The pattern of the X-Wing technique can appear in rows or in columns.
In a Sudoku puzzle, if a digit is a candidate in only two cells in each of two certain rows and the positions of these two cells are exactly in the same two columns, then this digit will occupy one of the cells in those two columns in such two rows. Therefore, this digit cannot be a candidate for other cells in those two columns. The following is an example to demonstrate this pattern.
3
6
9
3
6
9
3
9
2
4
2
4
2
3
4
2
3
4
9
2
4
3
9
1
3
3
4
8
9
1
5
9
5
8
9
3
4
7
9
3
4
7
9
2
9
2
9
1
3
4
1
2
2
3
4
2
4
4
6
7
9
2
9
4
6
7
9
2
5
4
5
3
7
8
3
5
3
5
7
8
2
4
7
2
4
2
4
5
1
7
1
5
In the two rows R4 and R8 of the puzzle above, the cells that contain the candidate digit 4 are highlighted in green. There are exactly two such cells in each of the two rows R4 and R8. Also, those two green cells in each of these two rows fall in the same two columns C3 and C9. All four green cells in the two rows form an X-Wing pattern in rows.
3
6
9
3
6
9
3
9
2
4
2
4
2
3
4
2
3
4
9
2
4
3
9
1
3
3
4
8
9
1
5
9
5
8
9
3
4
7
9
3
4
7
9
2
9
2
9
1
3
4
1
2
2
3
4
2
4
4
6
7
9
2
9
4
6
7
9
2
5
4
5
3
7
8
3
5
3
5
7
8
2
4
7
2
4
2
4
5
1
7
1
5
There are two possibilities for the digit 4 in these two rows. The digit 4 will occupy either
In either case, one of the two green cells in each of the two columns C3 and C9 must be 4. Therefore, other cells in columns C3 and C9 cannot be 4. If the digit 4 appears in other cells as candidates in columns C3 and C9 (those candidate digit 4's in the orange cells), they can be removed, as shown in Figure 1b.
The roles of rows and columns are exchangeable for this technique. The following is an example for X-Wing in columns.
1
2
8
1
2
8
7
8
6
7
1
5
8
1
5
6
8
4
8
2
4
8
2
8
1
9
8
9
4
6
1
4
6
4
6
8
1
5
7
8
1
5
7
8
1
5
7
1
2
2
4
8
9
2
4
8
2
9
1
6
5
8
1
2
2
8
5
6
6
8
4
5
9
4
8
4
8
9
5
6
1
4
6
7
1
6
7
1
2
9
1
2
6
2
4
5
9
2
4
5
6
2
5
6
9
2
6
2
6
1
4
6
4
6
1
6
9
4
6
9
In the two columns C5 and C8 of the puzzle above, the cells that contain the candidate digit 8 are highlighted in green. There are exactly two such cells in each of the two columns C5 and C8. Also, those two green cells in each of these two columns fall in the same two rows R3 and R5. All four green cells in the two columns form an X-Wing pattern in columns.
1
2
8
1
2
8
7
8
6
7
1
5
8
1
5
6
8
4
8
2
4
8
2
8
1
9
8
9
4
6
1
4
6
4
6
8
1
5
7
8
1
5
7
8
1
5
7
1
2
2
4
8
9
2
4
8
2
9
1
6
5
8
1
2
2
8
5
6
6
8
4
5
9
4
8
4
8
9
5
6
1
4
6
7
1
6
7
1
2
9
1
2
6
2
4
5
9
2
4
5
6
2
5
6
9
2
6
2
6
1
4
6
4
6
1
6
9
4
6
9
There are two possibilities for the digit 8 in these two columns C5 and C8. The digit 8 will occupy either
In either case, one of the two green cells in each of the two rows R3 and R5 must be 8. Therefore, other cells in rows R3 and R5 cannot be 8. If the digit 8 appears in other cells as candidates in rows R3 and R5 (those candidate digit 8's in the orange cells), they can be removed, as shown in Figure 2b.