My 12-year-old daughter argued that the hotel is too expensive to build. I postulated that room i+1 costs only half as much as room i, and that the guests shrink as they are moved to higher numbered rooms. She conceded that such a hotel could exist.
My 15-year-old daughter argued that the moving of guests fails. For example, what happens to the guest in room number infinity? I said "there is no room numbered infinity". She responded, "then what number is it?", and the whole family felt that she won.