### Brain Teasers

# Hotel Infinity

You need a place to rest for the night and come across a hotel called Hotel Infinity. It has infinite rooms. You walk in, ask for a room, and the clerk says, "We're full right now, but hold on a second." Then he gets the person in room one into room two. Then, room two moves into room three, and so on and so forth. You are getting settled in your room, when a bus from Busline Infinity pulls up an Infinite amount of mathematicians in town for the Big Number Expo. What order does the clerk give to make room for them?

### Hint

You can't do what he did the first time to make room for you.### Answer

He tells you in room one to move to room 2, the person in room 2 to room 4, room 3 to room 6, 4 to 8, so on and so forth.Hide Hint Show Hint Hide Answer Show Answer

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## Comments

i don't get it. surely if he has an infinite amount of rooms to begin with , then at any given time he should always have some empty, if for some reason they are all full, then he can't have had an infinate amount, because that would make impossible to run out of empty rooms. i think.

though i could be wrong!

though i could be wrong!

you have to think abstractly

also, your saying infite rooms is possible, but not infinite people

If the infinity hotel is booked how is he suppose to get the others in a room that he just moved into a room that will not be taken. Because at the end the Infinity person would have to go into room 1

Does infinity ever end? And don't say you have to think abstractly beacuse infinity os endless

er...aren't you the one that said "think abstractly"???

yes, but no matter how abstract you think, infinity still goes on forever!

you left out half of the solution. by multiplying all the room numbers by 2, that leaves all the odd numbered rooms available, of which there are infinitely many. Check out this link (it's a long read, but i'm guess it is also the "inspiration" for this teaser): http://www.c3.lanl.gov/mega-math/workbk/infinity/inhotel.html

ahhh so moggmatt ripped off this teaser

well, thecically i made it into a teaser

I like this, but it is a bit of a rip - off!

This a famous problem of course, posed by Sam Cantori and follows a topic hotly debated and studied by George Cantor (some say he went mad thinking about infinity), The topic of the Hotel and the buses is well set out at http://www.c3.lanl.gov/mega-math/workbk/infinity/inhotel.html

Sheesh... if was previously on floor 5,000,000,000, I'd be in for a nice couple of months on the elevator... or worse... if they didn't have an elevator..

I didn't even try to guess the answer, but even after reading it, I had to actually think about it. It's really good though. My old Trig teacher would love it.

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