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5 pirates and 100 gold coins puzzle
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5 pirates and 100 gold coins puzzle

5 pirates of different ages have a treasure of 100 gold coins. On their ship, they decide to split the coins using this scheme:
The oldest pirate proposes how to share the coins, and all pirates remaining will vote for or against it.
If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain.

Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math) what will happen?

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Lets name the Pirates as
P1 = youngest pirate
P5 = eldest pirate

Explanation: Working backwards makes it easier to solve.

(two pirates remaining)
P1: 100
P2: 0

P2 must give all his coins to P1, otherwise P1 would vote to have P2 removed, leaving him with the remaining coins. Although this situation leaves him with no coins, it is the only situation that he is able to live.

(three pirates remaining)
P1: 0
P2: 1
P3: 99

P1 will vote to NO unless he is given 100 coins, as voting no will lead to the situation where he gets all coins. In order to be certain that P2 votes yes, P3 must only give 1 coin.

(four pirates remaining)
P1: 1
P2: 2
P3: 0
P4: 97

P1 and P2 know that the three-pirate situation will lead to them receiving less, so they vote YES.

(five pirates remaining)
P1: 2
P2: 0
P3: 1
P4: 0
P5: 97

P1 and P3 know that the four-pirate situation will lead to them receiving less, so they vote YES.

P1 will vote "yes" and get 2 coins
P2 and P4 will vote "no" and they won't get any coin.
P3 will vote "no" and get 1 coin
P5 will get 97 coins.

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