Logical thinking problem

Five pirates robbed 100 pieces of jewelry, each of which was the same size and priceless. They decided to allocate it like this: first, draw lots to decide their own serial numbers (1, 2, 3, 4, 5); In the second step, 1 first puts forward the distribution plan, and then five people vote. When and only when more than half of the people agree, he will distribute it according to his proposal, otherwise he will throw it into the sea to feed the sharks. Step 3: After the death of 1, the distribution plan will be put forward on the 2nd, and then four people will vote. If and only if more than half of the people agree, they will be distributed according to his proposal, otherwise they will be thrown into the sea to feed sharks; The fourth step, and so on.

Conditions: Every pirate is a very smart person who can rationally judge gains and losses and make choices.

Question: What is the final distribution result?

Tip: The principle of judging pirates: 1. Life-saving; 2. Get as many gems as possible; 3. Kill as many people as possible.

Answer:

This problem should be solved by backward recursion.

First of all, suppose that all the schemes of 1, 2 and 3 are rejected, and they are all thrown into the sea to feed the fish, leaving 4 and 5.

At this time, No.4 has only one result: being thrown into the sea, because no matter what plan he puts forward, it will be rejected by No.5, and his plan will not pass half.

Now add No.3. No matter what plan No.3 puts forward, No.4 must agree to save his life, so No.3 can keep all 100.

Add No.2, and then No.2 only needs to give No.4 and No.5 a gem to ensure that the plan will pass, because No.4 and No.5 clearly know that if No.3 shares it, they won't get any, so if No.2 gives them a piece, they can agree to their plan and get 98 by themselves.

Add 1 at the end. 1 Just give No.3 a gem, which is not available in No.2 scheme. Give No.4 or No.5 a 2, and the scheme will be guaranteed to pass.

The final distribution method is: 65438 +0 97, 2, 3 1, 4, 5 (or 4, 5).