January 26–February 1, 2010

Problem

A ship of five pirates have 2010 gold coins and agree on a process for dividing up the money:

The most senior pirate—the captain—proposes a distribution. All the pirates vote. If more than half agree, this becomes the distribution, and the process ends. If not, the most senior pirate must walk the plank, and the same process is carried out with the remaining pirates. If only one pirate remains, he gets all the coins.

These pirates think its great fun to make others walk the plank. If they can do this for free, they won't hesitate. However, they are so greedy that, given a choice between throwing somebody overboard and getting some money, they will always opt for the money.

All the pirates are very clever logicians.

The problem: What is the greediest distribution that the captain can get away with?

Solution

here

List of solvers

Enkhbileg Ganbat, Daniel Jeffrey Nollette, Mel Jen, Matthew Inouye, Daniel Nollette, Benjamin Eilers, Eric Bensley (undergrad); Hardik Bati, Benny Zhang, Congpa You, Brad Heller, Joshua Towne, Philipp K. Janert, Lloyd Sakazaki (outside).

Benjamin Eilers wins the prize!