Extra rules for Complete Sudoku

Within each group of three rows, the values 1,2,3 (shown here in red) all have to be in different columns. The values 4,5,6 also have to be in different columns as do 7,8,9. Similarly, within each group of three columns, the values 1,2,3 all have to be in different rows as do 4,5,6 and 7,8,9. For example

8 5 1

2 9 4

6 3 7

3 7 6

5 1 8

9 4 2

4 9 2

7 3 6

1 5 8

1 8 5

7 6 3

4 2 9

6 9 3

8 2 4

1 5 7

2 4 7

9 1 5

6 8 3

5 7 2

3 4 8

9 1 6

4 8 1

2 6 9

7 3 5

3 6 9

5 7 1

8 2 4

is valid, but the following is not because (for example) in the first three rows there is a 1 in the same column as a 2.

8 5 1

9 4 2

7 6 3

3 7 6

5 1 8

9 4 2

4 9 2

7 3 6

1 5 8

5 1 8

6 3 7

4 2 9

6 9 3

8 2 4

1 5 7

2 4 7

9 1 5

6 8 3

2 7 5

3 8 4

1 9 6

4 8 1

2 6 9

7 3 5

3 6 9

5 7 1

8 2 4

In the SuDoku applet, clicking the checkbox "Complete" means that these extra constraints are incorporated. Generated puzzles can be solved using them, and will have a unique solution if this is requested. Note that a puzzle with only one "Complete" solution may well have multiple solutions if the extra constraints are ignored.

It is not yet clear whether the difficulty arising from having to use the extra constraints is offset by the fact that the constraints reduce the number of possibilities to consider.

Back to puzzle