5 Pirates Fight for 100 Gold Coins

♠ Posted by GeekyFry in , at 9:44 AM

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.
Now how does Pirate 5 devise a plan which will be accepted for sure and also maximizes his gold?
(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 :)

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