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?
No, because if you have a room empty, you now have to identify the vacated room, which could take an infinite amount of time
Also, it would take up to an infinite amount of distance to walk to or from the front desk, so we just be dealing with immortal guests who have no time sensitivity at all
Furthermore, the room must be made ready and guests tend to check out at a certain time of day, so you would have to decentralize everything while accounting for light speed limiting the speed of information
Some of these problems are solvable if you add more constraints to the puzzle. Like, if you have a rate of check-in to checkout you could do something with statistics and discrete math to divide the infinity into an infinite number of sub hotels, and in doing so possibly guarantee availability for the guest in a long but linear amount of time
It would be an interesting programming/math puzzle. My intuition tells me it is solvable, but it might not be
Thanks very helpful :)
I’m glad. It was an entertaining thought puzzle
I hope you keep asking interesting questions
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.