Dividing up the loot…
Five rational and extremely greedy pirates, ranked from most senior to most junior, have 76 gold coins to divide amongst themselves. They have agreed to use the following method to divide them, and we know that they will all abide by the final result:
The most senior pirate will propose a split, and all the pirates will vote on it. If 50% or more vote for the proposal, then they split the coins as proposed, otherwise the most senior pirate has to walk the plank and the next most senior pirate will propose a split to begin the system again.
However, apart from this agreement, the pirates do not trust each other and they will not make or honour any other agreement. The pirates are also a murderous lot, and would rather another pirate walked the plank so long as they got the same number of coins themselves. Knowing all this and that all of the other pirates know it too, what should the most senior pirate propose so that he gets as much treasure as possible?