The Pirate Puzzler

Since my prisoners' hats post seems to be the most frequently read post on my blog, I thought I'd put up another riddle. This was one of my favorites that a friend told me when he was practicing for finance job interviews.

4 pirates come across 1000 gold pieces. After a fair amount of arguing, the following system is chosen for divvying up the loot:

  • The pirates will draw straws. The order of straws will determine a fixed order for the remainder of the divvying process.
  • The first pirate (from the straw order) will propose a distribution of the gold. This proposal is put to a vote. If a majority (greater than 50%) of the pirates agree on the proposal, they distribute the gold appropriately and they are done. Otherwise, the first pirate is killed and they move onto the next pirate.
  • Assume that pirates are perfectly rational actors that vote based upon the following desired outcomes (in preferred order):
    1. A pirate wants to live.
    2. All else being equal, a pirate wants the most gold.
    3. If a pirate is going to live and will get the same amount of gold through two different outcomes, the pirate will vote to see more blood.

Given all of this, what does the first pirate propose, and what is the maximum amount of gold he can take?

The Prisoner's Hats

In an effort to encourage reader participation, I bring to you my first ever blog riddle. This riddle was told to me by Mike Metcalfe over dinner during the March meeting.

There was an evil king that wanted to kill 4 of his subjects, but worried that there would be an uprising if he simply had them executed, he decided to provide them with a way to escape their fate. What he did was to bury each of them in the ground up to their neck and he put a white or black hat on each of them. One of the subjects was placed behind a wall, so that he was not visible to the others. Example configuration: The Prisoner's Hats

Each prisoner could now only see what was in front of him. The king told the subjects that two of them were wearing white hats and two were wearing black hats, and if one of them could shout out the color of his own hat, all four of them would be set free. If any of them said something other than the color of his own hat, they would all be killed.

How do the prisoners escape?

The solution will be posted in the comments about a week from now, if someone out there doesn't post it first. UPDATE: Solution now available in the comments.