tell just by looking at it. If you enter the puzzle in Sudoku Next-Move Hints, its difficulty is rated: Advanced means it needs a Hidden Pair, a Naked Triple or an X-Wing, and Expert means it needs a Swordfish. If you ask for a hint when stuck, it shows the name of the technique needed at that point.