# 5 Pirates Fight for 100 Gold Coins Puzzle

Puzzle: There are 5 pirates in a ship. Pirates have hierarchy C1, C2, C3, C4 and C5.C1 designation is the highest and C5 is the lowest. These pirates have three characteristics : a. Every pirate is so greedy that he can even take lives to make more money.  b. Every pirate desperately wants to stay alive. c. They are all very intelligent.There are total 100 gold coins on the ship. The person with the highest designation on the deck is expected to make the distribution. If the majority on the deck does not agree to the distribution proposed, the highest designation pirate will be thrown out of the ship (or simply killed). The first priority of the pirates is to stay alive and second to maximize the gold they get. Pirate 5 devises a plan which he knows will be accepted for sure and will maximize his gold. What is his plan?

Solution:
To understand the answer,we need to reduce this problem to only 2 pirates. So what happens if there are only 2 pirates. Pirate 2 can easily propose that he gets all the 100 gold coins. Since he constitutes 50% of the pirates, the proposal has to be accepted leaving Pirate 1 with nothing.

Now let’s look at 3 pirates situation, Pirate 3 knows that if his proposal does not get accepted, then pirate 2 will get all the gold and pirate 1 will get nothing. So he decides to bribe pirate 1 with one gold coin. Pirate 1 knows that one gold coin is better than nothing so he has to back pirate 3. Pirate 3 proposes {pirate 1, pirate 2, pirate 3} {1, 0, 99}. Since pirate 1 and 3 will vote for it, it will be accepted.

If there are 4 pirates, pirate 4 needs to get one more pirate to vote for his proposal. Pirate 4 realizes that if he dies, pirate 2 will get nothing (according to the proposal with 3 pirates) so he can easily bribe pirate 2 with one gold coin to get his vote. So the distribution will be {0, 1, 0, 99}.

Smart right? Now can you figure out the distribution with 5 pirates? Let’s see. Pirate 5 needs 2 votes and he knows that if he dies, pirate 1 and 3 will get nothing. He can easily bribe pirates 1 and 3 with one gold coin each to get their vote. In the end, he proposes {1, 0, 1, 0, 98}. This proposal will get accepted and provide the maximum amount of gold to pirate 5.

Difficulty level of the puzzle : High

### 3 Thoughts on “5 Pirates Fight for 100 Gold Coins Puzzle”

1. Don’t quite understand the solution.
1. Why would Pirate 4 (in 4 pirate case) or Pirate 5(in 5 pirate case) die?? Is it not the highest designated Pirate who is at risk i.e. Pirate 1 who is in charge of doing the distribution??

2. Mohit chouhan on March 30, 2017 at 11:09 am said:

“So what happens if there are only 2 pirates. Pirate 2 can easily propose that he gets all the 100 gold coins. Since he constitutes 50% of the pirates, the proposal has to be accepted leaving Pirate 1 with nothing”

I don’t understand the base itself..it is clear that majority should agree with the decision, so how come in case of two pirates one says he will take all 100. pirate 2 constitutes equal percentage as the pirate 1 so both 50% no majority..if one plans to get all 100 the other can disagree at the same time

3. Patrick Wooldridge on August 12, 2017 at 10:06 pm said:

In the last line of the question and in the answer, you have reversed the numbering system. The question should be, “What plan can C1 propose that is certain to be accepted and which maximizes his share?” and in the answer, you should continue the designations Cn.