The reason why this problem has become a classic game problem can become a test question for Microsoft applications, and it is also related to its ingenious solution. When analyzing this problem, we need to use the idea of recursion, that is, to transform a complex problem into a small-scale model of the same problem. This is a very common method to solve problems, and it is also an indispensable idea when writing programs and algorithms.
Push from the back to the front to reduce and simplify the scale of the problem. If 1-3 pirates don't get more than half of the votes because of their own decision-making mistakes, feed them to sharks. Therefore, there are only two pirates, No.4 and No.5, and No.5 pirate will definitely not agree with any proposal of No.4 pirate, so that no proposal of No.4 pirate will get more than half of the support rate. As long as No.4 dies, No.5 will get all the gold coins. Pirates are not only mercenary, but also vicious. - -||)。 Because all pirates are extremely clever, of course, pirate No.4 won't let things go this far, so he must at least ensure the survival of No.3. Therefore, put the problem back. If pirates 1 and 2 are killed, only proposal 3 remains, and he can put forward a plan (100,0,0). Since proposal 4 must ensure the survival of proposal 3, he will agree to proposal 3 even if he doesn't get a gold coin. In this way, the third proposal was passed with the consent of the two people. Pushing the problem back, when only 1 hangs up and pirates 2-5 are still there, No.2 proposes that he only needs to ensure that No.4 and No.5 have a gold coin, that is, the scheme of (98,0, 1, 1), so that the proceeds obtained by No.4 and No.5 can be higher than those obtained when No.2 hangs up. Thus, we are close to the original problem, that is, the situation when the proposal 1 was put forward. Through the clever pirate mind, No.1 analyzed what the strategy would be when No.2 died. So the proposal of number one can be passed as long as the income of two people is greater than that of number two. 1 At the time of death, the proposal of No.2 was (98,0, 1, 1). So 1 can choose to let No.3 and No.4, or No.3 and No.5 make more profits, regardless of the ideas of the other two people. So he can propose (97,0, 1, 2,0) or (97,0, 1, 0,2), so that his plan will be recognized by himself and two others.
In the process of solving this problem, we use recursive means to find the most primitive essence of a complex problem, and on the basis of this source, we "shell" layer by layer, analyze step by step, and finally solve the problem. This is the main idea of recursion, which transforms a complex problem into a simple model of the same problem. Then gradually push back to the original question. This problem-solving idea can be applied to solve many problems at the same time.
This classic game problem can cause us a lot of thinking. It is not only a logical problem, but also reveals many social phenomena.
For example, if any distributor wants to pass his scheme, the key is to consider clearly what the distribution scheme of Challenger is (here refers to the relationship between two pirates with adjacent numbers), get the maximum benefit at the least cost, and win over the most dissatisfied people in the distribution scheme of Challenger. Think about the peasant uprisings of past dynasties, the constant court battles, the alliance betrayal everywhere in our time, the intrigue within the enterprise, and the stumbling politics at the foot of the office. Which winner doesn't adopt a method similar to "pirates divide the money"?
Why do revolutionaries always look for the poor? Because they are the most frustrated people. Why does the terrorist Osama bin Laden have no market in Saudi Arabia, but he is very popular in Afghanistan, because Afghanistan is an outcast of globalization. Why do senior leaders of an enterprise often abandon the No.2 person and get on well with accountants and cashiers when they are engaged in insider control? Isn't it because the little people in the company are easy to buy, but the number two is always ambitious to replace them?
At the same time, this problem also fully embodies the "first-Mover advantage" and "slightly late-comer potential" 1 seems to be in the most dangerous position, and his wrong decision will make him feed sharks. Then, at the same time, he also holds the first opportunity to put forward a plan. As long as he fully analyzes and makes decisions, he can save the day and strive for the greatest benefit for himself. No.5 seems to be the safest and can even take advantage of fishermen. But because he didn't have the right to make a decision first, he could only look at other people's faces and get a very small share. It can be seen that in dealing with people, I always want to put myself in the fifth position, always want to wait and wait, and eventually I will miss many opportunities and be at the mercy of others. If China stays in the fifth place in the world market for a long time, it will eventually get nothing.
This simple question reveals countless complicated truths. In fact, in the world we live in, many simple mathematical and logical problems reveal many complex social essence. At the same time, many complex social essences can be abstracted and analyzed by simple mathematical methods and logical thinking methods.