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X-Wing

The best-known advanced technique: one number, two rows, the same two columns, and you can clear those columns. Master puzzles on puzuru need X-Wing or one of the related techniques below.

What is an X-Wing?

Pick one number. If, in two different rows, that number can only go in two cells each, and those cells are in the same two columns, you have an X-Wing.

The four cells form the corners of a rectangle. In each row, the number goes in one of the two corners, and the two rows must use opposite corners (they can't share a column). Either way, both columns get their number from these four cells.

1122334455667788998452521988819158786492988848884958788318482746858812358

the four corners of the X-Wing its rows and columns candidates you can remove blue numbers: already filled in with the basics

Example from a real puzuru puzzle. Rows and columns are numbered 1 to 9 from the top left.

The example

The diagram shows only the candidates for 8. In row 4, an 8 can only go in column 3 or column 5. The same is true for row 7.

So one 8 sits in row 4 and the other in row 7, and between them they cover columns 3 and 5. No other cell in those two columns can be 8.

Remove 8 from R5C3, R5C5, R8C3, R8C5.

How to find an X-Wing

Fill in candidates, then choose one number. For each row, count the cells that can still hold it.

Note every row where the number has exactly two places. If two of those rows use the same two columns, check for removals in those columns.

Do the same with columns: two columns where the number has two places in the same two rows. Then remove it from the rest of those rows.

The same thing with columns

An X-Wing works sideways too. In the second example (below), a 7 can only go in rows 2 and 9 of column 5, and the same two rows of column 8.

So rows 2 and 9 get their 7 from those four cells. Remove 7 from the rest of those rows: R2C6, R9C2, R9C6.

112233445566778899579315779744967574268157391937578539413745729757839247972477375

the four corners of the X-Wing its rows and columns candidates you can remove blue numbers: already filled in with the basics

Second example: an X-Wing on 7 based on columns 5 and 8.

Why it works

Think of the two possible worlds. If row 4 takes column 3, then row 7 must take column 5. If row 4 takes column 5, row 7 takes column 3. In both worlds, columns 3 and 5 each already have their 8. That is all the proof you need.

What comes next

Swordfish is the same idea with three rows and three columns. XY-Wing is a different pattern built from three two-candidate cells. Master puzzles on puzuru need at least one of these three.

Practice on Master puzzles →

← Pointing Pair　Next: Swordfish →

FAQ

What difficulty needs X-Wing?

On puzuru, Master puzzles can't be finished with singles, pairs, triples and pointing, and are solvable once you add X-Wing, Swordfish or XY-Wing.

Can an X-Wing be based on columns?

Yes. Swap rows and columns: two columns where a number has two places in the same two rows. Remove the number from the rest of those rows.

Is X-Wing the same as Swordfish?

Swordfish is the three-row version of the same idea. X-Wing uses two rows and two columns.

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