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.
hexaflexagonbear [he/him]
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Cake day: July 29th, 2020
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> 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
111·1 year ago“How do you remember how to do this?”
“… I have the documentation I sent you open”
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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.