Ok here's a real math riddle.?

Question

Ok you are an expert on the concept of Infinity. One night very late, you check into the Infinity Hotel, which happens to have an infinite number of rooms.

But the desk clerk tells you that even though they have an infinite number of rooms, there are an infinite number of people staying there that evening, and only one person is allowed in a room at a time. You, being an infinity expert, come up with a simple way to get a room for the night. How do you do it? (no, you don't go in a room and kill somebody and throw the body out or something like that)

Answer 1

Yawn....have everyone move to the next room down. Then I take the first room.

Now, what if there are infinitely many new customers? Just have each old customer go to the room whose number is double the one they started in. Then the new customers go to the odd-numbered rooms.

Here's an even better version:
http://answers.yahoo.com/question/index;_ylt=AgsY4PrQxhKVKw_6oFT0hr3sy6IX?qid=20060710132524AAVviJt

Answer 2

You don't need to worry.
For infinite number of people, there are always infinite number rooms in Infinity hotel. You as an individual is part of that infinity, therefore the will always be an n^th room for the n^th person and a (n+1)^th room or the (n+1)^th person.
Enjoy your stay at the Infinity Hotel.

Answer 3

For this question:
"infinite" = "infinite +1" = "infinite -1" = "infinite +/- anything".
Therefore, there will be room for the "infinite +1" person

For Nancy:
After the 2 dollars taken by the bell hop, the three guys actually paid 25 + 2 = $27 ($2 for bell hop, $25 for room)
On average , each person paid for the room 25/3 = $8.33

Bell hop $2
Customer A paid $8.33
Customer B paid $8.33
Customer C paid $8.33
The total is $27 ($30 paid to counter - $3 refund)

Answer 4

I don't know the answer to this one, but I have another one for you. Three friends check into a hotel for the night. They ask the man at the front desk how much it will be. He tells them it is $30 for the night. They each hand over $10 and pay the man at the fron desk. The 3 friends go up to their room and the man at the front desk and the bell hop start talking. The man at the front desk feels guilty because he over charged them. The room rate is really only $25. He takes $5 out of the register and gives it to the bell hop and tells him to give it back the the 3 friends. On the way up to the room the bell hop decides that he is going to keep $2 for himself, and give each man back $1. After he gives them back their dollar each, each of the friends has paid $9 for the night. 9 x 3 = 27 add the 2 that the bell hop kept = 29. Where did the other dollar go?

Answer 5

If there is an infinite number of rooms for an infinite number of people, you are covered and have a room.

I'll bet room service would take forever though. Not to mention the wait for the elevator.

Answer 6

As I am a mathmetician, I noticed the question says that " you check into" the infinity hotel. As I am checking in they already have my reservation and room. No moving people required.
However we mathematicians also like our solitude and this hotel sounds infinitely crowded, so I think I will leave and go someplace that has a pool and a free breakfast.

Answer 7

Well since there are an infinite number of rooms. Here is the solution.

Move person in room #1 to room #2

Move person in room #2 to room #3

and so on...since there is an infinite number of rooms there are enough rooms to accomodate this procedure. Now through this procedure room #1 is empty and everyone who had a room to begin with still has a room.

Answer 8

For nancy -

The $2 the bellhop is holding is part of the $27 (9 x 3) paid by the guests. You can't add it to the $27; that would be double counting. The guests paid $25 for the room, the bellhop is holding $2, that's a total of $27.

Answer 9

Ask for your key and go back to your room. If there are an infinite number of people with rooms, and you are a "people", then you already have a room.

Answer 10

Simple, infinity + 1 = infinity, there's still room left.