But the hotel of interest has infinitely many rooms , so if you move the guest occupying room NUMBER@1 to room NUMBER@2 , the guest occupying room NUMBER@2 to room NUMBER@3 and so on , you can fit the newcomer into room NUMBER@1 .

First , move the guest in room NUMBER@1 to room NUMBER@2 , the guest in room NUMBER@2 to room NUMBER@4 , the guest in room NUMBER@3 to room NUMBER@5 , the guest in room NUMBER@4 to room NUMBER@6 , and so on .
