He thought very hard, then picked up his radio and asked everybody to move to a room with number twice as large as his current room's number. So the person from room 1 moved to room 2, and so on. Mentor draws the movements, asking the student where should people from different rooms go. Now let's look at the rooms. The guy from room 1 went to room 2, so the first one is empty.
Mentor draws full rooms and empty rooms, every time asking the student if the room is full or empty.
Mentor stops a couple of rooms after the student notices the pattern . Every next room is empty now. Yeah, all the rooms with odd numbers are empty, and all the rooms with even numbers are full. Mentor shortly discusses multiplication by 2. One of the most impressive paradoxes in mathematics happens when people start to move out of the Hotel Infinity.