Pirate Split: 5 pirates grab 100 gold coins

Correct answer: No. 1 97, No. 2 0, No. 3 No. 1, No. 4 No. 2, No. 5 0 Reverse Deduction Method: If No. 1--3 are all thrown into the sea, and only No. 4 and No. 5 are left, No. 5 must vote against No. 4 to feed the shark and swallow the gold coins alone.

Because as long as No. 5 disagrees, No. 4's proposal cannot reach a majority) Therefore, No. 4 can only save his life if he supports No. 3's plan. Knowing this, No. 3 will propose a plan of (100,0,0), and will keep all the gold coins for No. 4 and No. 5, because he knows that No. 4 will vote in favor of it even though he does not get the gold coins but can save his life, and he can pass it by adding No. 3's own vote. However, if No. 2 deduces No. 3's plan, he will propose a plan (98,0,1,1) that is, give No. 3 and give No. 4 and No. 5 a gold coin each.

Since the scheme is more beneficial for No. 4 and No. 5 than when they were assigned to No. 3, they will support No. 2 and do not want him to be out of the game and assigned by No. 3. In this way, 2 will take 98 gold coins. Similarly, No. 1 will also see No. 2's plan and will propose (97,0,1,2,0) or (97,0,1,0,2) allotments, giving up No. 2 and giving one to No. 3 and two coins to No. 4 (or 5).

Since the 1st plan is better for 3 and 4 (or 5) than the 2nd allocation, they will vote in favor, and with 1's own vote, the 1st plan will be passed, and 97 gold coins will be obtained.

Deuce. Each person gets 20 gold coins.

This section introduces a very classic model in economics: the pirate divide.

The five pirates were given 100 gold coins, and they were distributed by lot: pirate 1 was distributed first, and if he received half of the distribution or the pirate admitted, his distribution was followed. Otherwise, he will be thrown into the sea to feed the sharks, which will then be distributed by Pirate 2, and so on.

So how exactly can Pirate 1 ensure that his interests are maximized?

Of course, there are two basic assumptions here:

1.First of all, the requirements must be allocated and executed in strict accordance with the rules.

2.Secondly, all pirates are required to be completely rational, which means that they do not joke with their lives and do not gamble for the benefit of uncertainty. will ensure their most secure income.

Here is a few words inserted, and interested readers can think of the solution to this problem on their own. See if you can come up with a plausible explanation.

In "Nine Songs of Tianxing", there is also a section where the problem of "Three Ji Dividing Gold" explained by Han Fei arises, which is essentially the same problem as pirate dividing gold. This will soon be formalized in the following explanations.

End of interjection

Let's look at the solution to this problem: it doesn't seem easy to solve by starting straight away. So we can make use of reverse induction. Start with a pirate situation and go backwards.

A pirateTwo pirates

When there are only two pirates left, it only takes the consent of Pirate 2 to reach half of the numbers. Therefore, he does not need to consider number 1, and directly assigns: 0 100 [0 for 1 and 100 for 2].

Three pirates

When there are three pirates left, 2 will inevitably not support 3's plan, because as long as 3 is thrown down, 2 can take the gold alone.

Then No. 3 must strive for the support of No. 1, and need to pay No. 1 more than 0 gold coins, 1 can be. Therefore, the distribution result is 1 0 99 [i.e. 1 1 2 0 3 99].

At this point, it isNine Songs of TianxingMediumSanji divides the goldThe question is answered, [the result is that the first singer can get 99].

Four pirates

Similarly, when Pirate 4 is assigned, he will not spend a lot of money to seek the support of Pirate 3, and will invest in Pirate 2 and choose to win over 2, resulting in [0 1 0 99].

Five pirates

Similarly, the result of 5 pirates is [1 0 1 0 98]. That's the answer to the 5 pirate gold points.

To put it simply, in the case of absolute rationality of all people: strike first to strengthen, and then to suffer.

Just to introduce the mathematical idea of "reverse induction", the big things in the world must be done in detail, and the difficult things in the world must be done in the easy. When we have a hard grasp of a problem or a problem, we might as well go back to the source, start with a simple model, and analyze it step by step to get the desired result. I think that's the true meaning of induction.

Hello! Here's how five pirates split their gold coins:1

Complete game missions: In the game of pirate coins, completing missions is the most common way to get gold. Missions may include collecting treasure, defeating pirate ships, unlocking new maps, and more.

2.Daily check-in: You can get a certain amount of gold coins by checking in every day.

If you check in for multiple canopy rushes in a row, the amount of gold awarded will also increase. 3.Attend the event:

There are often various events in pirate split gold games, such as flops, scratches, etc., and participating in these events can also be rewarded with coins. 4.Invite Friends:

Invite friends to play the game and get extra gold rewards. You can invite friends through social**, SMS, email, and other ways to invite friends. 5.

Buy Coins: If you want to accumulate coins faster, consider buying them. In the game, there are sometimes special deals on gold packs, and you can consider buying these packs to get more coins.

It is important to note that you should not easily trust some unofficial pirate cent coin games to avoid being scammed.

Summary. Hello, dear, I'm honored to answer for you! <>

5 pirates divide the gold coins method of the boss proposes the pro of the law. The pirate leader proposes the distribution plan, the other pirates vote on it, and if more than half of the pirates agree, the plan is passed. Sequential Assignment Method:

Pirates are distributed according to their level or contribution, and pirates with higher rank or higher contributions receive more gold. Random allocation method: Random allocation by drawing lots or rolling dice to avoid bias or controversy.

5 Pirates divide the gold coins.

Hello, dear, I'm honored to answer for you! <>

5 pirates divide the gold coins of the lead method leader proposed the pro of the law. The pirate leader proposes the distribution plan, the other pirates vote on it, and if more than half of the pirates agree, the plan is passed. Sequential Assignment Method:

Pirates with high level or contribution will receive more gold. Random allocation method: Random allocation is carried out by drawing lots or rolling dice to avoid bias or controversy.

The following is the method of dividing the gold coins among the 5 pirates: Negotiation and negotiation method: The pirates negotiate with each other, distribute them according to their respective needs and interests, and divide the silver after reaching a consensus.

Fair Distribution Law: Distribute the gold evenly among each pirate to ensure that everyone gets the same share and avoid unfair situations.

Hello dear<>

The answer you're looking for: Let's say there are 5 pirates A, B, C, D, E, and they grab 100 gold coins, according to the pirate rules, they need to distribute the gold according to the following method: propose a distribution plan, all pirates vote, if more than half of the pirates agree, then distribute according to the plan, otherwise continue to the next round of voting until a consensus is reached.

2.If there is no consensus, all the pirates will start threatening each other, asking the other pirates to vote for their plan until a consensus is reached. The following is a possible scheme for the distribution of the year, for reference:

It was proposed that the 100 gold coins be divided into 51, 0, 49, 0, and 0, with A and C getting 51 and 49 Rotten Lands respectively, and the other pirates not getting any gold. 4.If A's scheme is supported by B, C, and D, then the scheme is passed, and A and C receive gold, and B, D, and E do not receive any gold.

5.If A's plan is not supported by B, C, and D, the plan will not pass and the next round of voting will continue. 6.

In the next round of voting, B proposes to divide 100 gold coins as 0, 1, 0, 99, 0, with D getting 99 gold coins and B getting 1 gold coin. 7.If B's scheme is supported by C and E, then the scheme is passed, D and B get gold, and A, C, and E don't get any gold.

8.If Plan B fails to receive support from C and E, the plan will not be approved and the next round of voting will continue. 9.

In the next round of voting, C proposes to allocate 100 gold coins as 0, 0, 34, 0, and 66, with E getting 66 gold coins and C getting 34 gold coins. 10.If C's scheme is supported by D and E, then the scheme is passed, E and C get gold, and A, B, and D don't get any gold.

11.If C's plan fails to be supported by D and E, the plan is not approved and the next round of voting continues. 12.

In the next round of voting, D proposes to allocate 100 gold coins as 0, 0, 0, 100, 0, 0, where D gets 100 gold coins. 13.If D's scheme is supported by E, then the scheme is passed, and D gets gold, and A, B, C, E don't get any gold.

14.If D's plan fails to get E's support, the plan does not pass and all pirates do not receive any gold. Summary:

According to the above scheme, only D received gold, and none of the other pirates received any gold. This is a possible scenario, and the actual situation may vary, but under the rules of piracy, each pirate needs to consider his own interests and deterrence, and find the optimal distribution.

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 (0,100) to keep 5 alone for the gold, 5 may still feel that it is dangerous to keep 4 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.