just for fun, here is what is supposed to be the shortest program, in python, that can solve a sudoku grid:
def r(a):i=a.find('0') if i<0:print a [m in[(i-j)%9*(i/9^j/9)*(i/27^j/27|i%9/3^j%9/3)or a[j]for j in range(81)]or r(a[:i]+m+a[i+1:])for m in`14**7*9`]r(raw_input())
hmm ok it's quite cryptic and I don't think it matchs your question so I apologize for this noise :)
Anyway you'll find some explanation of these 173 characters here.
There's also an explanation in french here