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.
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.