In a 9-cell unit (a row, a column, or a 3x3 block) of a Sudoku puzzle, if two certain digits appear only in the same two cells as candidates, then these two digits have nowhere to go in this 9-cell unit but these two cells. They must each occupy one of these two cells. As a result, other candidate digits cannot occupy any of these two cells. So if other digits appear in these two cells as candidates, they can be removed.
Let's demonstrate this technique visually with the following examples.
1
4
8
1
3
4
8
3
4
6
8
1
5
3
4
6
5
8
4
6
9
4
6
6
9
1
3
6
9
3
6
8
1
5
3
6
8
9
5
6
9
4
8
4
8
9
4
8
9
2
6
2
6
2
6
2
6
1
4
7
8
1
3
4
8
9
3
4
8
9
4
5
7
8
1
5
7
8
1
3
8
9
3
8
9
1
2
7
9
3
8
2
4
9
7
9
3
8
4
5
9
1
2
7
9
2
5
9
2
3
9
3
9
3
7
8
8
9
2
3
7
8
In row R8 of the puzzle in Figure 1a, the two candidate digits 4 and 5 (marked in red) appear in the same two cells (R8,C1) and (R8,C6) (marked in orange), but nowhere else. These two cells are the only choices for these two digits in this row. In this situation, the digits 4 and 5 each will occupy one of these two orange cells, and no other candidate digits can occupy any of them. As a result, other candidate digits in the orange cells can be removed, as shown in Figure 1b below.
1
4
8
1
3
4
8
3
4
6
8
1
5
3
4
6
5
8
4
6
9
4
6
6
9
1
3
6
9
3
6
8
1
5
3
6
8
9
5
6
9
4
8
4
8
9
4
8
9
2
6
2
6
2
6
2
6
1
4
7
8
1
3
4
8
9
3
4
8
9
4
5
7
8
1
5
7
8
1
3
8
9
3
8
9
1
2
7
9
3
8
2
4
9
7
9
3
8
4
5
9
1
2
7
9
2
5
9
2
3
9
3
9
3
7
8
8
9
2
3
7
8
3
6
2
3
5
2
3
5
2
6
3
5
8
2
3
5
6
8
1
3
5
1
2
3
5
2
3
5
2
5
6
3
5
9
3
9
2
3
5
2
3
5
8
9
8
9
1
5
9
1
5
8
1
5
9
1
5
8
1
3
3
5
1
5
1
3
6
2
3
2
6
1
3
1
3
4
8
1
2
3
6
8
1
3
4
5
1
2
3
5
1
2
5
6
1
3
1
2
1
2
3
1
3
4
1
2
3
9
1
3
4
9
1
2
3
In column C5 of the puzzle in Figure 2a, the two candidate digits 6 and 8 (marked in red) appear in the same two cells (R1,C5) and (R7,C5) (marked in orange), but nowhere else. These two cells are the only choices for these two digits in this column. In this situation, the digits 6 and 8 each will occupy one of these two orange cells, and no other candidate digits can occupy any of them. As a result, other candidate digits in the orange cells can be removed, as shown in Figure 2b below.
3
6
2
3
5
2
3
5
2
6
3
5
8
2
3
5
6
8
1
3
5
1
2
3
5
2
3
5
2
5
6
3
5
9
3
9
2
3
5
2
3
5
8
9
8
9
1
5
9
1
5
8
1
5
9
1
5
8
1
3
3
5
1
5
1
3
6
2
3
2
6
1
3
1
3
4
8
1
2
3
6
8
1
3
4
5
1
2
3
5
1
2
5
6
1
3
1
2
1
2
3
1
3
4
1
2
3
9
1
3
4
9
1
2
3
5
9
2
4
6
3
9
2
3
4
6
4
5
6
7
8
9
3
7
8
9
3
7
8
1
9
1
3
9
3
5
9
2
4
6
2
4
2
9
4
6
9
3
4
5
9
1
5
7
8
1
7
8
1
2
5
7
1
2
7
1
5
7
4
8
4
8
1
5
5
7
1
9
5
7
9
3
8
1
3
6
4
6
1
3
4
5
6
3
5
8
1
3
5
1
2
7
8
1
3
7
8
1
5
8
9
1
3
8
9
1
3
5
8
1
2
3
8
9
1
3
5
8
1
3
2
3
6
8
1
3
9
3
6
8
9
1
2
8
9
2
3
8
9
In block B3 of the puzzle in Figure 3a, the two candidate digits 3 and 5 (marked in red) appear in the same two cells (R1,C7) and (R3,C9) (marked in orange), but nowhere else. These two cells are the only choices for the two digits in this block. In this situation, the digits 3 and 5 each will occupy one of these two orange cells, and no other candidate digits can occupy any of them. As a result, other candidate digits in the orange cells can be removed, as shown in Figure 3b below.
5
9
2
4
6
3
9
2
3
4
6
4
5
6
7
8
9
3
7
8
9
3
7
8
1
9
1
3
9
3
5
9
2
4
6
2
4
2
9
4
6
9
3
4
5
9
1
5
7
8
1
7
8
1
2
5
7
1
2
7
1
5
7
4
8
4
8
1
5
5
7
1
9
5
7
9
3
8
1
3
6
4
6
1
3
4
5
6
3
5
8
1
3
5
1
2
7
8
1
3
7
8
1
5
8
9
1
3
8
9
1
3
5
8
1
2
3
8
9
1
3
5
8
1
3
2
3
6
8
1
3
9
3
6
8
9
1
2
8
9
2
3
8
9
List of Sudoku Solving Techniques
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