Describe a problem you've solved or a problem you'd like to solve. It can be an intellectual challenge, a research query, an ethical dilemma-anything that is of personal importance, no matter the scale. Explain its significance to you and what steps you took or could be taken to identify a solution.

Imagine you are a foreign tourist that has just arrived to a town. In that town theres the Hilbert´s Hotel, internationally recognized for being the only hotel with infinite rooms. When you arrive to the lobby, you ask the manager to give you a room:

Manager: "Im terribly sorry, but an infinite group of people has just arrived and all the rooms are full"
You: "How is that possible? I thought you had infinite rooms
Manager: "Indeed, but they are now full"
You: "But that´s impossible... if there are infinite rooms they can´t all be full. I know there´s a way for me to get a room"

What would you do? You really need that room to spend the night...

NOTES: All the rooms are listed from one to infinity and only 1 person is able to stay per room.

SOLUTION

You: "Look friend, all you have to do is tell the infinite group to move up one room, so the person staying the room 1 will move to the 2, the 2 to 3, the 3 to 4 and so on to infinity and i can take the room number 1. That way all the tourists, including me, would have a room."

EXTENSION OF THE PROBLEM

What would you do if two infinite groups of tourist´s arrives? How would you place them in the Hilbert hotel?

(hint: pair numbers are also infinite)

Significance of the problem

This particular problem is very interesting to me because it forces me to think out of the box something not only amusing but necessary to sort out day to day events.