How do pirates divide the gems? Typical gambling problems

Standard Answer:

Pirate 1 gives 1 gem to 3 and 2 to Pirate 4 or 5, for 97 pieces. The distribution scheme is: 97,0,1,2,0 or 97,0,1,0,2.

Reasoning process: Pushing back to forward, if pirates 1-3 have fed sharks, and only No. 4 and No. 5 are left, No. 5 must vote against letting No. 4 feed the sharks in order to monopolize all the gems. Therefore, No. 4 can only save his life by supporting No. 3.

Knowing this, No. 3 will propose a (100,0,0) distribution plan, and will keep all the gems for No. 4 and No. 5. Because he knows that No. 4 has nothing, but he will still vote for it, and his plan can be passed with his own vote. However, when No. 2 learns about No. 3's plan, he proposes a plan (98,0,1,1) that is, give up No. 3 and give No. 4 and No. 5 one gem each.

Since the scheme is more advantageous for No. 4 and No. 5 than when assigned on No. 3, they will support him and do not want him to be out and assigned by No. 3.

In this way, No. 2 will take 98 gems. However, the 2-digit scheme will be understood by the 1st, who will propose (97,0,1,2,0) or (97,0,1,0,2) to give up the 2nd and give 3 a gem and 4 (or 5) 2 gems. Since No. 1's solution is better for No. 3 and No. 4 (or No. 5) than when No. 2 is assigned, they will vote for No. 1 in favor, plus No. 1's own vote, and No. 1's plan passes, and 97 gems can easily fall into the bag.

This is undoubtedly the plan that can get the most out of No. 1.

In"Pirates share the spoils"model, any"Distributors"The key to getting your plan approved is to think it through beforehand"Challenger"What is the distribution plan, and obtain the maximum benefit with the minimum cost, and pull in"Challenger"Distribute the most undesirable people in the scheme. No. 1 looked like he was most likely to feed the sharks, but he held on to his first-mover advantage, and as a result, he not only eliminated the threat of death, but also made the most gains. And No. 5, who seems to be the safest, has no threat of death, and can even reap the benefits of fishermen, but can only get a small piece of the pie because he has to look at other people's faces and act.

A: The scheme of 1 is:

You can use the backwards method:

If only 4 and 5 are left, 4 will not be thrown into the sea until 5 gives 100 diamonds.

So, the distribution scheme at this time is: 4-0, 5-100

And so on, when there are 3, 4, 5 trio left.

3 knew that as long as 4 was given a diamond, 4 would agree to his plan. Because if he doesn't agree, he won't get a diamond.

So, the distribution scheme at this time is: 3-99, 4-1, 5-0

And so on, when 1, 2, 3, 4, 5 are all on board.

The distribution scheme is as above: 1-97, 2-0, 3-1, 4-0, 5-2

Bandit No. 1 gives 1 gold coin to Bandit No. 3 and 2 to Bandit No. 4 or 5, for 97 coins. The distribution scheme can be written as (97,0,1,2,0) or (97,0,1,0,2).

Here's how it works: Pushing back to front, if robbers 1-3 feed sharks, and only 4 and 5 are left, 5 must vote against feeding 4 to sharks in order to keep all the gold coins alone. Therefore, No. 4 can only save his life if he supports No. 3.

Knowing this, No. 3 will propose a (100,0,0) distribution plan, and will classify all the gold coins as existing for No. 4 and No. 5, because he knows that No. 4 will get nothing but will still vote in favor, and his plan can be approved with one vote from himself. However, when No. 2 deduces No. 3's plan, he will propose a plan (98,0,1,1) that is, give up No. 3 and give No. 4 and No. 5 a gold coin each. Since the scheme is more advantageous for No. 4 and No. 5 than when they are assigned to No. 3, they will support him and do not want him to be out and assigned by No. 3.

In this way, the number 2 will take 98 gold coins. However, the 2-digit scheme will be understood by the 1st, and the 1st will propose (97,0,1,2,0) or (97,0,1,0,2) by giving up the 2nd and giving the 3rd a gold coin and the 4th (or 5th) 2 gold coins. Since the 1st plan is better for the 3rd and 4th (or 5th) than the 2nd allocation, they will vote for the 1st, and with the 1st's own vote, the 1st's plan will be approved, and the 97 gold coins will easily fall into the pocket.

This is undoubtedly the plan that can get the most out of No. 1.

27 for No. 1, 0 for No. 2, 1 for No. 3, 0 for No. 4, 2 for No. 5. or 27 on the 1st, 0 on the 2nd, 1 on the 3rd, 2 on the 4th, and 0 on the 5th.

For these 5

pirate points. 100 gems, the fairest division of each person.

20 capsules. But I divide it like this, and I remain.

4 pirates won't agree because.

4 pirate points.

100 can be taken per person.

25 capsules. But so divided, left.

3 pirates will not agree either.

And so on, and so on, and so on.

2 pirates, regardless of the first.

How to divide the 4 pirates, first.

All 5 pirates can choose not to agree.

In this case, life-saving becomes the first.

4 pirates first choice, so he must agree to the first.

3 pirate divisions. And the 3rd

pirates raised (

100,0,0).

4 pirates will not object. Article 2

Pirates can be raised (98,0,1,1) in consideration of the above. Finally the 1st

Taking into account all of the above, the maximum profit of the pirate is (97,0,1,0,2) or (97,0,1,2,0).

In fact, pirates must meet the following in order when dividing gems.

3 principles:1Stay alive.

2.Get as many gems as you can.

3.Kill as many people as you can.

In fact, why bother to give No. 3 one, it doesn't matter if he agrees or not, as long as he gets the support of the last two, he can get more than half.

Because No. 2 is looking forward to No. 1's death, he definitely doesn't agree.

If it's the turn of number two, then number two will give one to number four, one to number five.

Because if it's the turn of number three, then neither of them will have to give, and they will win.

Because if 4 doesn't agree, and as a result, 3 dies, and 4 will definitely disagree, and 4 will definitely not agree, and 4 will be fed to the sharks, so as long as 3 is alive, his turn is the greatest.

So you, as the first person, to maximize your benefits, just give more than if it's the turn of number two, and don't give anything else, so that you can win 3 to 2 (if you give as much as number two, then as a pirate's cruel nature, they will feed you sharks, so be sure to give more).

So the distribution scheme should be: No. 1, 96, No. 2, No. 3, No. 3, No. 4, No. 2, No. 5, No. 2.

The previous ones are all right, and in the end, it only needs three people to agree to pass, so you only need to give d2 or e2, and you don't need to give 2.

So: (97,0,1,2,0) or (97,0,1,0,2) will do.

The reverse calculation is that if 60 gems are divided between two people, the distribution is, so when three people divide it, the distribution is so that the first and the third will agree, and the third one will not agree, and he will not get anything! In the same way, if the 4th person does not agree with Dehua, he will get nothing; By analogy, 5 people is ,!! The 3rd and 5th people will definitely agree, otherwise they will get nothing!

Final answer.

When I was doing this question, my thought process was like this: For this.

pirate points. A jewel, the fairest division of each person.

grains. But I divide it like this, and I remain.

A pirate wouldn't agree because.

pirate points. Each person can take it.

grains. But so divided, left.

Pirates wouldn't agree either.

And so on, and so on, and so on.

pirates, regardless of the first.

How to divide the sea and prepare for thieves, first.

Any pirate can choose not to agree.

In this case, life-saving becomes the first.

A pirate's first choice, the sedan was ruined, so he had to agree to the first.

The division of pirates. And the first.

pirates raised (

Division, section.

A pirate would not object. Clause.

Pirates may raise (

Finally, the first. Considering all the above-mentioned hunger situations, the pirate's plan for maximum profit is (or(

In fact, pirates must meet the following in order when dividing gems.

Principle: Stay alive. Get as many gems as you can.

Kill as many people as you can.