Sudoku Solving Techniques

XY-Wing (Row-Column)

The XY-Wing technique involves three cells, and each of them has two candidate digits. Below, we will use a real Sudoku puzzle to demonstrate the Row-Column pattern of this technique as an example.

Example
C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
8
1
5
3
9

6

7

4

6

7

2
2
4
7

1

6

5
8

3

6

1

3

6

9
3
6
9
4
2

1

7

1

7

5
8
6
8
4
9

3

7

3

7

5
2
1
9
7
1
5
2
4

6

8

6

8

3
2
3
5
8
1
6
9
7
4
2

3

4

3

8

7

4

5

6

9
1

4

5

6

6

8

1

7

9
6

3

4

8

1

3

8

2

5

3

4

7

8

3

8

2

5

5

4

8

1

7

1

6

4

8

2

3

6

7

9

2

3

Figure 1: XY-Wing (Row-Column) Pattern in a Sudoku Puzzle

In this puzzle, the pink cell (R3,C7) and the two yellow cells (R3,C2) and (R8,C7) each have two candidate digits. The yellow cell (R3,C2) shares the same row R3 with the pink cell, and they have a candidate digit 7 in common. The other yellow cell (R8,C7) shares the same column C7 with the pink cell, and they have a candidate digit 1 in common. Also, the two yellow cells have a common candidate digit 6. These three cells form an XY-Wing (Row-Column) pattern.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
8
1
5
3
9

6

7

4

6

7

2
2
4
7

1

6

5
8

3

6

1

3

6

9
3
6
9
4
2

1

7

1

7

5
8
6
8
4
9

3

7

3

7

5
2
1
9
7
1
5
2
4

6

8

6

8

3
2
3
5
8
1
6
9
7
4
2

3

4

3

8

7

4

5

6

9
1

4

5

6

6

8

1

7

9
6

3

4

8

1

3

8

2

5

3

4

7

8

3

8

2

5

5

4

8

1

7

1

6

4

8

2

3

6

7

9

2

3

Figure 2: The Orange Cell Cannot be 6

There are two possibilities for the pink cell:

So in either case, the orange cell (R8,C2) cannot be 6. The candidate digit 6 in the orange cell can be removed, as shown in Figure 2.

Examples for Other Patterns

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