01 Oct '11 19:57

A hotel has an infinite number of rooms, which are all fully booked, but that's no problem as the guests are flexible. They are accustomed to being moved to another room, up to once a day, to make more space, as long as they are clearly told where to go.

On the first day, a thousand new people show up and need rooms. This is easy for the manager, everyone is given a new room by moving from room n to room n + 1,000, which vacates rooms 1 .. 1,000 for the new arrivals.

On the second day, an infinite number of new people arrive. How are they given rooms?

On the third day, an infinite number of buses arrive, each with an infinite number of people. How does everyone now get a room?

On the first day, a thousand new people show up and need rooms. This is easy for the manager, everyone is given a new room by moving from room n to room n + 1,000, which vacates rooms 1 .. 1,000 for the new arrivals.

On the second day, an infinite number of new people arrive. How are they given rooms?

On the third day, an infinite number of buses arrive, each with an infinite number of people. How does everyone now get a room?