Five ferocious pirates sacked Shanghai and escaped with 100 gold sovereigns. It’s now time to divide the booty between them. In decreasing order of seniority, they are: Able Ahab, Barnacle Bill, Crusty Chris, Dangerous Dave, and Eloquent Ed. Whatever they do, in dividing the loot, they must obey the Pirate’s Code. The Pirate’s Code: The most junior pirate begins by suggesting a distribution of the gold coins then all the pirates take a vote. If at least half of the pirates reject the offer then the junior pirate is executed and the bargaining continues with the next most junior pirate. Otherwise, the offer is accepted.
The Puzzle: Assume that the pirates are clever logicians, so that they can analyze this problem completely. Also assume that the pirates have the following priorities (in order): to protect their own lives, to maximize their profits, to kill their fellow pirates. What distribution of the gold sovereigns should Ed propose?
Further thoughts: If you manage to solve this problem, think about what would happen if there were 6 pirates. To start with, we need to clarify one of the conditions. Rather than saying that the pirates try ‘to maximize their profits’ (a somewhat vague notion), we’ll insist that each pirate tries to maximize their minimum profit.
For example, Ahab may be faced with two choices. Following the first path, he may win 90 gold coins or 10 gold coins, depending on the choices of the other pirates. However, let’s suppose that following the second path he could win 50 gold coins or 11 gold coins. According to our principle, he’d choose the second path. The reason is that the minimum winnings are 10 coins and 11 coins respectively. So the second path maximizes his minimum profit.
Using this idea, you should be able to solve the 6 pirates problem, then solve the n-pirate problem for arbitrary n. Can you write a computer program that simulates the arbitrary problem?