this post was submitted on 18 Aug 2023
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Oh, I think there is actually an open room at the hotel but it's all the way in the back. Just keep rolling, you'll find it.
> go to hilbert hotel
> "currently all the rooms are occupied but maybe we can do something for you"
> get placed in the first room
> woken up every 5 mins and asked to move one room over
Hah i remember getting asked to solve weird stuff with this hotel like: an infinite number of busses contanining infinite people show up at the hotel. How do you sort everyone by bus number? And stuff like that
Assuming an empty hotel the simplest solution i can think of is placing person k from bus b into room 2^b 3^k
For a filled hotel I'd move everyone from room n to room 5^n first I guess.
Our solution was to assign every bus to a prime number. Everyone on each bus would get the new bus number^n room. It broke the rules kinda but the teacher accepted it
Yeah, that's the same basic premise of using the fundamental theorem of arithmetic, I'm not sure of any particular pitfalls that come of it otoh. I'd probably mark it correct if I saw it on an assignment and move on. Though I guess it doesn't generalize as easily.
Idk to where the course went, but ultimately what the argument is getting at is that you can map the rational numbers, or pairs of integers (a,b) into the natural numbers without mapping to the same number twice.