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Email your solutions to solution@math.colostate.edu. Indicate your status (undergrad/grad/faculty/other) and school affiliation or city of residence if you are not affiliated with a school.
One winner each week is eligible for a free ice cream and topping, courtesy of Cold Stone Creamery.
Correct solutions for Part 1: Tim Ellis, Kyle Thayer (CSU undergrads), Byungsoo Kim (South Korea), Andrew Johnson (Colorado School of Mines). Andrew was the only one who managed a flawless solution to the difficult bonus problem (Part 2). Kyle drew the ice cream. Congratulations to all solvers!
The problems again: Let us generalize the pirate puzzle to the case of n pirates and m coins (see Challenge 6). As we will see, a shortage of coins can cause the pirates to get meaner.
Part 1 (For the ice cream): Suppose m = 0, that is, there is no money to fight over, and they are just voting on whether different people go overboard, stopping when somebody gets a majority to vote in his favor. Which of the n pirates will go overboard? Consider what happens for different values of n.
Part 2: Solve the general problem of n pirates and m coins. The problem breaks down into a few simple cases where you can tell whether a pirate is doomed, and, if not, how he should distribute the bribes.
For this problem, it is necessary to clarify something about the pirates' behavior. Given a choice of one gold coin in the hand or an uncertain payment of a larger amount, a pirate will opt for the gold coin in the hand. (Though this seems to runs counter to pirates' reputation for taking risks and gambling, the explanation is that the pirates are all broke at the moment and the boat is coming into port that evening.)