Aye Aye, Captain!
Five pirates have obtained 10000 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).
The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye" (which means they agree), the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.
If the captain fails to obtain the support of at least half his crew (which includes himself), he and the pirates agreeing with him faces a mutiny, and all pirates will turn against him and the ones who support him and make them walk the plank. The pirates start over again with the next senior pirate as captain.
What is the maximum number of coins the captain can keep without risking his life?
Clarification: Assume that if a pirate gets coins than he would vote for the captain's proposal.
The answer is 9998.
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1 solution
The answer is 9 9 9 8 .
There are 5 pirates. So at least two other pirates have to vote for the captain's decision so that the pirate need not to risk his life. If the captain takes gives a very small amount of coins to two pirates, those two pirates will vote for him and thus he does not have to risk his life. So the minimum value the captain can give to one pirate each is 1 coin (Giving 0 coins would mean that they would not get the coins and thus would turn against him). So if gives 1 coin each to any two other pirates, he will win the vote and thus have 1 0 0 0 0 − 1 − 1 = 9 9 9 8 coins for himself.