Sudoku Solving Techniques

Locked Candidates - Block Within Row

In a row of a Sudoku puzzle, it may happen that a specific digit cannot be determined its exact position yet, but it is locked in a few cells as a candidate. That means the digit must be in one of a few cells. If these cells happen to fall in the same block, then this digit cannot be a candidate for other cells in that block.

Let's demonstrate this more clearly with an example.

Example
C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9

1

6

4
8

1

3

5
7

3

6

2
9

1

2

5

1

5

3
6
9

1

2

7

4

8

4

8

9

6

7

2

6

7

4

2

3

8
5
1

3

6

4

5

6

8

1

4

5

6

8

2
9
7
3

2

3

4

5

8

3

4

5

6

8

2

4

5

6

8

9
7

4

5

6

8

1

2

4

8

1

4

8

1

2

4

8

7

2

8

9
1

3

8

3

4

6
5

2

4

7

1

9

5
2

1

3

9

6
8

1

3

9

4

1

8

2

1

6

8

9

1

3

4

5

1

3

4

5

1

4

5

9

1

3

5

1

3

5

6

7
3
4

1

6

8

7

9

1

5

7

2

6

9

1

5

6

Figure 1: In Row R6, Digit 8 is Locked in Three Yellow Cells

In row R6 of this Sudoku puzzle, the digit 8 is a candidate for three yellow cells (R6,C4), (R6,C5), and (R6,C6). In other words, the digit 8 in row R6 is locked in these three yellow cells, and one of them must be 8.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9

1

6

4
8

1

3

5
7

3

6

2
9

1

2

5

1

5

3
6
9

1

2

7

4

8

4

8

9

6

7

2

6

7

4

2

3

8
5
1

3

6

4

5

6

8

1

4

5

6

8

2
9
7
3

2

3

4

5

8

3

4

5

6

8

2

4

5

6

8

9
7

4

5

6

8

1

2

4

8

1

4

8

1

2

4

8

7

2

8

9
1

3

8

3

4

6
5

2

4

7

1

9

5
2

1

3

9

6
8

1

3

9

4

1

8

2

1

6

8

9

1

3

4

5

1

3

4

5

1

4

5

9

1

3

5

1

3

5

6

7
3
4

1

6

8

7

9

1

5

7

2

6

9

1

5

6

Figure 2: Three Yellow Cells Fall in the Same Block B5

The three yellow cells (R6,C4), (R6,C5), and (R6,C6) happen to fall in the same block B5.

C1
C2
C3
C4
C5
C6
C7
C8
C9
R1
R2
R3
R4
R5
R6
R7
R8
R9

1

6

4
8

1

3

5
7

3

6

2
9

1

2

5

1

5

3
6
9

1

2

7

4

8

4

8

9

6

7

2

6

7

4

2

3

8
5
1

3

6

4

5

6

8

1

4

5

6

8

2
9
7
3

2

3

4

5

8

3

4

5

6

8

2

4

5

6

8

9
7

4

5

6

8

1

2

4

8

1

4

8

1

2

4

8

7

2

8

9
1

3

8

3

4

6
5

2

4

7

1

9

5
2

1

3

9

6
8

1

3

9

4

1

8

2

1

6

8

9

1

3

4

5

1

3

4

5

1

4

5

9

1

3

5

1

3

5

6

7
3
4

1

6

8

7

9

1

5

7

2

6

9

1

5

6

Figure 3: Digit 8 Cannot be a Candidate for Orange Cells in Block B5

Since one of the three yellow cells in block B5 must be 8 and each block cannot contain the same digit more than once, other cells (marked in orange) in block B5 cannot be 8. Therefore, the candidate digit 8's in these orange cells can be safely removed.

Other Examples

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