X-Wing
The X-Wing is the classic single-digit pattern. Find two rows in which a digit can go in only two cells each, with those cells lying in the same two columns. The four cells form a rectangle, and the digit must occupy diagonally opposite corners — one placement per row, one per column. Whichever diagonal turns out true, both columns receive the digit inside the rectangle, so it can be removed from those two columns everywhere else.
A worked example: suppose the digit 5 can only go in columns 3 and 8 of row 2, and only in columns 3 and 8 of row 6. If r2c3 is the 5 in row 2, then column 3 is used up, forcing row 6's 5 into r6c8. If instead r2c8 is 5, row 6's 5 lands on r6c3. Either way, columns 3 and 8 get their 5s from rows 2 and 6 — so 5 comes off every other cell of columns 3 and 8, such as r4c3 or r9c8.
The pattern is perfectly symmetric between rows and columns. An X-Wing found in two columns (the digit restricted to the same two rows in each) eliminates along those two rows instead. Always note which orientation you found: base lines are where the digit is confined; cover lines are where you eliminate.
Reach for X-Wings when the basics stall and one digit has been widely placed. Scan digit by digit, listing rows (then columns) where the digit has exactly two candidate cells, and look for a matching pair.
- Work one digit at a time — X-Wing is a single-digit technique and mixing digits hides the pattern.
- Two rows confined to the same two columns eliminate in the columns; two columns confined to the same two rows eliminate in the rows.
- The four corners keep their candidates — eliminations only apply to cells outside the rectangle on the cover lines.