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.
If you switch tracks he can always destroy the ship, it's not necessarily the same ship he approached but it's still a ship to destroy.
If he goes to the grand Hilbert Hotel he will be pushing tyne boulder forever because there are infinite rooms so he can never get it done.
But a man is content with a job, so they say. However i only looking forward to being finished at work for the day so i can move onto my own goals.
Unfortunately I'm not part of the 1% where i only need to work on my own goals, but there are many people born into wealth and so nothing with their lives but really enjoy it. They can do what ever they want when ever they want.
So Sisyphus will be happier destroying the ship and then moving into what ever he wants to really do.
To my admittiddly basic knowledge they never specify height to floor size or sisyphus's boulder size. So if he has a big enough boulder and the hotel is infinitely tall with 1 room per floor he could take out the building with just rolling through a single weight bearing wall.
This being a hypothetical, Sisyphus only exists inside our imaginations. We MUST imagine Sisyphus as happy, regardless of whether or not he actually is. Those are the rules.
Happy Sisyohus, unknown artist - 2023.
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