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The Infinite Hotel Paradox

Hilbert's Grand Hotel has infinitely many rooms, all occupied. A bus with infinitely many new guests arrives. Design an algorithm to accommodate all new guests without anyone losing their room. Then handle infinitely many buses, each with infinitely many passengers.

Constraints
Rooms are numbered 1, 2, 3, ... to infinity. Each guest must have exactly one room.
Examples & Scenarios
Scenario: Single infinite bus
Hint: Consider moving existing guests
Scenario: Infinite buses
Hint: Think about prime numbers

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Submitted By

Coders Crush Team

12/11/2025

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