Sudoku boards are traditionally rank 3. That means there are 3^2 rows and 3^2 columns and 3^2 possible digits.
We will begin testing with a rank 1 board. Such a board has one row,
one column, and only one valid number: 1. Thus there is only one solution. [[1]].
Then we'll move on to the rank 2 board. This has 4 rows, 4 columns, and
4 valid numbers [1 2 3 4]. They have the form:
[[d d d d]
[d d d d]
[d d d d]
[d d d d]]
Once that is solved, I expect the general case to be solved as well.