1. A cat hops on posts arranged in a circle. There are 2n posts, with n red and n black. The cat can start at any post, and always hops to the next post in the clockwise direction, until it visits all posts. It wins" if, at every point during its trip, the number of red posts visited so far is always at least the number of black posts visited so far. In the figure below, the cat wins by starting at post 3, but loses if it starts at any other post. 2. 5 3 Prove that the cat can always win, if it starts on the right post. Prove this by induction on n for n > 1. Let your IH be that the cat can always win in the case where there are between 2 and 2(n 1) posts