In a 9-cell unit (a row, a column, or a 3x3 block) of a Sudoku puzzle, if three certain digits appear only in three cells as candidates, that is, only three cells in a 9-cell unit contain some of these three candidate digits, and the other cells do not have any of them, then these three digits have nowhere to go in the 9-cell unit but these three cells. They must each occupy one of these three cells. As a result, other candidate digits cannot occupy any of these cells. So if other digits appear in these three cells as candidates, they can be removed.
Please note that:
We will demonstrate this technique visually with the following examples:
5
9
2
4
5
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
9
2
3
4
5
9
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 row R1 of the puzzle in Figure 1a, the three digits 2, 4, and 6 (marked in red) may appear only in three cells (R1,C3), (R1,C8), and (R1,C9) (marked in orange) as candidates, but nowhere else. These three cells are the only choices for the three digits in this row. In this situation, the digits 2, 4, and 6 each will occupy one of these three orange cells, and no other 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.
5
9
2
4
5
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
9
2
3
4
5
9
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
3
5
7
8
2
5
7
9
2
3
5
7
8
9
3
5
7
8
9
2
5
7
9
2
3
5
7
8
9
3
5
7
8
3
5
8
3
5
7
8
9
3
7
9
3
4
5
7
8
9
3
4
5
8
9
3
5
7
8
2
3
5
7
8
2
3
5
1
2
5
9
1
2
3
5
9
3
5
9
3
9
2
3
7
3
7
3
9
2
3
9
3
4
2
3
4
2
3
2
3
7
9
5
7
9
5
7
8
9
1
5
1
5
8
7
9
7
9
5
8
3
5
8
3
5
8
In column C6 of the puzzle in Figure 2a, the three digits 2, 4, and 9 (marked in red) may appear only in three cells (R3,C6), (R5,C6), and (R6,C6) (marked in orange) as candidates, but nowhere else. These three cells are the only choices for the three digits in this column. In this situation, the digits 2, 4, and 9 each will occupy one of these three orange cells, and no other 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
5
7
8
2
5
7
9
2
3
5
7
8
9
3
5
7
8
9
2
5
7
9
2
3
5
7
8
9
3
5
7
8
3
5
8
3
5
7
8
9
3
7
9
3
4
5
7
8
9
3
4
5
8
9
3
5
7
8
2
3
5
7
8
2
3
5
1
2
5
9
1
2
3
5
9
3
5
9
3
9
2
3
7
3
7
3
9
2
3
9
3
4
2
3
4
2
3
2
3
7
9
5
7
9
5
7
8
9
1
5
1
5
8
7
9
7
9
5
8
3
5
8
3
5
8
1
4
9
3
4
6
9
4
6
7
1
6
7
1
4
9
3
4
9
3
4
5
1
2
3
5
1
5
1
5
8
3
4
1
2
3
8
2
4
5
6
9
2
6
9
1
2
4
4
5
6
1
4
8
2
4
9
1
2
4
8
5
8
5
8
1
5
5
7
1
5
7
2
9
2
9
4
9
1
2
1
5
5
6
7
1
2
6
7
4
5
8
9
4
5
6
7
8
9
2
6
7
2
9
3
5
7
3
5
7
2
9
5
7
1
2
4
1
2
6
2
6
2
4
In block B7 of the puzzle in Figure 3a, the three digits 4, 8, and 9 (marked in red) may appear only in three cells (R7,C2), (R9,C1), and (R9,C2) (marked in orange) as candidates, but nowhere else. These three cells are the only choices for the three digits in this block. In this situation, the digits 4, 8, and 9 each will occupy one of these three orange cells, and no other 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.
1
4
9
3
4
6
9
4
6
7
1
6
7
1
4
9
3
4
9
3
4
5
1
2
3
5
1
5
1
5
8
3
4
1
2
3
8
2
4
5
6
9
2
6
9
1
2
4
4
5
6
1
4
8
2
4
9
1
2
4
8
5
8
5
8
1
5
5
7
1
5
7
2
9
2
9
4
9
1
2
1
5
5
6
7
1
2
6
7
4
5
8
9
4
5
6
7
8
9
2
6
7
2
9
3
5
7
3
5
7
2
9
5
7
1
2
4
1
2
6
2
6
2
4
List of Sudoku Solving Techniques
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