text: morethan inifinty? consider a hotel that has an infinite number of rooms. each room contains a person and hence the hotel is full since all rooms and all people stretch to infinity.  now a coach turns up with 10 more people looking for rooms. how does the hotel manager fit the ten new people into his hotel? an excellent question.  here's what to do:  coach sends the first guy to room #1 and tells him to say "coach says this is my room.  move to the next one, and pass it on."  so he moves into room #1 and bumps the guy in #1 to #2, who bumps the guy in #2 to #3, etc.    in most hotels, you eventually get to a guy who was bumped out of his room and has no place to go because he was in the last room and the hotel was full, causing a problem.  but this is hotel infinity, so that kind of problem can never happen, even when every single room in the hotel has somebody in it, because there is no last room.    as soon as the first guy gets moved into room #1, coach sends the next new guy into room #1 and bumps everybody again, just like you just did.  when coach gets his 10 new guys moved in, he hits the showers.