5 Pirates

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?

Hints and solutions available here.

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?

7 Responses to “5 Pirates”

  1. So, I have a couple of questions about the rules. But my solution is as follows:
    A : 1
    B : 1
    C : 0
    D : 0
    E : 98
    Am I close?

  2. Hi Dave, that’s really close and is basically the answer for the 4 pirates problem! Have you looked at the hints on the original page?

    With the 1, 1, 0, 0, 98 proposition, neither of Ahab, Bill, Chris, nor Dave will vote for Ed. Dave knows he can do better. Ahab, Bill, Chris, and Dave can’t do any better than what Ed’s offered them, but they’ll vote to kill Ed anyway as they can’t do any worse, and they’re bloodthirsty!

  3. Aha! So that was one of my questions. So you’re telling me if a pirate can do no worse then he will vote to kill, right?

  4. Absolutely. These pirates take the free market concept to the ultimate extreme. Unless you profit from their lives, kill your competition!

  5. Thank you for sharing!

  6. I came up with the same solution as David, but after reviewing it against the actual solution I realised I needed that small calibration. 🙂

    These are excellent quizzez! Thanks a lot!

  7. my grand father used to have those old spanish gold coins in stock-;~

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