So here is an interesting question. This actually appeared in a job interview at Google too. 🙂 So give it a shot if you’re keen. There are many ways to solve this, one can solve it mathematically using optimisation, or using Game Theory’s Backward Induction.
There are five pirates who have to split 100 gold coins. They all line up and proceed as follows:
1. The first pirate in line gets to propose a way to split up the gold coins (for example: everyone gets 20 gold coins).
2. The pirates, including the one who proposed, vote on whether to accept the proposal.
3. If the proposal is not accepted by more than half the number of pirates, the pirate who made the proposal gets killed, and the next pirate in line then makes his proposal for voting.
4. If the proposal is accepted by a majority, they then split the gold coins according to the proposal and enjoy them.
5. The process continues until a proposal is accepted or there is only one pirate left.
6. Assume that
(a) every pirate above all wants to live;
(b) if a pirate will be alive, he wants to get as much gold as possible;
(c) if a pirate will receive a same amount of gold, he prefers to see any other pirate killed, just for fun;
(d) each pirate knows his exact position in line;
(e) all of the pirates are excellent puzzle solvers.
What proposal should the first pirate make in order to maximize his share while live to enjoy it?
The solutions will be posted in a few days here.