The Hanover Collaboration

Sorry it’s been so long. I think this one comes from Drysdale in which case several of you have heard it already.

You’re minding the desk at the Infinity Hotel that has infinity¹ rooms, an infinitely large lobby and a very impressive intercom system that allows you to speak with everyone at once just by pressing a button.

It’s labor day and the entire place is booked. Not a single empty room.

0: A weary traveller comes to your desk and asks, “Do you have any vacancies?” to which you reply, “No, but I can still give you a room.”

How do you do it?

Rules: Everyone has to have a finite room number assigned to them. You are only allowed to say finitely many words.

Convenience: This hotel uses keycards that can be reprogrammed automatically.

1: Infinity Bus drops off an infinite tour group who queue to your desk. You’re like, “Shit, my girlfriend will be pissed if I work late tonight.” The tour director comes up to you and says, “Do you have room for us?” to which you reply, “But of course, this is the Infinity Hotel.”

How do you do it and still make it home for dinner?

Convenience: You have a machine that takes a credit card and issues a keycard.

¹ Math geek notice: I’m going to use the word infinite with deliberate sloppiness. Pretend I don’t know better. Let’s not needlessly complicate the discussion. If I see even one aleph in the comments, you’re not getting another puzzle for months.