Can You Solve the Pirate Riddle?

In the video riddle below, we explore the distribution of pirates' booty. It gets complicated.

The scenario is this: Amaro is the captain of a pirate ship. His mateys, Bart, Charlotte, Daniel, and Eliza, are the other members of the crew. The group has come upon a bounty of 100 gold coins, and now must divide it up among the group according to "the pirate's code."

The code stipulates that Amaro, as captain, gets to suggest the first plan for distributing the coins among the five pirates. After that proposal, each pirate (including Amaro) votes "yarr" or nay on whether to accept the proposal. If the proposal results in either a tied vote (equal numbers "yarr"/nay) or a majority of "yarrs," it passes and the coins are immediately distributed. If it fails to meet this threshold, Amaro must walk the plank, making Bart the next captain. (Amaro walking the plank removes him from future votes, as well as eligibility for coin disbursals, on account of his death. Yuck.)

This process now repeats with Bart as captain, and the captain's hat will be passed on, in order, to Charlotte, Daniel, and finally Eliza. (If it gets all the way to Eliza without a passing proposal, she gets the booty.)

To make the situation more complex, there are rules governing how the pirates act. First, they each want to stay alive (that's their highest priority), but their next priority is maximizing their personal gold horde. Second, they distrust each other—there are no alliances and they cannot collaborate on a strategy. Third, they are bloodthirsty, and would love to see a fellow pirate walk the plank if they think it won't affect their own gold distribution. Fourth, each pirate has excellent logical deduction skills, and they're aware that everyone has the same skills. For the purposes of the puzzle, we can assume everyone is logical and obeys all the rules.

So we arrive at the key problem for Amaro: What distribution should he propose to ensure he lives and maximizes his own gold return? In order to figure this out, we have to walk through the chain of events and sort it out. Get your scratch paper ready!

The video below explains this puzzle (and its solution); here are the "rules" as stated at the 1:48 freeze-frame:

1. The captain makes a proposal for splitting up the 100 gold coins, which everyone votes on. A proposal that gets a tie or a majority of yarrs passes. A proposal with a majority of nays fails, and the captain has to walk the plank. The new captain then makes a proposal. The order of succession is Amaro, Bart, Charlotte, Daniel, and Eliza. 2. Each pirate's primary objective is to stay alive. 3. Each pirate's secondary objective is to maximize his or her gold. 4. Each pirate will vote to make the others walk the plank, all other results being equal. There are no abstentions. 5. Each pirate knows that the others share the same set of preferences. 6. Pirates cannot collaborate, make promises to each other, or form alliances; there is no communication outside the proposal and the votes, and no other trickery like murder or bribery. Even though they're pirates. 7. Each pirate is a perfect logician and all of them know this about each other.

Think on this a bit, and for the answer, have a look:

For more on the puzzle, check out this TED-Ed page. For a solution (and longer/more complex versions), read this PDF of an article by Ian Stewart.