5 pirates sharing the booty
You have five pirates, ranked from 5 to 1 in descending order. The highest ranked pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. And the process begins again. How should he allocate the gold in order to maximize his share but live to enjoy it? (Hint: One pirate ends up with 98 percent of the gold.)
Don't trust an indifferent pirate to vote for you.
Pirates be nasty folk (Arrgh!), and for that reason #5 can't count on votes from #1 and #2 unless he actually gives them a better deal than they can get from #4. They might sadistically decide to enjoy #5's demise before collecting their loot. So he can give just 1 gold to#3, but he has to give 2 to #1 or #2.
Also, #3 doesn't have to give any gold to #2 in the 3-pirate scenario, because if #2 doesn't vote for #3's proposal, #2 will die in the next round.
In some formulations of this puzzle, the ambiguity is resolved by assigning pirates' motives, in descending order of importance:
- seeing others killed
For pirates who aren't bloodthirsty
If the pirates don't care one way or the other about seeing their comrades killed, so that they vote randomly yes or no when presented with a choice between two otherwise equal rewards, then my solution is still best because it guarantees pirate 5 will survive even if the random votes go against him.
To allow him to give away only 2 gold and still be sure that his solution will be accepted, we must change the pirates' motivations to
Dividing the loot as equally as possible in 3 (or 5) portions doesn't meet the puzzle's constraint that the pirate in control should maximize his personal return. I take your point, though: this particular pirate society isn't going to survive very long unless they change their rules.
- shedding as little blood as possible