Murder you
Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).
The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.
If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain.
What is the maximum number of coins the captain can keep without risking his life?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
I'll start by numbering the pirates from the least senior (pirate 1) to the captain (pirate 5). Working backwards, let's start by considering what happens if there are only two pirates. Only 1 vote is needed for the proposal to be approved, so pirate 2 would take all 100 coins and vote for his own proposal. Pirate 1 would vote against it, but it wouldn't matter.
If there were 3 pirates, 2 votes would be needed to approve the proposal. Pirate 3 will of course vote for his own proposal, but he needs 1 more vote. He can't possibly get pirate 2 to vote for it, but it only takes 1 coin to get pirate 1 to vote for his proposal. This is because pirate 1 knows that if the proposal is voted down, he gets no coins. So pirate 3 will keep 99 coins and give 1 to pirate 1, and pirates 1 and 3 will out-vote pirate 2 in that scenario.
If there were 4 pirates, 2 votes would be needed to approve the proposal. Pirate 4 will vote for his own proposal, and he needs one more vote. The cheapest way to get that vote is to offer pirate 2 one coin, since pirate 2 would otherwise expect to walk away with nothing.
Now we consider what happens if there are 5 pirates. It takes 3 votes to approve the proposal, so pirate 5 needs to give two other pirates an incentive to vote to approve whatever he proposes. In the 4 pirate scenario, pirates 1 and 3 don't get any coins, so if pirate 5 offers them each a single coin, he can get their votes and survive. He can also keep the other 98 coins.