Puzzles
Can generals surrounding a city ever fully trust a message passed by hand?
Several army divisions, each led by a general, surround an enemy city and can only communicate by sending messengers. They must unanimously agree to attack together or retreat together, since a divided attack would fail, but some generals might be traitors sending contradictory orders to sabotage the plan. Can the loyal generals always reach agreement despite the traitors?
Reveal the answer
Only if fewer than a third of the generals are traitors, and only using a specific messaging protocol; below that threshold, no algorithm using unsigned messages can guarantee agreement. Computer scientist Leslie Lamport posed the problem in 1982 to model how fault-tolerant computer systems can reach reliable consensus even when some components fail or lie.