Hilbert imagines a hypothetical hotel with rooms numbered 1, 2, 3, and so on. The hotel is full and new guest arrives wanting a room. I can not move any guest. So i say to new guest wait 1 sec a new room must become available as Infinite guests one must leaving at any time.
is this good answer?
Those would all also a problem in the original and are never relevant. For the bus with infinite guests, every current guest has to move. So some of the now vacant rooms are infinitely far away and also none of them are ever prepared by staff etc.
The problem with OPs take is the wrong assumption that a room will be ensured to become available.
I wouldn’t call it a wrong assumption, it’s just ambiguous. We don’t know the constraints
An infinite hotel would need either infinite housecleaners or none at all, so it’s a relatively minor part of the problem
OPs assumption is: “there are infinite guests, so at any point someone will be checking out at that exact moment.”
Under the information given by the problem, making that assumption is wrong. In fact, assuming any of the guests will ever check out is already wrong. The problem never makes any mention if checkout at all. All guests checking out a millisecond after checking is just as likely of a scenario as them never checking out until the death if the universe.