Here’s a puzzle I just came across; I think I’ve seen it before but I don’t remember the answer:
You have five pirates, ranked from 5 to 1 in descending order. The top 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. How should he allocate the gold in order to maximize his share but live to enjoy it?
Presumably only the bottom 4 pirates vote, not all five, and presumably if the top pirate gets killed, the process begins anew with Pirate 4 proposing a division and Pirates 1-3 voting.
My answer’s in the comments. Do you agree?
Also: suppose all the surviving pirates vote — including the one proposing the division. Does that change the answer?