The Paradox: A hotel with infinite rooms can always accommodate more guests, even when completely full.
1 Guest: Everyone shifts to room n+1. Room 1 is free.
Bus (∞ guests): Everyone moves to room 2n. All odd rooms are free.
∞ Buses: Uses prime factorization: 2^bus × 3^seat
The Answer: The hotel never runs out of space for countably infinite guests!
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