5 pirates discover a chest containing 100 gold coins. They decide to sit downand devise a distribution strategy.

The pirates are ranked based on their experience (Pirate 1 to Pirate 5, where Pirate 5 is the most experienced).

- The most experienced pirate gets to propose a plan and then all the pirates vote on it.
- If at least half of the pirates agree on the plan, the gold is split according to the proposal.
- If not, the most experienced pirate is thrown off the ship and this process continues with the remaining pirates until a proposal is accepted. The first priority of the pirates is to stay alive and second to maximize the gold they get.

(Assume all the pirates are intelligent and rational)

Possible Solution:

This solution needs a backward approach like many other puzzles.

Let us start with 2 pirates (starting with 1 pirate doesn’t make sense). In this case pirate 2 (more experienced) gets the 1st chance to decide and obviously he will choose to keep all the 100 gold coins as he himself constitutes 50% vote.

In case of 3 pirates, Pirate 3 gets the 1st chance to decide the distribution. He knows if his distribution is not accepted, pirate 2 will get everything (he is next one to decide) and pirate 1 will get nothing. So he needs to bribe pirate 1. He can give 1 gold coin to pirate 1, 0 to pirate 2 and rest 99 to himself –> {Pirate 1, Pirate 2, Pirate 3} = {1,0,99}

Since pirate 1 is rational and knows if he doesn’t accept this proposition, he will end up getting nothing (case of 2 pirates). So 1 is better than nothing and he will accept this proposal.

Now, lets discuss the situation in case of 4 pirates. Pirate 4 knows if his proposal is not accepted, he will die and pirate 3 will get 99 gold coins and pirate 1 will get 1 gold coin

**while pirate 2 will get nothing.**So he needs to bribe pirate 2. So pirate 4 would propose the distribution as {0, 1,0,99} . Pirate 2 would accept it as he knows if he doesn’t, he will end up getting nothing.

Now let’s come up with the actual solution in case of 5 pirates. If pirate 5’s proposal is not accepted, pirate 1 and pirate 3 end up getting nothing. So he needs to bribe these 2. So he would propose a s distribution as

**{1, 0, 1, 0, 98}**.

This should be accepted by Pirate 1 and Pirate 3

## 0 comments:

## Post a Comment