Here is a considerably harder version of the Forty thieves puzzle.
Five bloodthirsty pirates have just procured 100 gold pieces, which they must now divide up amongst themselves. They agree that the captain will propose a settlement, deciding how many gold pieces each pirate receives. Then all five pirates will vote on the proposal. If more than half of the pirates accept the proposal, it will stand, otherwise the captain must walk the plank. Then, the next highest ranking pirate would propose a new settlement, with the same rules. Each pirate is perfectly logical, greedy and bloodthirsty. How should the captain divide the loot to maximize his take and save his neck?
Forty thieves - same idea, but a vote passes if 'at least' half of the thieves accept the proposal, making it a good deal easier to solve.