X-Wing: The First Advanced Sudoku Technique Worth Learning

An x-wing happens when a digit can only go in the same two columns in two different rows. Those two rows must use up both columns for that digit, so you can remove it from every other cell in those two columns. It's the first technique that looks across the whole board instead of inside one row, column or box.

You'll want notes and comfort with pairs and triples first. X-wings show up on Hard and Expert puzzles once the simpler techniques stop working.

The pattern

Pick one digit. Say 7. Now look for two rows where 7 has exactly two possible cells:

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

Those four cells form the corners of a rectangle, the "X" in x-wing. Row 2 needs a 7 in one of its two cells, and so does row 6. There are only two ways that can work: row 2 takes column 3 and row 6 takes column 8, or the other way around.

Either way, column 3 gets its 7 from row 2 or row 6, and so does column 8. So no other cell in column 3 or column 8 can be a 7. Erase 7 from every other cell in those two columns.

It works sideways too

Swap rows and columns and the logic holds. If 7 can only go in rows 4 and 9 within column 1, and only in rows 4 and 9 within column 5, those two columns claim the 7s for rows 4 and 9. Remove 7 from every other cell in rows 4 and 9.

The rule to remember: the lines where the digit is confined are the ones you search in. The lines that cross them are the ones you clean up.

How to spot one

1. Work one digit at a time. Highlight every cell where that digit is still a candidate. In Kodiak Sudoku, selecting any filled cell with that digit highlights it in the notes of every empty cell, which makes this much faster.
2. Find rows (or columns) with exactly two candidates for that digit.
3. Look for two that line up on the same pair of columns (or rows).
4. Check that the crossing lines have something to remove. An x-wing that eliminates nothing is real but useless. Move on.

Common mistakes

• Three candidates in one of the rows. If row 2 can hold a 7 in columns 3, 5 and 8, it isn't an x-wing. That might be part of a swordfish instead.
• Removing from the wrong lines. You never remove anything from the two rows that formed the pattern. Only from the columns they cross.
• Mixing digits. All four corners must be about the same digit.

Practice

Work through the X-Wing lesson, then try a Hard or Expert puzzle on the play page. When you're stuck and singles, pairs and pointing pairs have run dry, go digit by digit looking for an x-wing.