5 Pirates Puzzle

5 pirates want to distribute 1000 coins among themselves

5 Pirates and 100 Gold Coins

There are 5 pirates who want to distribute a 100 coins amongst themselves.  Following are the rules they set up for coins distribution:-
  • The senior most amongst the 5 will propose a distribution.
  • If he gets at least a 50% approval, then his idea will be accepted and the coins will be distributed accordingly.
  • If he does not get a 50% approval, he will be thrown overboard and the next senior most pirate will give a distribution.
  • Again his proposal will go through the same procedure as above.
However since these are pirates we are talking about, each pirate wants two things:
  • To survive
  • To get the most coins
  • To see the other pirates die
Assuming all this, how would you think the pirates will go about the distribution? Also calculate the maximum coins each of the pirates can get through their proposed methods.

5 Pirates and 100 Gold Coins

There are 5 pirates who want to distribute a 100 coins amongst themselves.  Following are the rules they set up for coins distribution:-
  • The senior most amongst the 5 will propose a distribution.
  • If he gets at least a 50% approval, then his idea will be accepted and the coins will be distributed accordingly.
  • If he does not get a 50% approval, he will be thrown overboard and the next senior most pirate will give a distribution.
  • Again his proposal will go through the same procedure as above.
However since these are pirates we are talking about, each pirate wants two things:
  • To survive
  • To get the most coins
  • To see the other pirates die
Assuming all this, how would you think the pirates will go about the distribution? Also calculate the maximum coins each of the pirates can get through their proposed methods.
5 pirates want to distribute 1000 coins among themselves

Solution

Let us name the pirates A, B, C, D and E, such that A is the senior most pirate and from there the hierarchy goes down alphabetically.

Understanding all the facts, the following cases can arise for each pirate.

Case:1- Where pirates A , B and C are dead.

D will propose  the following distribution

D = 100 , E = 0 

between himself and E. Since there are only two pirates who are alive D gets 50% of the votes and his proposal is accepted. E won’t get any coins but will survive.

Case 2:- Where pirates A and B are dead,

 

C being next in line will propose the following distribution

C = 99 , D = 0 , E = 1

C will not give D any coin because if C dies, D can get all the coins(as seen in case 1).

E will vote in favor of this distribution because if C dies D will take all the coins and E will get nothing (case 1) here at least he is getting 1 coin.

Case 3:- Where pirate A is dead.

 

B will distribute the coins like this:

B99 , C0 , D = 1 , E0

He will not give C any coin because C will most likely vote against B. Since C profits more with B dead(case 2).

B will also not give any coin to E for the same reason. B will give a coin to D, and secure 50% of votes, because D knows that if C distributes he will get no coins(case 2)

Case 4: Where A distributes the coins.

 

A distributes the coin in the following way:

A = 98 , B 0 , C =  , D = 0  , E = 1

He will not give any coins to B and D as they know they will profit more from A’s death(case 3), and therefore will vote against A.

Since there are 5 pirates, A needs to bribe two pirates C and E to get the majority. C and E will support E because if A dies B will not give them any coins(case 3)

Therefore these are the possible cases that will happen. 

From the above the maximum number of coins that each of the pirate can get following their distribution:

  • E-0 (will not get any chance of proposing a distribution)
  • D-100 (case 1)
  • C-99 (case 2)
  • B – 99 (case 3)
  • A-98(case 4
there are 5 pirates who want to distribute 100 coins
there are 5 pirates who want to distribute 100 coins