What Is X-Wing in Sudoku? How to Spot and Use It Correctly

X-Wing uses four positions of the same candidate

Suppose candidate 5 in row 2 can only be in column 3 or column 8. If row 7 can also place 5 only in columns 3 or 8, the four positions form a rectangle. Each row must contain one 5, so those two columns must also receive exactly two 5s at the four corners of the pattern.

Therefore candidate 5 can be removed from other cells in columns 3 and 8. You do not yet know which corner pair is the answer, but in either case those two columns are occupied by the 5s from the two source rows.

Scan a candidate row by row or column by column

Choose a candidate and find rows where it has exactly two possible positions. Compare the column pair for those rows; if two rows share the same two columns, you have a row-based X-Wing. You can reverse the process: find two columns with the same two row positions to create a column-based X-Wing.

You do not need to scan every digit at all times. X-Wing is most useful when Notes are fairly complete and basic techniques no longer make progress.

• Choose a candidate that appears frequently on the board.
• Find two rows/columns with exactly two positions for the candidate.
• Confirm the two pairs of positions lie on the same two columns/rows.
• Eliminate the candidate from the rest of the intersecting columns/rows.

A row with a third position is not an X-Wing

The most common mistake is seeing four neat corners while a source row or column still has a third candidate elsewhere. In that case you cannot prove the digit must occupy the two corners, so any elimination based on the rectangle is invalid.

Another mistake is eliminating the candidate from the four corners themselves. The corners are the positions that must remain; X-Wing only removes the same candidate from other cells on the two intersecting lines.

After an X-Wing, return to simpler techniques

An X-Wing usually creates eliminations, and those eliminations are what produce singles, hidden singles, or locked candidates. So do not immediately hunt for a second X-Wing; rescan the whole board to use the progress you just created.

If you are learning X-Wing, practice at Expert or Master level, but accept that not every puzzle needs this pattern. Use the technique when its conditions appear, not because you want to force it into the board.