In the universe Roomeron, there are infinitely many planets. Each planet has an infinite number of hotels, and each hotel has an infinite number of rooms. Since the business is so great, you decide to build a hotel of your own, also with an infinite number of rooms. To keep track of the rooms, each is numbered starting at 1. The hotels and planets are similarly numbered.

During the current tourist season, every room of every hotel, (including yours) on every planet is full. A freak catastrophe occurs in every other hotel besides yours and their rooms become trashed. The guests from those hotels ask to stay in your unwrecked hotel.

How can you put the infinitely many guests from infinitely many hotels from infinitely many planets in your already full hotel?

(In reply to Another solution by Avin)

I was really taken aback by the criteria of assigning guests to atheron's piece of paradise.

At first I couldn't understand the reason of assigning each new guest with a set of numbers unique to the planet, hotel and room of their departure and attempt to map it to atheron's hotel.

The formula is clever.

Posted by brianjn on 2007-02-01 09:34:59