This question was posed in my Discrete Mathematics class:

Hotel Infinity is a hotel with one hallway. Doors on the right are odd numbered while doors on the left are even numbered. You enter Hotel Infinity tired and you want a room but the manager says that it is full. How can you get a room? (*Hint: The guests are very accomodating so long as each has a room to themselves.)

If you figured that question out, you return to Hotel Infinity with an infinite number of friends. How do you and your friends each get your own room?

And lastly, if you figured that out you truly have superior intelligence. Here is my question to you...You return finally with an infinite number of friends who each brings an infinite number of friends. How do you all have a room?

Thank you for reading.

-Dan