IT-CESENATICO 1995 Problem 3

In a town there are four pubs, $A,B,C,D$ , and any two of them are connected to each other except $A$ and $D$ . A drunkard wanders about the pubs starting with $A$ and, after having a drink, goes to any of the pubs directly connected, with equal probability. (a) What is the probability that the drunkard is at $C$ at its fifth drink? (b) Where is the drunkard most likely to be after $n$ drinks ( $n > 5$ )?