5 Pirates Puzzle
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.
- To survive
- To get the most coins
- To see the other pirates die
5 Pirates and 100 Gold Coins
5 pirates want to distribute 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 50% approval, then his idea will be accepted and the coins will be distributed accordingly.
- If he does not get 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.
Solution
Let us name the pirate’s 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 him 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 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:
B = 99 , C = 0 , D = 1 , E = 0 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 the 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 = 1 , 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 pirates 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
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