Required Mathematical Intelligence

Chapter 89 How to Divide Gems

5 pirates snatched 100 gems, each of the same size and priceless.They decided to:

1. Draw lots to determine your own number (1, 2, 3, 4, 5).

2. First, No. 1 proposes a distribution plan, and then 5 people vote on it. When half or more people agree, the distribution will be made according to his proposal, otherwise it will be thrown into the sea to feed the sharks.

3. If No. 1 dies, No. 2 will propose a distribution plan, and then 4 of you will vote. When half or more people agree, the distribution will be made according to his proposal, otherwise it will be thrown into the sea to feed the sharks.

4. By analogy...Conditions: Every pirate is a very smart person, able to judge gains and losses rationally, and thus make a choice.

Question: What kind of allocation plan does the first pirate propose to maximize his profit.

[Answer: If there are only numbers 4 and 5 left, 5 will definitely oppose 4, because there is no more than half, 4 must be killed, and 5 will get all the gems;

所以如果只剩3，4，5号4号一定会支持3号这样才能活下去；

And the plan proposed by No. 3 will definitely pass, and it is beneficial to oneself, that is, 100, 0, 0;

因此3号一定想除掉前面的1，2号，3肯定会反对1的方案；
2暂时忽略。如果1给4，5号每人一个宝石就比没有强，4，5号一般会支持；

So consider their psychology, but if 1 dies, 2 will give 4 and 5 one each. In this case, 4 and 5 may not necessarily support No. 1, and No. 4 can only give another one to 5 or 3. Let’s look at No. 1 again. If No. [-] doesn’t give him some, he will agree to it later, so the correct answer is:

96 or 0]
(End of this chapter)