Consider the Byzantine Generals problem. Two generals are on hills either side of a valley. They each have an army of 1000 soldiers. In the woods in the valley is an enemy army of 1500 men. If each general attacks alone, his army will lose. If they attack together, they will win. They wish to send messengers through the valley to coordinate when to attack. However, the messengers may get lost or caught in the woods (or brainwashed into delivering different messages). How can they devise a scheme by which they either attack with high probability or not at all?