Junior Mathematical Olympiad 2013 Section B Q14

On the $4\times5$ grid shown, I am only allowed to move from one square to a neighbouring square by crossing an edge. So the squares I visit alternate between black and white. I have to start on a black square and visit each black square exactly once. What is the smallest number of white squares that I have to visit? Prove that your answer is indeed the smallest. (If I visit a white square more than once, I only count it as one white square visited).