Intelligent Pirates, huh?
There is a gang of five pirates, all of them having different ages. It is the time to share the loot among themselves.
Now, the sharing follows this mechanism:
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The eldest pirate proposes a plan to share the coins among themselves.
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All the pirates have to vote either in favor or against the plan.There is no possibility of any third opinion about the plan, like accept in bits and parts, and also no pirate can abstain from voting.
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Now, if the plan gets passed by half or more pirates then the loot is shared according to the proposal. For example, if there are five pirates then at least three need to say yes to the plan and if there are four pirates at least two of them need to approve it.
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However, if it is not passed by majority ,that is, by more than or equal to fifty percent, then the eldest pirate is killed and the same process continues with the new eldest pirate until the loot is shared.
Now, imagine you are the eldest pirate. Decide the way in which you will propose to share the coins in order to gain an approval of more than half the pirates and also have the maximum possible number of coins ( And, Of course you have to stay alive!).
Assumptions:
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All the pirates are as intelligent as you are.
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All the pirates (including you) are very greedy.
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Your gang has a loot of a total of 100 coins.
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Enter your Answer as follows: If you think that the ideal sharing pattern would be 90 to you, 4 to the pirate just younger than you, 3 to pirate number three, 2 to the second youngest and just a coin to the youngest give your answer as 9004030201.
Suggestion and tip: Do not focus on the "Hundred" coins, stress more on the approach to enjoy the sum.
The answer is 9800010001.
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The oldest pirate will propose a 98 : 0 : 1 : 0 : 1 split, in other words the oldest pirate gets 98 coins, the middle pirate gets 1 coin and the youngest gets 1 coin.
Let us name the pirates (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie.
Working backwards:
2 Pirates: Duncan splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal.
3 Pirates: Colin splits the coins 99 : 0 : 1. Eddie will accept this deal (getting just 1 coin), because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing.
4 Pirates: Billy splits the coins 99 : 0 : 1 : 0. By the same reasoning as before, Duncan will support this deal. Billy would not waste a spare coin on Colin, because Colin knows that if he rejects the proposal, he will pocket 99 coins once Billy is thrown overboard. Billy would also not give a coin to Eddie, because Eddie knows that if he rejects the proposal, he will receive a coin from Colin in the next round anyway.
5 Pirates: Alex splits the coins 98 : 0 : 1 : 0 : 1. By offering a gold coin to Colin (who would otherwise get nothing) he is assured of a deal.
(Note: In the final deal Alex would not give a coin to Billy, who knows he can pocket 99 coins if he votes against Alex's proposal and Alex goes overboard. Likewise, Alex would not give a coin to Duncan, because Duncan knows that if he votes against the proposal, Alex will be voted overboard and Billy will propose to offer Duncan the same single coin as Alex. All else equal, Duncan would rather see Alex go overboard and collect his one coin from Billy.)