The Screwy Pirates Brain Teaser

The screwy pirates teaser goes like this:

Five pirates plunder a chest filled with 100 gold pieces. Being democratic pirates, they agree on the following method of deciding the distribution:

The most senior pirate will propose a method of distribution, which is then voted on. His proposal succeeds if he gets at least 50% of the votes, and fails otherwise. If his proposal fails, he is made to walk the plank and the process repeats until a proposal is agreed to. You can make the following assumptions about the pirates:

1. They care about their lives first and getting as much gold as possible second

2. Given a choice of equal outcomes, they will choose to reduce the number of pirates by voting against the senior.

How will the gold be distributed?

The problem may seem a little daunting at first (it certainly was for me), but the solution is simple once you have broken the problem down by reducing the number of pirates the problem includes. Lets start with two pirates as having one pirate is irrelevant. We will define our pirates as pirate 5-1 in order of the seniority.

Two pirates: Pirate 2 will claim all the gold as he will get 50% of the gold regardless.

Three pirates: Knowing pirate 1 will vote against him if he offers him nothing, but also knowing that pirate 1 will get nothing if his proposal is not accepted, pirate 3 only needs to offer pirate 1 a single gold.

Four pirates: Pirate 4 knows that pirate 2 will get nothing if his proposal is voted against, as such, he only needs to offer pirate 2 a single coin to secure 50% of the vote.

Five pirates: Pirate 5 knows that pirate 3 and 1 will get nothing if his plan is voted down, therefore he only needs to offer pirate 3 and 1 one gold each to secure enough votes.

So we can see that, after the fifth case, a clear pattern has emerged. For any 2n + 1 pirates; n < 99, the most senior pirate will only need to offer pirates 1, 3, ..., 2n - 1, a single coin. For any 2n pirates; 1 < n < 99, the most senior pirate will only need to offer pirates 2, 4, ..., 2n - 2, a single coin.

Subjects

Math for Quant Interviews

Lessons

Brain Teasers - Problem Simplification