The answer to the pirate dividing gems, an intellectual question of pirate dividing gems

Check out the encyclopedia's entry for "pirate gold". There is detailed reasoning inside. The result can be obtained for any number of pirates.

The part that follows the heading "Formulation of the Question" in the entry was provided by me.

They're not smart pirates Clever pirates don't offer to be distributed by lot, because if they're smart, they should know it's 97 0 1 2 0. Before getting the gems, they should divide them equally between 20 gems each. Because the chance of each person getting 0 1 2 is 4 5, and the chance of getting 97 is 1 5.

Assuming that every pirate is extremely intelligent and rational, they are able to perform rigorous logical reasoning and judge their own gains and losses very rationally, that is, they can get the most gold coins on the premise of saving their lives. At the same time, assuming that the results of each round of voting can be carried out smoothly, what kind of distribution plan should the pirate who draws the number 1 propose so that he can not be thrown into the sea and get more gold?

The accepted standard answer to this question is: Pirate 1 gives 1 gold coin to 3, 2 gold coins to 4 or 5, and 97 gold coins for himself, i.e. (97,0,1,2,0) or (97,0,1,0,2). Now let's look at the rational analysis of each person as follows:

Start with Pirate 5 first, because he is the safest and does not risk being thrown into the sea, so his strategy is also the simplest, that is, it is best to have all the people in front of him die, then he can get the 100 gold coins alone.

Looking at No. 4 next, his chances of survival depend entirely on the survival of people in front of him, because if all the pirates from No. 1 to No. 3 feed the sharks, then with only No. 4 and No. 5 left, no matter what distribution plan No. 4 proposes, No. 5 will definitely vote against letting No. 4 feed the sharks in order to swallow all the gold coins. Even if 4 curries favor with 5 in order to save his life and proposes a plan such as Kyosuke drinking the Russian Barrel Domain (0,100) to keep 5 to monopolize the gold, 5 may still feel that keeping 4 is dangerous and vote against it to feed the sharks. Therefore, the rational No. 4 should not take such a risk and pin his hope of survival on the random selection of No. 5, and he can only guarantee his life by supporting No. 3.

Looking at No. 3 again, after the above logical reasoning, he will propose such a distribution plan as (100,0,0), because he knows that No. 4 will still unconditionally support him and vote in favor even if he gets nothing, so adding his own 1 vote can make him secure the 100 gold coins.

However, if No. 2 also learns about No. 3's allocation plan through reasoning, then he will propose a plan of (98,0,1,1). Because this plan is relative to the distribution plan of No. 3, No. 4 and No. 5 can get at least 1 gold coin, and the rational No. 4 and No. 5 will naturally feel that this plan is more beneficial to them and support No. 2, and do not want No. 2 to be out of the game and be distributed by No. 3. In this way, Number 2 can take 98 gold coins in a hurry.

Unfortunately, Pirate 1 is not a fuel-efficient lamp, and after some reasoning, he also has insight into the distribution plan of No. 2. The strategy he will adopt is to give up the 2nd and give the 3rd 1 gold coin, and at the same time give the 4th or 5th 2 gold coins, i.e. propose a distribution of (97,0,1,2,0) or (97,0,1,0,2). Since the distribution plan of number 1 can get more benefits for number 3 and number 4 or 5 than the plan of number 2, then they will vote for number 1, and with the number 1 vote of 1 itself, 97 gold coins can easily fall into the pocket of number 1.

Let's think about E and D first, and if A, B, and C have been thrown into the sea, then D will offer to take 100 gems himself, and then his own vote is 50%, and E is very clear - if only he and D are left, then he will not get anything himself, so even if he can only get a little sweetness, he will prevent the situation where only he and D are left. Taking a step forward, let's say C, D, and E survive, then C knows that if E gets nothing, he will be thrown into the sea, that is, as long as he gives E a little sweetness, E will vote in favor, and then C will choose to take 99 for E1. And in the distribution of C, D, and E, D gets nothing, so he will try his best to prevent this, assuming that he succeeds in preventing it, and B is not thrown into the sea, then there are 4 people sharing the gems, and B knows that D is facing him, and D can only be left empty in his pocket, so B only needs to give D1 gem, let D vote for himself, and the remaining 99 gems can be taken by himself.

So C and E have to hope that A will not die, although A always bullies, eats more, and hates the most - but even if you can get 1 gem, it is better than not getting nothing, right? So A only needs to give C and E 1 gem each, anyway, if they don't vote for it, they won't get anything, which means A can get up to 98 gems, while B and D can only cry.

Many people may already know, forgive me for being unheard, the title is like this:

Five pirates have grabbed 100 gems, each of the same size and price. They decided to divide it like this:

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

2. First of all, No. 1 proposes a distribution plan, and then all 5 people vote, and if and only if more than half of the people agree, they will be distributed according to his proposal, otherwise he will be thrown into the sea to feed the sharks.

3. If No. 1 dies, No. 2 proposes a distribution plan, and then the four of us vote, if and only if more than half of the people agree, the distribution will be made according to his proposal, otherwise he will be thrown into the sea to feed the sharks.

4. And so on until a distribution plan is finally reached.

Conditions: Every pirate is a very intelligent person, and can judge the gains and losses very rationally, so as to make a choice.

I won't list all the answers.

This question makes me feel very deeply, in real life, people always can't tell the difference between friend and foe. Otherwise, everyone should be able to find the answer to the above question. But when I show that question to others, most people don't know where to start.

First of all, people don't know what the criteria for dividing the relationship between friend or foe are. Secondly, people don't understand that the relationship between friend and foe is changing all the time. For example, when it comes to our husbands (wives), we are accustomed to thinking that they belong to the "me" side.

When we are hurt by our own husband (wife), we realize that things are not so simple. In fact, in most cases, one's husband (wife) is one's own enemy. You have to spend the money you earn with him (her), support your family together, and support your parents together, at this time you think that he (she) is your friend, but in fact he (she) is your enemy.

Because if you give more, he (she) will give less, and if you don't give at all, he (she) will have to take all the responsibility. You are in a completely hostile relationship. In the end, many people are not unintelligent enough to distinguish the relationship between friend and foe, but they are too lazy to distinguish such a relationship, or they are blinded by feelings, commitments, etc., and fail to distinguish the relationship between friend and foe.

There was a slight problem with the upstairs analysis, and the upstairs didn't notice the condition that "the pirate wants someone else to die on the premise of getting the same gold coins".

Pay attention to the conditions, it must be more than half to pass, and on the premise of getting the same gold coins, they want someone else to die.

The result of this question is unexpected, and the final result is 97,0,1,0,2 or 97,0,1,2,0

That is, the number 1 will get most of the gold coins alone.

The analysis is as follows: This question should start with the 4th pirate: if 4 is distributed, then 4 will die, because 5 will definitely vote against, even if 4 gives all 100 gold coins to 5, 5 will also object, because after 4 dies, 5 can still get all the gold coins.

Therefore, No. 4 will not let this happen, he will definitely support No. 3 unconditionally, so No. 3 will definitely propose such a distribution plan, 100,0,0, that is, he will get all the gold coins alone, because he knows that No. 4 will definitely support himself in order to save his life, so it is useless for No. 5 to oppose it, because there are already two people who support it.

Thinking further: what should he do as No. 2, he only needs to make the following plan, 98, 0, 1, 1, at this time No. 4 and No. 5 will each get a gold coin, so they will definitely support No. 2 (if they oppose it, No. 2 will die, but if No. 3 is distributed, the two of them will get nothing), so that 2, 4, and 5 will support it, and No. 3 and 1 person will oppose it, and it will pass.

Think further: what should I do with No. 1? He has to buy two people, No. 2 will definitely not be able to buy them, because if No. 1 dies, No. 2 will get most of the gold coins, and No. 1 only needs to give No. 3 1 gold coin, and then give No. 5 2 gold coins, and these two can be bought (because if these two people don't agree, they will be distributed by No. 2, and they will get less), so that No. 1's distribution plan is 97,0,1,0,2.

If the allocation scheme No. 1 is changed to 97,0,1,2,0, the result will be the same, and No. 3 and No. 4 can be bought.

Of course, this ending is ideal, not very realistic, but this is the correct solution to this question as a topic.

Number 1 directly said that he wanted 100 and then killed the others.

I think there is only one answer, which is 1 to 97, 2 to 0, 3 to 1, 4 to 0, 5 to 2The analysis is as follows:

If there are only 4 and 5 left, then there are only two results, 4 is dead, 5 gets 100, or 4 gets 0, 5 gets 100

There are 3, 4, and 5 left, then if 3 wants 4 to support him, then give 4 1, 5 get 0, and 3 get 99, because 4 knows that if he opposes 3, 5 must also oppose 3, so that the best result for 4 is also 0. 3. If you want 5 to support him, you have to give 5 101. So the plan of 3 must be to hope that 4 will support him, then give 4 1, 5 get 0, and 3 get 99.

There are 2, 3, 4, 5 left, then 2 hopes that 3 and 4 support him, 3 gets 100, 4 gets 2, 5 gets 0(In this way, 3 and 4 get more than 2 die, but there are not so many gold coins, so this plan does not work).

I hope that 3 and 5 will support him, 3 will get 100, 4 will get 0, and 5 will get 1 (still more than 100).

If I hope that 4 and 5 support him, 3 will get 0, 4 will get 2, and 5 will get 1, then 2 will get 97, so this is the best solution for 2.

There are 1, 2, 3, 4, 5 left, then 1 thinks 2 and 3 support him, 2 gets 98, 3 gets 1, 4 and 5 gets 0, and 1 can get 1

If 1 wants 2 and 4 to support him, 2 gets 98, 3 gets 0, 4 gets 3, 5 gets 0, this is also over 100, it doesn't hold...

If 1 wants 2 and 5 to support him, 2 gets 98, 3 and 4 get 0, 5 gets 2, and 1 gets 0

If 1 wants 3 and 4 to support him, 2 gets 0, 3 gets 1, 4 gets 3, 5 gets 0, and 1 gets 96

If 1 wants 3 and 5 to support him, 2 gets 0, 3 gets 1, 4 gets 0, 5 gets 2, and 1 gets 97 (that is).

If 1 wants 4 and 5 to support him, 2 gets 0, 3 gets 0, 4 gets 3, 5 gets 2, and 1 gets 95

I think that No. 5 will definitely not agree to anyone, anyway, by the time he arrives, everyone is dead, and he has all the gems, so it is necessary to eliminate No. 5.

How many people are left at the end? Uh, how many people do you want left? You make it clear and I'll help you.

Title: If and only if more than half of the people agree, it will be distributed according to his proposal, with one's own life first, gems second, and others' lives third.

a.When there are only 4 and 5 left, the assignment of 4 must be (0,100), which is 0 for 4.

b.When there is 3, 4 and 5 left, the division is (100,0,0); This division number 4 will be in favor, because if number 4 is against, number 3 will be sacrificed, and he will still end up with 0 gems, and by the title, he will choose to be in favor.

c.When there are numbers 2, 3, 4, 5 left, the allocation is (100,0,0,0); This division No. 4 and No. 5 will be in favor, because if one of them opposes it, it will go to the division of B, and in that division 4 and 5 are both 0, so the sacrifice of No. 2 is a sacrifice in vain, and it can be seen from the title that No. 4 and No. 5 will not object.

d.So the division of number 1 is (100,0,0,0,0); Nos. 4 and No. 5 will agree to this division, and if they do not agree, according to the above, No. 1 will be sacrificed in vain, and they will not get any of them, and it is clear from the title that they will not object.

So the most correct solution is 100,0,0,0,0 Of course, No. 1 can also point them arbitrarily if he is in a good mood, but if the benefits are maximized according to the question, the result is 100,0,0,0,0