This won't work for anything but the most basic puzzles. Brute force just constitutes basic gameplay. To solve a moderately advanced Sudoku puzzle you need to compare potential candidates in groups. Then it gets even more advanced with a handful of trial and error techniques.
This is not correct. If a Sudoku puzzle has one and only one solution, brute force can always find it. It is trial-and-error for every single cell and every possible value, which is guaranteed to succeed eventually. Sounds crazy for a human, but a 3 GHz computer microprocessor can rip through that in a second or two.
Well, a few seconds unless someone goes and feeds you a worst-case puzzle like the one in that wikipedia page anyway. (Yes, that is an entirely valid sudoku with a unique solution. In theory it can even be solved by hand quite easily by applying a simple set of rules. I checked both of these, though not manually.)
