(a) Anton is at vertex A of a square ABCD. Each second he moves to an adjacent vertex, picking at random. (For example, if he is at vertex B, then he moves to vertex A or C with equal probability.)

He stops when he reaches vertex C. What is the average (ie mean) time he takes to stop?

(b) Now Anton is at one vertex of a cube; he moves each second to a randomly chosen adjacent vertex. He stops when he reaches the opposite vertex (ie the one furthest away from his starting vertex). What is the average time he takes to stop?