8. Recall that Hilbert’s hotel has rooms numbered 1, 2, 3, 4, 5, . . . – one room for each positive integer. Guests are sometimes asked to move rooms, but never more than once a day. Guests are never asked to share a room with anyone else, and guests are never turned away. (a) Hilbert’s hotel is full when three more guests arrive. How can he find rooms for them? Be specific. (b) Hilbert’s hotel is still full the next day when a sudden electrical issue forces him to empty out the even number rooms. How can Hilbert find rooms for all the guests? Be specific