How do you solve this?
At a HOTEL INFINITY, the clerk claims to have infinitely many rooms. A man thought that it was for reals so he brought his friends to the hotel to check it out. When the man came there, there was a sign that says, "NO VACANCIES". The man was bummed out but insisted to the clerk that there was a way to fit all of this friends. (Note: the man brought infinitely many of his friends with him) The man told the clerk that there was a way to fit him and his infinitely friends in the hotel without kicking or sharing anyone out of their rooms - everyone will have their own room and will be happy! By the end of the day, the man and his infinitely many friends managed to get their own rooms without kicking or sharing with anyone.
QUESTION: How did he do it?
- Sorry if it was a bit confusing...
It was easy, but a very long day. At the end of the day, time had finally ran out.
Can you explain that a bit more? I'm still a bit confused...
You just move the persons to the next room. Person in room 1 goes to room 2 person in room 2 goes to room 3 etc. Then room 1 will be free.
No problem! Let's break down the problem and see how the man and his friends managed to get their own rooms without kicking anyone out or sharing.
First, let's establish some key points:
1. The hotel has infinitely many rooms.
2. The initial scenario was that there were no vacancies, meaning all the rooms were occupied.
To find a solution, we need to think outside the box and consider the infinite nature of the hotel. Since the man brought infinitely many friends with him, we can take advantage of this concept.
The solution is based on the idea of "shifting" occupants from one room to another. Here's how the man accomplished it:
1. The man asked the occupant of Room 1 to move to Room 2.
2. Then, the occupant of Room 2 moved to Room 4.
3. The occupant of Room 3 moved to Room 6, and so on.
By following this pattern, the occupants of all odd-numbered rooms shifted to the next highest even-numbered room. This created an infinite number of vacancies in all odd-numbered rooms.
Now, the man and his infinitely many friends could move into the odd-numbered rooms since they were previously occupied but now vacant. Therefore, everyone had their own room without kicking or sharing with anyone.
This solution illustrates the infinite nature of the hotel, allowing for the continuous shifting of occupants and resulting in everyone having a room.