Considering this simple case, it will take just the time for the slowest guest to move to the next room as they can all take their luggage and move to the next room that should be vacant by the time they reach it.
However, this is considering a magic comms system that lets all guest know to move a room instantly. In the case this is not available, the speed of light is the limiter and then it takes forever.
Using the case with instantaneous communication, it is possible to take forever by trying to host a countable infinite amount of people as this is usually done by moving the original guests to the room that is double the current one and the new guests to each odd number left. In this situation, the original guests will take forever as for bigger numbers, the guests have to move more and more rooms each time.
Sorry for the rant, I’ve seen too many Hilbert hotel videos
Considering this simple case, it will take just the time for the slowest guest to move to the next room as they can all take their luggage and move to the next room that should be vacant by the time they reach it.
However, this is considering a magic comms system that lets all guest know to move a room instantly. In the case this is not available, the speed of light is the limiter and then it takes forever.
Using the case with instantaneous communication, it is possible to take forever by trying to host a countable infinite amount of people as this is usually done by moving the original guests to the room that is double the current one and the new guests to each odd number left. In this situation, the original guests will take forever as for bigger numbers, the guests have to move more and more rooms each time.
Sorry for the rant, I’ve seen too many Hilbert hotel videos
Perhaps the hotel staff bring in a guest each day at a preset time. They just have to all move rooms at 5pm.