Hilbert's Infinite Hotel
A hotel that's always full — but never has to turn anyone away
How can a hotel with no empty rooms still make space for a new guest?
Picture a hotel with infinitely many rooms. Not a thousand, not a million. Endless.
Tonight it is completely full. Every room has someone in it. Then one more guest walks up to the front desk.
There is no spare room anywhere, and yet nobody has to be turned away. Here is how.
Some thought needed