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The Byzantine Generals' Problem

Imagine a time during the dark ages, where a pirate ship is under attack. There are 200 pirates aboard the pirate ship surrounded by six army ships of 50 warriors each, who've anchored, surrounding the pirate ship. Each army ship is commanded by a captain. The 300 warriors can easily overpower the 200 pirates aboard the pirate ship. However, if they don't all attack simultaneously, there is a very real risk that the warriors will be outnumbered by the pirates and they'll go on to lose the battle.

Figure 1.2: Pirate ship (200) surrounded by arm ship (50)

So, how can the captains all agree on the same time to attack the pirate ship? These days, we'd simply need a quick group video-conference call, and the captains would have to agree to attack at 22:00 hours (10 PM).

However, back in the dark ages, things were a little more complicated:

The 22:00 attack message could only be passed on by a sailor on a small boat. He has to sail around each army ship, visiting each captain in turn to confirm.
Any captain may be a traitor and in league with the pirates in the pirate ship.