How few filled cells could appear on a valid Su Doku puzzle?
I aim to produce a definitive answer to this question shortly – the answers are at most 8 for 3×2 Su Doku, 19 for 3×3 Su Doku and 42 for 3×4 Su Doku. (See the Su Doku Brain of Britain page for examples of such puzzles.) I haven’t constructed a mathematical proof in order to demonstrate these values – it’s just that, as yet, I haven’t been able to build puzzles with fewer initially-filled cells.