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multiple solutions to the original pirates problem

IMHO, there is more than one solution to the original pirates problem posted on this website. Let me explain with an example.

Say there are 10 pirates and 100 gold coins. The solution I propose here is that the first pirate, P1, could keep 96 coins to himself, and can distribute the remaining 4 gold coins to pirates P3, P4, ..., P10, one each, in any combination (Note that P2 doesn't get any). All P1 has to do is to randomly pick 4 guys from the set {P3, P4, P5,.., P10}, give them a coin each, and they are guaranteed to vote for him.

Why?

The pirates that get the one coin are guaranteed to vote in favor of P1, for that is the maximum they are ever likely to get even if P1 gets killed and P2 gets to distribute the loot; Being non-violent, they'd happily take the one coin they are offered, and vote in favor of the first person that offers it.

PS: The number of ways P1 can distribute the 4 coins among {P3, P4, P5,.., P10} is (8 choose 4), for a total of 70 solutions. In the original pirates problem posted on this website(5 pirates, 100 coins), the number of solutions is (3 choose 2) = 3.

Ashwin Bhagavatula
Wednesday, March 10, 2004

It never said they were non-violent, though - without that evidence, you'd have to assume that they're unswayed one way or the other by violence, and are just as likely to go for a solution in which someone dies as not. Do you want to trust your life to a 50/50 chance?

Mark Wotton
Friday, May 14, 2004

Mark,

The puzzle only mentions that the pirates are motivated by greed, and nothing else. Besides, I did make my assumption known that they are considered non-violent.

You do have a point nonetheless; If the pirates are assumed to be violent, there is only one distribution possible that does not have the distributor killed.   

Ashwin Bhagavatula
Wednesday, June 16, 2004

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