Riddle time!

[Mirasol]

Yes Jitter, you got it!

[Mebediel]

Aha whoops this thread was very active in the days I was away

latin riddle: (though I highly doubt this is the answer)

Spoiler: show

a nut

Yes! And there is one more possible answer!

[afreude]

I just joined the forum and immediately was intrigued by this riddles thread!


Is the other answer to the Latin riddle

Spoiler: show

a riddle?

Here's one:

There exists an infinite hotel with rooms numbered 1, 2, 3, 4 ... and so on forever.  All of the rooms are occupied.  An infinite tour bus arrives with another [countably] infinitely many guests.  Can the hotel accommodate them?  How?


(I did read through the whole thread to see the riddles, and I see that there is at least one member who probably already knows the answer to this.)

[wavewright62]

I just joined the forum and immediately was intrigued by this riddles thread!


Is the other answer to the Latin riddle

Spoiler: show

a riddle?

Here's one:

There exists an infinite hotel with rooms numbered 1, 2, 3, 4 ... and so on forever.  All of the rooms are occupied.  An infinite tour bus arrives with another [countably] infinitely many guests.  Can the hotel accommodate them?  How?


(I did read through the whole thread to see the riddles, and I see that there is at least one member who probably already knows the answer to this.)

I don't know, but our quarantine facilities would love to know the answer!

[Groupoid]

Came across this thread after/during the Great Forum Restructuring. The riddle about the infinite hotel could be an exercise of a maths lecture (some introductory course or a set theory lecture). Thread necromancy:

Spoiler: A solution • show

There are a lot of different approaches, here's one of them.

First make an infinite amount of room in the hotel, by moving every person to the room with double their current room number. (n -> 2n. For example the occupant of room 5342 goes to room 10684, or the occupant of room 111 goes to room 222).
This leaves all the (infinitely many) odd numbered rooms empty.

Then we enumerate the people in the buses. I don't want to write down the enumeration procedure yet, 'cause its a bit technical. Just assume, every person trom the buses has got their unique natural number. We may also require, that for every number there is a passenger with this number, if we like.
Now we assign the first passenger to the first odd-numbered room of the hotel, the second passenger to the second odd-numbered room etc. (passenger n goes to room 2n-1)
Then we're done and have filled the whole hotel again.

[SkyWhalePod]

I don't have anything smart to say, I just wanted to give a verbal thumbs-up at Groupoid's necromancy. Love the infinite hotel problem and its solutions.

[catbirds]

Thanks for the explanation, Groupoid!

I'm glad this sort of thing doesn't exist! If I were unfortunate enough to be in room, say, a million, I'd probably be a pile of dust before I got to room two million…

[afreude]

Groupoid, you are exactly right.  I think it's straight out of the first week or so of set theory (or possibly just intro to proofs, it's been a long time) showing why the sets of natural numbers, integers, rational numbers, etc. are all the same size.

I always thought it was a really clever and accessible way to help explain countably infinite sets.  It's pretty easy to take that idea and say: okay, everyone in the hotel is a positive integer, and everyone on the tour bus is a negative integer, and just line them up the same way so now we see that natural numbers and integers are sets of the same size.



What prompted your username?  I'm assuming topology or category theory/logic type interests?

[Groupoid]

Yeah, though it's only little more than name dropping, I haven't studied groupoids much. I know them as fundamental groupoids of a space and that ∞-groupoids form a model of some type theories and haven't yet encountered them in a lecture.

Sorry, only saw your question today and am going on holidays (with little internet) right now.