A jewel theft ring consists of five members. In decreasing order of rank they ar

Question

A jewel theft ring consists of five members. In decreasing order of rank they are the mastermind, the safecracker, the burglar, the lookout and the getaway car driver. Before getting out of “the business” forever, they pull off one last heist. It results in a supply of 27 perfect diamonds of equal value. The diamonds can not be cut without ruining them, so they decide on the following democratic procedure to divide the loot among themselves. The lowest ranking member of the ring makes a proposal about how to split the loot, and all members of the ring vote on it. If the proposal is supported by at least half of the members, then the diamonds are divided as suggested. Otherwise, the proposer is “eliminated” (ie, killed) and the process is repeated in the smaller ring.

Since this is the last “job”, all of the jewel thieves want as much of the loot as they can get. Each one will vote against any proposal that does not guarantee more diamonds than they could get later in the process.

All of the jewel thieves know that it is better to have fewer people who know their past, so they will also vote against a proposal if they are guaranteed to get the same number of diamonds later because it means there is one fewer potential informant alive.

Suppose you are the getaway car driver. You know the other members of the ring well, and you know that they have perfect logic skills. What do you propose? What is the maximum number of diamonds that you can get?

Explanation / Answer

Good question ...

Let's assume 5 persons are 1,2,3, 4 and 5 and is lowest ranked person which is getaway car driver...let's consider

a )3,4 and 5 proposed something ,get rejected and killed..so 1 and 2 are left..now 2 will proposed 27 diamonds for himself and 0 for 1 and will get 27 diamonds as he will vote for himself and will get 50% votes..So to avoid this scenario 1 will support 3rd and 3 can give hume 1 diamond for his life's sake

So now we are sure as all are intelligent...3 will give 1 to 1 and 26 to himself and 0 to 2

But to avoid this scenario 2 have to support 4 (may expect 1 diamond from him)...

So,if 4 is alive he may give 1 to 2 for his life...

Finally the solution is

1 diamond to 1 and 26 for 5th that is gateway car driver

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