Booked for Schoolies Week yet?

If not, how about trying Hotel Infinity, it's never full!

Quinn (from the TV show Sliders) runs Hotel Infinity.

It extends right through a wormhole connecting this universe to other possible universes and there are a countably infinity number of rooms.

Actually, on the 1st of April this year, Diane and I decided to try it. We arrived to find every room was occupied. Quinn however was not worried. He asked all the guests to shift to the room two doors down and gave us the keys to rooms 1 and 2. Only half an hour later an infinite number of avid sliders arrived for a conference. But every room was occupied. "Have the odd numbered rooms" said Quinn and he moved the existing guests into the even numbered rooms.

How did he do it?

Quinn moved every guest the following way. Diane and I had rooms 1 and 2 and we were moved to 2 and 4. Say you had room No. x then you would go to 2x.