Two armies must attack at the exact same time, but every messenger might be captured
Two allied generals camp on hills overlooking an enemy city, and can only win by attacking at exactly the same time. Their only communication is a messenger who might be captured crossing enemy territory. General A sends 'attack at dawn,' but can't be sure it arrived, so General B sends back confirmation, which General A then needs confirmed too, and so on forever. Can the two generals ever become certain enough to attack together?
Reveal the answer
No — no number of messages, however large, gives both generals simultaneous certainty, since the very last acknowledgment could always be the one that gets lost. The Two Generals' Problem, formalised in a 1975 paper, proves that perfect agreement over an unreliable channel is mathematically impossible, a foundational result behind why real networked systems settle for probabilistic guarantees instead.