The puzzle of distributing the pirates’ booty prompted some great analyses by readers (in addition to some nice words and video clip from Chris). What was particularly nice about the responses is that the puzzle itself was solved assuming things that are normal in logical puzzles, but the responses did not stop there. Several creative inputs explored other scenarios, and that adds to the fun.
To recap, five pirates want to distribute 100 pieces of gold. The captain proposes a distribution and the group votes on it. If at least half support it, the deal is done. If it fails, the majority mutinies and kills the captain. The next strongest pirate is elected captain and the process repeats. Each pirate knows where he is in the pecking order. The captain wants to keep as much of the loot as possible, but does not want to face mutiny. What is the most favorable distribution for the captain that will be guaranteed to pass?
Reader Chris Moore might be a physicist because he approached the problem the same way I did. Like many puzzles, this one can be solved by starting with the simplest version rather than tackling the puzzle as presented. If we assume that three distributions have failed and only two pirates are left, then the final captain simply takes the whole pot and the remaining pirate gets nothing. Once we see that, then consider the case immediately preceding with three pirates.
As Barry Etherridge pointed out, the second pirate will always be motivated to vote against any distribution that does not overwhelmingly favor him. If his vote tips the balance to a mutiny, he wins big. The captain knows this and so he gives the third pirate a single doubloon. This is more than he would get any other way, so he supports the vote.
The rest of the analysis goes essentially as Chris suggests with the final distribution of 98 — 0 — 1 — 0 — 1. I doubt many people would guess the captain could come away with that much.
However, the joy of solving puzzles includes stepping outside the logic box. Ramus wisely observes the captain can schedule the distribution to take place in the next morning and then throw a celebration party with lots of grog for his fellows. While they sleep it off, the captain can take all the money and split. There is a downside to this solution in that the “proper” method follows rules and even though the others might not like it, they have agreed to follow the rules. This might protect the captain. However, if he breaks the rules by essentially stealing the pot, then he can expect to be hounded by outraged pirates. That can disturb the tranquility of retirement.
In the original post, I said this puzzle had been presented to me and I did not know its origins. Here is a link to the same basic puzzle. It is a link to Wikipedia — what else? This link also refers back to a Scientific American issue, and that might be the origin. If I had not been enchanted with the surprising result, I might have tried searching for it a bit more diligently — at least I would have checked Wikipedia first! So what could have been a clever new puzzle turns out to be a classic of a sort used to illuminate the strange things that can happen in a economically driven situation.
Note that the answer would change greatly if the captain had an ongoing desire to continue to work with his crew. The Wikipedia version does not emphasize that aspect.
Also, the answer would change greatly if the captain had a code of conduct that demanded a “fair” distribution. This is not trivial. We would not have suffered the global economic meltdown of the last few years if most of the financial leaders had been less like the captain and more human. That sort of connection back to the real world promotes a pleasantly harmless puzzle into an object lesson of how money really gets distributed in our society.
Along that line, refer back to the comments. John Swallow introduced the concept of real Caribbean pirates and how they behaved. He quotes some of their agreements. Note that among the people we consider to be bloodthirsty and without law, that they limit the top guy to only one and a half share of prizes. Lesser officers got one and a quarter shares. What would our legitimate society look like if the CEOs of corporations were limited to one and half times the average salary for their companies and the CFOs got only one and a quarter?
Another interesting aspect of pirate life is that corporate funded medical care was part of the employment agreement.
So this puzzle is not only fun and a brain teaser/exerciser, but it can teach us something about the consequences of choices made for purely economic reasons and something about morality in management. Not bad for a little puzzle.
If you like puzzles and have found some you think can entice readers to exercise their minds in trying to solve them, please let me know. If they have some underlying meaning, so much the better. Making up new puzzles is fun, but it can be time consuming. Waiting for a colleague to present a challenge can mean waiting a long time.