Forty thieves, all of different ages, steal a huge pile of identical gold coins.
ID: 3145330 • Letter: F
Question
Forty thieves, all of different ages, steal a huge pile of identical gold coins. For whatever reason, they decide to divide the treasure according to the following procedure: The youngest divides the coins among the thieves however he wishes, then all 40 thieves vote on whether or not they are satisfied with the division. If at least half vote “Yes,” then the division is accepted. If a majority vote “No,” then the youngest is killed and the next youngest is allowed to divide the loot among the remaining 39. Again they all vote, with the same penalty if the majority votes “No,” and so on. Each of the thieves is logical and always acts in his (or her) own self-interest, ignoring the interest of the group, fairness, etc. How should the youngest of the forty thieves divide the treasure in order to keep as much as possible and stay alive?
To figure this out, you're supposed to start out with 2 thieves and show how much each gets, then 3, then 4, up to around 20. There is supposed to be a pattern; my teacher gave us a hint and started us out: 2 thieves: the youngest gets all the coins, the oldest gets none. 3 thieves: youngest gets all but 1, middle gets none, and oldest gets 1.
I just need some help with 4 thieves up to at least 5 or 6 so I can figure out the rest of the problem
Explanation / Answer
The youngest has the opportunity to divide the money in a way in which they ensure at least 50% of the vote while keeping the rest of the money they did not divide among the others. Let's look at a situation where there are 2 people alive. The younger of the two can take all of the money and the vote from the oldest would not matter. Let s move to a situation where there are three people. The youngest could offer the oldest a coin and because the oldest would not get anything if they reject the offer, they have to accept it (everyone is looking out for their own interests). The youngest of the three cannot bargain with the second youngest because if the second youngest rejects the offer of a coin, they end up with all the coins. Every time the number of alive people increases, the coins given to the top person has to increase by one.
So, now for 4 thieves, the youngest one need two votes. So, now he will give 2 coins to oldest one and rest of the coins, he will take for himself. the other two will not get anyone.
Now for 5 thieves, the youngest one need atleast three votes. so now he will give 3 coins to oldest one and he has to the second oldest one to his fold by giving him one coin so he will support him. The second oldest one will settle for one because he will not anything if he will not support the youngest one and get him killed.
so for 5 thieves, oldest one will get 3 coin, secod oldest will get 1 and youngest one will get toal - 4 coins and rest of two will not anything.
I am leaving this question here for your interprtation and pls write comment if you want full answer.