One day, Dumbledore assigns Harry Potter the task of obtaining the Philosopher’s Stone that lies in an inner chamber surrounded by many rooms. To guide him along, he is given the Marauder’s Map which contains the following graph
Harry wishes to color every wall with colors such that walls that meet at a corner get different colors. Harry also wishes to color every room so that adjacent rooms get different colors. What is the minimum number of colors to accomplish this?
(a) 4 colors for walls and 4 colors for the rooms
(b) 3 colors for walls and 4 colors for the rooms
(c) 2 colors for walls and 3 colors for the rooms
(d) 2 colors for walls and 5 colors for the rooms