Microsoft recruitment intelligence problem

3.

Analysis:

On the first day, if everyone sees that the other 49 dogs are alive and kicking, then he doesn't have to look at his own dog. According to the premise 1, everyone knows that at least one sick dog in the yard must be his own dog, so according to condition 2, one gun should be fired on the first day. Since there were no gunshots on the first day, it means that the assumption is wrong, that is, it is wrong for everyone to see the other 49 dogs alive and kicking. Conversely, everyone can see at least one sick dog.

The question now is: Everyone saw at least one sick dog, but why didn't there be a gunshot? Because the owner of a sick dog sees someone else's sick dog, if the owner of the sick dog he sees shoots his own dog, he will think: Thank God, my dog is not sick. On the first day, he didn't dare to kill his dog until the owner of the sick dog he saw shot him first. If he does this, he will mislead the owner of the sick dog he sees, and he will think that his dog is not sick. There were no gunshots on the first day, so everyone knew that there were at least two sick dogs in the yard.

The next day, if everyone sees 48 live dogs and a sick dog, then kill your dog without hesitation. But there were still no gunshots the next day, so everyone knew that there were at least three sick dogs in the yard, and that would have to wait until the third day.

On the third day, if you see 47 lively dogs and two sick dogs, don't hesitate. Your dog is sick and kill it. On the third day, there was a burst of gunfire, indicating that three dogs were killed.

2.

1) Assuming that only four or five people distribute the gems, No.4 will offer to take all the gems away, while No.5, whether it is the same or not, won't get a penny, and it won't affect the result. Meanwhile, number four and number five can save lives.

Then the 4 th and 5 th will not be executed anyway. After saving their lives, No.5 will try his best to save No.3' s life in order to maximize his own interests.

Pirate name: 4 5

Number of gems obtained: 100 0

2) Suppose there are three people (3, 4, 5) to distribute and three people to vote, then as long as the 5th can get a gem, it will support the decision of the 3rd (because it was analyzed in step 1). In this way, No.3 will make such a distribution plan, and No.5 will get 99 gems and 1 gem, so no matter what decision No.4 makes, it will have no effect on the result. Attention, everyone, this strategy prevented No.4 from getting the gem.

Pirate name: 3 4 5

Number of gems obtained: 99 0 1

3) Assuming that there are two people, three people, four people and five people for distribution, the decision will be based on the previous one, and the scheme proposed by No.2 must be supported by any of the other three people, so as to save his own life and ensure the maximization of interests. First of all, it must be clear that no matter what plan No.2 proposes, he can't get the support of No.3. He can only get the support of at least one person between No.4 and No.5 to ensure that he won't be executed, but in order to ensure the maximum benefit, he can only pay one person a gem.

If you choose No.5 as the alliance of No.2, he needs to pay at least two gems to get the support of No.5. (Because if you only give No.5 1 gem, No.5 will only get 1 gem in favor of Decision 2 and 1 gem distributed by No.3 who opposes Decision 2, so No.5 will still oppose No.2 in order to satisfy his desire to kill more people.

If you choose 4 as the alliance of 2, another result will appear. In the previous step, No.4 didn't get the gem, so as long as No.2 can satisfy him with the gem, he can get his support.

Pirate name: 2 3 4 5

Number of gems obtained: 98 0 0 2

or

Pirate name: 2 3 4 5

Number of gems obtained: 99 0 1 0.

As a rational individual, in order to maximize its own interests, No.2 will choose to form an alliance with No.4, which is the most stable structure.

4) Suppose not. 1, No.2, No.3, No.4 and No.5 * * * voted, and 1 will put forward the distribution plan.

Then 1 needs to form an alliance with at least two of the other four, but in order to maximize its own interests, it can only choose two of them. So which two will he choose?

1 has two options.

First, establish an alliance with No.2, but he has to sacrifice at least 99 gems (we know that as No.2, he has a third-step distribution plan) to save his life and maximize his own interests. Only when 1 has allocated him more than 99 gems will he be willing to form an alliance with 1 to support his plan, otherwise he will oppose it. )。 In this way, he still has the jewel of 1, but this one does not belong to him, because according to the previous analysis, 1 must have two alliances, and it must find an alliance to save its life.

According to step 3) 1, you can decide to give the remaining 1 gems to No.3, No.4 or No.5. If you give them to No.3, this will happen.

Pirate's name: 1 2 3 4 5

Number of gems obtained: 0 99 1 000.

Why won't No.3 object? If you object to the decision of 1, when it is the turn of No.2 to distribute gems, No.3 will not get the money. Therefore, No.3 will be willing to form an alliance with 1.

If you give it to number 5, this will happen.

Pirate's name: 1 2 3 4 5

Number of gems obtained: 0 99 0 1

At this time, the 5th meeting will be happy to form an alliance with the 1 crystal. Note: No.3 is not convincing to No.5, because if No.5 rejects the proposal of 1, 1 will only form an alliance with No.3, so No.5 will not get the gem.

This will happen if you give it to number 4.

Pirate's name: 1 2 3 4 5

Number of gems obtained: 0 99 0 1 0

At this time, No.4 may not form an alliance with 1. Because in step 3), the steady-state No.4 can only get 1 gem, and No.4 has no life-threatening, only get 1 gem, but in this state, more people can be killed, so No.4 will oppose the alliance with 1.

To sum up, after rational no. 1 Choose to form an alliance with No.2. He only needs to form an alliance with No.3 and No.5 to save his life, but as a result, he doesn't. 1 Can't get the gem.

Second, don't form an alliance with number two.

Here, 1 needs to find two allies in No.3, No.4 and No.5. In step 3), we know that in the scheme proposed by No.2, No.3, No.4 and No.5 get 0, 1 and 0 gems respectively, so there are three combinations Rational No. 1 optional.

If you form an alliance with No.3 and No.4, the number of gems that 1 needs to pay is 3, of which No.3 and No.4 get 1 and 2 respectively.

If you form an alliance with No.4 and No.5, the number of gems 1 needs to be 3, of which No.4 and No.5 get 2 and 1 respectively.

In case of alliance with No.3 and No.5, 1 needs to pay two gems, of which No.3 and No.5 get 1 and 1 respectively.

To sum up, 1 will choose to form an alliance with 3 and 5 instead of 2. So 1 got 98 gems.

So considering all the situations comprehensively, we get that 1 will choose to form an alliance with No.3 and No.5, and the distribution result is as follows:

Pirate's name: 1 2 3 4 5

Number of gems obtained: 98 0 1 0 1