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5 pirates of different ages got a treasure of 100 diamonds. First the oldest of them will propose a scheme how to divide the diamonds. If 50% or more voted for the oldest, the scheme will be followed. (Including the person making the scheme can vote). Else the oldest will be killed and the process will be repeated with the next oldest. How will the diamonds be divided? Each pirate wants to gain as much as possible. Can anyone please explain.

5 pirates of different ages got a treasure of 100 diamonds. First the oldest of them will propose a scheme how to divide the diamonds. If 50% or more voted for the oldest, the scheme will be followed. (Including the person making the scheme can vote). Else the oldest will be killed and the process will be repeated with the next oldest. How will the diamonds be divided? Each pirate wants to gain as much as possible. Can anyone please explain.

Grade:10

2 Answers

Arun
25763 Points
2 years ago
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.
SR Roy
128 Points
2 years ago
Respected Sir,This answer is already there in Google. Can you please make it simpler. I cannot understand this properly.Regards SR Roy

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