for the variant with conditions:-

Squares with circles must have numbers 1, 2, 3

Squares with squares must have numbers 4, 5, 6

and empty squares must have numbers 7, 8, 9.

Filled in below are numbers 4, 5, 6, 7, 8, & 9. but how do you determine where numbers 1, 2, and 3 go without resorting to advanced techniques.

- Code: Select all
`---------+----------+---------`

4 12 7 | 6 9 12 | 5 8 3

23 5 13 | 4 12 8 | 9 6 7

8 6 9 | 7 5 3 | 2 4 1

---------+----------+---------

5 9 2 | 8 4 7 | 13 13 6

7 8 6 | 1 3 5 | 4 9 2

1 3 4 | 2 6 9 | 8 7 5

---------+----------+---------

6 12 5 | 3 8 4 | 7 12 9

9 4 13 | 5 7 12 | 6 123 8

23 7 8 | 9 12 6 | 13 5 4

---------+----------+---------