The Pirate Problem for Discrete Math?
Five pirates, who are perfect logicians, have three priorities in the following order:
1. Staying alive.
2. Obtaining as much gold as possible.
3. Killing other pirates.
In other words, these pirates will do whatever it takes to stay alive. After that priority is met, every pirate will choose gold over killing.The five pirates come upon a treasure chest of 100 gold coins. They agree that they each will draw straws to determine order, first through fifth, and then each pirate in turn, starting with the one with the shortest straw, will suggest how to split the gold coins. All (living) pirates will vote on the proposal. If a proposal fails to receive a majority vote (more than 50%), the pirate making the proposal is killed, and the next pirate makes his proposal. Consider the order of the pirates to be A, B, C, D, and E. Which pirate’s proposal will be the one accepted? What is the proposal? Explain the logic.
I like this problem – it’s giving my brain a workout.
I think the way to tackle this problem is by looking at what would happen in reverse cronology.
If there were two pirates left, pirate E would vote against Pirate D no matter what he said because then E would get all the gold and kill another pirate.
If there were three pirates left pirate E would vote against pirate C no matter what and pirate D would vote for pirate C no matter what to avoid certain death if pirate C dies. Pirate C would then propose that he get all the gold to maximise his profit.
If there were 4 pirates left, pirate C would vote against pirate B no matter what to try to force the 3 pirate outcome. Pirate E would vote for any proposal where he gets any gold to avoid the 3 pirate outcome where he gets none. Pirate D would also vote for any proposal where he gets any gold also to avoid the 3 pirate outcome. Pirate B would propose to give one gold coin each to Pirate E and D and keep the rest for himself.
If there were 5 pirates, pirate B will vote against any proposal where he gets 98 coins or less. Pirate C will vote for any proposal where he gets at least one coin and pirates E and D will vote for any proposal whereby they get more than one gold coin to avoid the 4 pirate outcome. Pirate A will propose that pirate C gets one coing and pirate D or pirate E gets 2 gold coins.
Nobody needs to get killed and they all live happily ever after, especially pirate A.
Lloyd, a gold coin, and Fat Monster
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