Five ruthless pirates have just claimed an enormous treasure, and the time has come to divide it. As you might imagine, any sense of loyalty goes flying overboard, and each pirate plans to keep the largest share of the loot (or all of it if possible)… however, the division will take place under the "pirate code", which means the captain has the right to make the first proposal. If the majority does not accept, the captain is thrown into the sea and replaced by another pirate, but there is a way for him to remain in his post and keep a large part of the treasure. Can you solve this riddle?
The Crew and the Code
The crew of our theoretical pirate ship consists of Captain Amaro, and in order of rank appear Bart, Charlotte, Daniel, and Elizabeth. This group has just obtained a chest with 100 gold coins, and of course, they clash. The first thing that comes to mind is an equal distribution, but if there are two things pirates are particularly known for, they are greed and their quickness to betray.
The only thing separating them from a fight is the "pirate code." This code establishes that the captain has the right to make the first proposal in the division process. If the rest do not agree (the vote includes the captain), he is thrown overboard and replaced by the next member. If Bart's idea is also rejected, he will share the same fate as the captain, and so on until only Elizabeth remains, or a division plan is accepted.
The Rules in Detail
Now, several details: The five are very intelligent, with a superlative ability to solve logical problems, and they know everyone is in the same condition. Any idea of collaboration or alliance is automatically discarded: They possess a large amount of information about their rivals' strategies, but the desire to cooperate is zero. And the pirate code allows a proposal to pass with a majority vote or a technical tie, something that cannot be applied at the beginning due to the odd number of pirates. If the captain wishes to live and keep the larger share of the loot, he must force the others' hands without breaking the code.
Working Backward from Elizabeth
To better understand the solution, it is convenient to start from the other end, which is Elizabeth. Being the last, she is the one who must consider the greatest number of conditions. If the first three proposals are rejected and Daniel becomes captain, he can say, "I keep the entire loot," tie the vote 1-1 and get away with it. On the other hand, if Charlotte is the captain, she will say, "I keep 99 coins and give one to Elizabeth." Daniel will say no immediately, but given the possibility of ending up empty-handed if Daniel is captain, Elizabeth will vote in favor of Charlotte.
If Charlotte tried to give the coin to Daniel instead of Elizabeth, Daniel would only need to vote against (which Elizabeth will also do for receiving nothing) and take the captain's seat to keep everything. With Bart as captain, the pressure point shifts: He must give a coin to Daniel, who risks receiving nothing if Charlotte is captain. By obtaining Daniel's vote, Bart achieves a tie of 2-2. The point is that Amaro knows all this just as well as the others. With Bart as captain, Charlotte and Elizabeth remain at zero, therefore his solution is to claim 98 coins, give one to Charlotte, and one to Elizabeth. The final result is 3 to 2, Amaro wins... and probably gets assassinated while he sleeps.
