Sudoku Solving Techniques

Forcing Chain (candidate confirmed)

The example below demonstrates the Forcing Chain technique that leads to confirming a candidate digit in a cell.

The example below demonstrates the Forcing Chain technique that leads to eliminating a candidate digit in a cell.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 1: Two Candidate Digits 6 and 9 for Cell (R2,C4)

In this puzzle, the cell (R2,C4) has two candidate digits 6 and 9. That means there are two possibilities for this cell. It can be either 6 or 9, but not others. Let's see what conclusion we can draw with the Forcing Chain technique.

Case 1: Cell (R2,C4) is 6
C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 2a: Suppose Cell (R2,C4) is 6

In the first case, suppose that the cell (R2,C4) is 6.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 2b: Cell (R4,C4) Must be 8

The cell (R4,C4) cannot be 6 since the cell (R2,C4) in the same column C4 is 6. As a result, the cell (R4,C4) must be 8, as it turns out to be the only candidate for the cell.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 2c: Cell (R6,C4) Cannot be 8

The cell (R6,C4) cannot be 8 since the cell (R4,C4) in the same column C4 is 8.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 2d: Cell (R6,C9) Must be 8

The cell (R6,C9) must be 8 since it is the only possible position for the digit 8 in row R6.

Case 2: Cell (R2,C4) is 9
C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 3a: Suppose Cell (R2,C4) is 9

In the second case, suppose that the cell (R2,C4) is 9.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 3b: Cell (R3,C6) Cannot be 9

The cell (R3,C6) cannot be 9 since the cell (R2,C4) in the same block B2 is 9.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 3c: Cell (R3,C9) Must be 9

The cell (R3,C9) must be 9 since it is the only possible position for the digit 9 in row R3.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5

8

9

6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 3d: Cell (R6,C9) Must be 8

The cell (R6,C9) cannot be 9 since the cell (R3,C9) in the same column C9 is 9. As a result, the cell (R6,C9) must be 8, as it turns out to be the only candidate left for the cell.

As we can see in both cases, the cell (R6,C9) must be 8. We can conclude that the cell (R6,C9) can be confirmed to be 8, as shown in Figure 4.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9
9
6
8
3
5
7
2
4
1
4
1
7

6

9

8
2
3
5

6

9

5
3
2

1

9

1

6

9

4
8
7

6

9

1
2
9
5
8
4
7
3
6

6

8

3
5

2

6

9

7

6

9

2

8

9

4
1
4

6

8

7

1

2

3

9

1

9

3

6

9

2

9

5
8
6
9
3
4
7
5
8
1
2
5
2

4

8

1
9

3

8

7
6

3

4

7

4

8

1
6
2

3

8

3

9

4

9

5
Figure 4: The Cell (R6,C9) Confirmed to be 8

Back to Forcing Chain

List of Sudoku Solving Techniques

Home Sudoku Privacy About
©2026 sudoku9x9.com - All Right Reserved.