Five pirates have obtained 100 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”, 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 support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him 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?
98.
He gives a coin to the most junior and the second senior explains as follows:
If there are two pirates the most senior just votes for himself and gets all of the loot
If there are three pirates the most senior gives a coin to the most junior and then the junior realizes that if he doesn’t vote for the most senior it will come to the 2 pirates and he’ll get nothing.
If there are four the most senior does the same as if there were 3 giving the coin to the most junior and explaining that is there comes to 3 or 2 pirates he gets nothing
But there are 5 so the second senior and the most junior realize that they will get nothing if they don’t go along.