Elmer Fudd is still trying to catch Bugs Bunny in the network of caves. Recall the rules: Bugs must move to an adjacent cave each day, and Elmer looks in one cave each day.
a) If there are 4 caves, is 2323 a winning strategy for Elmer (i.e., looking in caves 2, 3, 2, 3 on the first day)? Can Bugs hide in a sequence of caves to avoid capture?
b) If there are 5 caves, is 234234 a winning strategy? If yes, explain why it always works. If no, provide a sequence of caves that Bugs can hide in to avoid capture.
c) Suppose that, instead of being connected in a line, there are 6 caves connected in a circle so that there is a tunnel from the last room back to the first room. Come up with a strategy that guarantees Elmer will catch Bugs, or explain why no such strategy exists.
d) Consider again the circular case as in the previous question. Elmer Fudd has now enlisted the help of Yosemite Sam to catch Bugs. If there are 6 caves, come up with a strategy that will guarantee they will catch Bugs (Sam and Elmer each look in one cave each day). You will receive more marks for coming up with a more efficient solution.