X-Wing Sudoku Technique: How to Spot It and Why It Works

What an X-Wing looks like

Choose one digit and look only at its pencil marks. In most rows it can still go in three or more cells. Now find a row where it fits in exactly two cells. Then find a second row where it also fits in exactly two cells, in the same two columns. Those four cells are the corners of a rectangle. That rectangle is the X-Wing.

Why it works

Row 2 needs a 7, and it can only go in column 3 or column 7. Row 7 needs a 7 too, with the same two choices. The two rows cannot both use the same column, because a column holds each digit once. So there are only two possibilities:

• Row 2 takes column 3 and row 7 takes column 7, or
• Row 2 takes column 7 and row 7 takes column 3.

Either way, column 3 gets its 7 from row 2 or row 7, and so does column 7. Neither column has room for another 7 anywhere else. That is why every other 7 in those two columns can be erased, even though you still do not know which diagonal is the right one.

The column version

The pattern works with rows and columns swapped. If a digit fits in exactly two cells of one column, and exactly two cells of another column, and those cells share the same two rows, the digit can be removed from the rest of those two rows. A quick way to remember it: the lines where the digit has only two spots are the “base”, and you eliminate along the other direction.

How to find one

1. Make sure your pencil marks are complete and up to date. An X-Wing hides behind a missing candidate.
2. Pick one digit. Ignore every other number in the grid.
3. For each row, count the cells where that digit can go. Note the rows with exactly two.
4. Compare those rows. If two of them use the same pair of columns, you have an X-Wing.
5. Look down both columns for other candidates of that digit and erase them. Then repeat with columns as the base.
6. After any elimination, check for new singles before hunting again.

In our game, turn on Notes (or press N) and fill in candidates first. A digit with few remaining copies on the board is the best place to start, because it has the fewest open cells.

Common mistakes

• Three candidates in a base row. If the digit can go in three cells of one of the rows, it is not an X-Wing (but it might be part of a Swordfish).
• Eliminating in the wrong direction. With rows as the base, you erase in the columns, never in the two rows themselves.
• Mixing digits. All four corners must be about the same digit.

Swordfish and beyond

A Swordfish is the same idea with three rows and three columns. If, in three rows, a digit fits only within the same three columns (two or three cells per row), the digit can be removed from the rest of those three columns. A four-line version is called a Jellyfish. They are rarer and harder to see, so learn to find X-Wings quickly first.

On Silvera PuzzleClub, Expert sudoku are the grids where singles, pairs and pointing are not enough. Many of them open up with an X-Wing; some need a Swordfish or a chain of reasoning. Our techniques guide covers the easier patterns to try first.

Practice: today’s daily sudoku · easy · medium · hard · expert