A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the 5 pirates: 1, 2, 3, 4, and 5 in order of rank. The pirates have the following important characteristics:
* Infinitely smart.
* Bloodthirsty.
* Greedy.
Starting with pirate 5 they can make a proposal how to split up the treasure. This proposal can either be accepted or the pirate is thrown overboard. A proposal is accepted if and only if a majority of the pirates agrees on it.
What proposal should pirate 5 make?
The idea behind the solution to this puzzle is that a pirate will accept a proposal only if he knows that in case he would not accept the proposal, he would get less of the treasure.
If pirate 1 would be the only one left, he would get all the golden coins. If only pirates 1 and 2 would be left, pirate 2 would die for sure, since pirate 1 is bloodthirsty and will reject all proposals of pirate 2 (since he will get all coins anyway). So:
When also pirate 3 would still be alive, he needs the agreement of one of the other two. Pirate 2 will agree with every proposal since, as we have seen, he would die if he didn’t. So pirate 3 should propose to keep everything for himself.
When we have four pirates, pirate 4 should make two other pirates agree with his proposal. So he proposes to give one coin to pirate 1, one coin to pirate 2, and the rest to himself. Pirates 1 and 2 will accept the proposal, since they are greedy, and if they wouldn’t accept, they would get less.
But as we know, there are five pirates. If pirate 5 gives both pirate 1 (or 2) and pirate 3 one coin more than in the previous case, they are willing to accept the proposal. Then a majority (three out of five) of the pirates will support the proposal, and pirate 5 can keep the rest of the treasure to himself.
Conclusion: Pirate 5 should propose to give two coins to pirate 1 (or 2), one coin to pirate 3, and the remaining 997 coins to himself.