The well-renowned hotel of Bilzebab is famous for having an infinite number of rooms, and, being such a famous and well-renowned hotel, the hotel is fully booked.
Ten tourists arrive at the hotel and ask if there are any rooms available for them.
Bilzebab is also famous for having a smart and quick-thinking manager. The manager thinks for a minute, and then says:
"Yes, of course, I'll just reorganize the current arrangements, and you will all get a room".
In which rooms will the newcomers stay?
Please note: After the manager has reorganized the room arrangements, no one will share a room, no one will be thrown out, and the hotel will still be fully occupied.
Each person, including the one already with rooms, will have to be given a specific, calculable, new room number. Saying "go to room infinity plus 1" is not valid.