After a long season of plunder, a pirate team of five Prudent Pirates has amassed a booty of 500 golden coins. Before they part their ways, the five decide to divide the treasure.
They that they will each propose a division strategy in order of their seniority: first the oldest pirate will propose the strategy for the division of coins. All five will then vote on it, and if at least half vote "Yes", the strategy will be used to divide the coins. If the majority rejects the plan however, the oldest pirate will be killed, and the whole process will be repeated with the remaining pirates, with the second oldest proposing his strategy.
Since all the pirates are very prudent, each one will want to claim as many coins for himself without getting killed. Given this, how many coins will each of the pirates (5 - 1, with 5 being the oldest) get, and why? What strategy will the oldest pirate propose?
Label the pirates A-E with A being the most senior and E being the most junior (presumably wearing a bandana reading "Trainee"). If it got down to D and E, D would propose to keep the entire set of 500 gold coins, and E would have no recourse.
C knows this, so if it got down to C, D, and E, he (or she, so as not to be sexist, but I'll use "he" in the generic sense for the rest of this comment) would propose that at least one of them would be better off in the three-way deal than the 2-way. He can't offer D more than 500 pieces, so he would offer E a single gold piece to gain E's vote, nothing for D (why bother?) and the rest for himself.
B knows all this, and needs to keep one pirate other than himself happy. I'll assume that if one pirate is equally well-off regardless of the fate of his companions, then there is the risk that he'll vote for execution regardless. To ensure a 2-2 vote, B must make at least one of C, D, or E happier than in the previous case. In this case, either giving D or E an extra coin will make them happy, so a division of 498-0-0-2 or 498-0-1-1 will work.
A knows this, but doesn't know which of the two divisions B would propose. He needs to better that for two pirates. There are three ways to do it: 496-0-1-1-2, 496-0-1-0-3, or 496-0-0-1-3. Any of these will gain him the two votes he needs to keep most of the gold and his own life.
Solution
