Problem #27 MEDIUM
The Hotel That Never Fills Up
Microsoft Meta Pattern Recognition Math
Problem Statement
Imagine a hotel with a room for every positive integer — room 1, room 2, room 3, and so on without end. Every single room is currently occupied. A new traveler arrives at the front desk and asks for a room. The manager smiles and says there is no problem. Later that evening, an infinitely long coach arrives carrying a passenger for every positive integer. The manager accommodates all of them too. How?
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