I have been reading this thread with interest. I too have delved into SU Doku a bit, writing an Excel based (VB) solver without resorting to matrix math. I was able to program solution techniques that worked for easy and medium puzzles, but the difficult puzzles require deeper insight than I have been able to distill into code. I may resurrect it some day...
In the process, I also came to appreciate that producing the starting puzzle (for which there is one and only one possible solution) is maybe a more difficult problem. I've seen several puzzle producing programs that rely on "testing" to verify uniqueness.
Obviously there are a finite number of arrangements of the numbers (0-9) in the 9x9 Su Doku square. What's fascinating me (and what bears on the OP question) is how many valid puzzles can be formed with the same arrangement as their answer.
For each arrangement, there must be a minimum number of squares that reveal just enough to allow it to be solved. I'm sure that these numbers have to be in certain locations. I wonder if there are multiple valid minimum solutions. On the flip side, I wonder what the maximum number of numbers one can reveal without revealing enough to allow a solution. I also wonder if these answers vary from arrangement to arrangement.