8 smart questions and answers

Question 1:

"There are two doors in front of you, one of which contains hidden treasures, but if you accidentally break into another door, you can only die slowly ......".
There are two people behind these two doors. Both of them know which door has a treasure and which one is good at death. But the two men only tell the truth, one person speaks only false words. Who tells the truth? It depends on whether you have the intelligence to find out. The game rule is that you can only ask one question to each of them. So what do you ask? Who asked? Based on their answers, what should you do?

The best answer for job seekers:

Ask one of them casually: "If I ask another person, what kind of door will he tell me? If you ask the person who is telling the truth, the answer he gave you is the door to death, because he will honestly tell you what the lie man will say. If you ask the lie-only answer, what you get is also the wrong answer, because the other person is telling the truth, people who lie will tell you the opposite answer from people who tell the truth. So you just need to ask a person the above questions, and then choose the opposite door as they say.

Question 2:

"You have stood up for five people, and there is only one person among them telling the truth ......"
This problem is more difficult than the previous one. You only know that one of them only tells the truth, but the other four, sometimes tell the truth, sometimes tell lies, only one thing is certain. These four people will tell the truth and lie in a regular pattern: if the truth is told this time, they will tell the truth next time. If the truth is told this time, they will tell the truth next time. Your task is to find out one of the five people who only tell the truth.
You can ask two questions. You can ask two questions to the same person or ask two people respectively. What do you want to ask?

TIPS: You can arrange the tasks for two questions as follows: First, you can ask a question, no matter what the answer is, the answer to the next question is true or false.

The best answer for job seekers:

If you want to find someone, first ask: "Are you the one who only tells the truth ?" If the answer is yes, ask the person again: "Who is telling the truth ?"; If the answer to the first question is no, you can ask the other party "who is not only telling the truth ?"
As prompted by this question, the value of the first question is that if you get the answer "I am", then either the person you ask is the one who only tells the truth, either this round of "half-truth and half-truth", no matter who he is, he will surely tell the truth in the next round. So you can continue to ask this person: "Who is the only one who tells the truth ?" The answer is the correct one.
If the answer to the first question is "I am not", the respondent cannot be the one who only tells the truth, it can only be a "half-truth half-Story" person who tells the truth in this round. This person will say false things in the next round, so you should ask him, "who is not just telling the truth ?" He also told you that only the one who tells the truth is allowed.

Question 3:

"Aliens are planning to use the Earth to plant mushrooms, and they have captured ten humans ......"
Aliens use these 10 people to represent 6 billion people on Earth. They will test these 10 people by using aliens and decide whether the earth is eligible to join the cross-interstellar committee. If not, turn the earth into a mushroom farm.
Tomorrow, these ten people will be lined up in a dark room. Aliens will wear a hat in purple or green, then the aliens will turn on the light. These ten people will not be able to see the color of their hats on their heads, but they will be able to see the color of hats on each head at the front of you.
The color of the hat is random, which may be purple, green, or any combination.
Aliens will ask everyone from the back: "What is the color of your hat ?" If this person is correct, the person will be able to answer the question, and the 0.6 billion people on the earth he represents will also be rescued. Otherwise, this person will be shot up, and aliens will turn the 0.6 billion people he represents into Mushroom fertilizer. Everyone's answer can be heard in the room.
Now, with the fate of mankind in your hands, you can design a plan for these 10 people to make a plan in advance, which must save as many people as possible.

Tip: there is a solution for saving at least nine of you.

The best answer for job seekers:

The tenth person calculates whether the green hats of all people are odd or even and sends a signal to the people above, in this way, the first person can determine the color of his/her hat by checking whether the parity of the green hat in front of everyone changes. If the parity of the green hat changes, then you are the "green hat" that leads to changes. If there is no change, you are the "purple hat ".
Because all people cannot speak except to answer questions from aliens, the "signal" of the tenth person can only be included in his own answer. For example, if the first nine people have an odd number of green hats, this human tells aliens that their hats are "green". If they are even numbers, they guess their hats are "Purple ". This is equivalent to giving a dark sign to the person in front of him. The person in front of him can determine whether his hat is green or purple by calculating the parity changes of everyone in front of him.
The person at the end had no choice for the public interest. According to the hats of the previous person, the aliens were told whether they were "green hats" or "purple hats ", his answer is 1/2 likely to be correct, but the people above him must be able to answer correctly.
Not yet understood? For example, when the tenth person saw an odd number of green hats in front of him, he told the aliens that he was green. The person before him knew that he meant an odd number of green hats in the first nine, this is the ninth person who counts the first eight people. If there are odd numbers in the first eight, they are purple hats. The ninth person told the aliens that they were purple hats. The eighth person knew that the green hats were not reduced or odd, and then the seven men before the green hats were odd and even, they could judge their hats; if the ninth person tells aliens that they are green hats, the eighth person should know that the number of green hats has been reduced from an odd number to an even number, and then let's look at all the previous green hats to make judgments. One by one, as long as everyone listens carefully to the answer from the following person and calculates the parity change of the remaining green hats in their hearts, the first nine people will be rescued.
Of course, you can also calculate the parity of the purple hat.

Question 4:

"100 perfect Logistics' sitting in a room ......"
This is a reality TV show, where 100 people with flawless logical thinking ability sat in a room in a circle. Before entering the room, these 100 people were told that at least one of the 100 people had a blue forehead. You can see other people's forehead color, but you cannot see your own, you need to guess whether your forehead is blue, when the room light is turned off, if you guess your forehead is blue, you need to stand up and leave the room.
Then the lights in the room were turned on again, and those who thought their forehead was blue were no longer in the room. Next, the light will be turned off again, and the rest of the people speculate that their forehead is blue and leave the room.
The question is, what will happen if the foreheads of the 100 people are blue? Note that these 100 people have flawless logical reasoning capabilities, and they will make reasonable reasoning and guesses based on other people's forehead colors.

Tip: What happens if 100 people are not all blue foreheads?

The best answer for job seekers:

The following will happen: when the light is turned off and turned on and off, when it is repeated for 100th times, everyone will leave at the same time.
Why? Think about it, everyone sees the other 99 people's forehead in blue, turn off the light and turn on again, and find that the companions of The 99 blue foreheads have not left, and then turn off the light again, after repeating 100 times, everyone leaves the room at the same time.
To understand this, let's assume that only one person's forehead is blue. As the 100 person was notified in advance that only one person's forehead is blue, if this person sees that other 99 people's forehead is not blue, immediately you know that you are blue, so when the light is turned off, this person will leave the room.
What if two men have blue foreheads?
One person with a blue forehead may think: My forehead may be blue or not blue. Now there are 99 other people with a blue forehead. If I am not blue, so this person is the only one, so he can see that we are not blue forehead, he can be pushed out, then he will leave when the light is off, I will wait, turn on the light. If he has already gone, it will prove that my forehead is not blue.
On the contrary, if my forehead is blue, the person with the blue forehead will wait for the first time as I thought, in this way, if the person with the blue forehead is still there, it proves that my forehead is also blue. In this way, we will leave when the light is switched off for the second time.
And so on, if there are three people with blue foreheads and you see the other two people with blue foreheads, you should calculate that if your foreheads are not blue, when the light is switched off for the second time, the two of them will leave at the same time. If they do not leave at the same time, it will prove that my forehead is blue and I should leave when the light is switched off for the third time. As a result, the three blue foreheads left while turning off the light for the third time.
Repeat the above logic for one hundred times and you will get the most correct answer.

Question 5:

"The logic experts sat around in a circle, and there were numbers on their foreheads ......"
The three persons with perfect logical reasoning ability sat in a room in a circle, and each person's forehead was painted with a number greater than 0. The numbers of the three persons were different, everyone can see the numbers of the other two and their own.
In the case of these three numbers, one of them is the sum of the other two numbers, and the other is known. One of the Logics is 20, and the other is 30.
The game organizer walked behind the three logical operators and asked the three men what the numbers on their foreheads were. But in the first round, each logologist answered that they could not speculate on what their numbers were. The game organizer had to ask questions in the second round. Why? Can you guess the numbers of the three logical operators?

The best answer for job seekers:

The result depends on the answer of the third logologist. The three numbers are 20, 30, and 50 respectively.
Assume that the number on the forehead of the second and third logistician is 20 and 30. If the number of the first logistician is 10, then the second logistician will see that the other two are 10, if one is 30, you will think: "I am either 20 or 40."
The third logologist saw two other people, 10 and 20, and thought, "I am either 30 or 10, but I am not 10, because every number is different, so I should be 30."
In this way, the third logologist will guess that his number is 30, but he does not. In the first round, no one has accurately deduced his number. This shows that our premise is incorrect, the number of the first logistician is not 10, so he can only be 50.

Question 6:

"You have one hundred bulbs in front of you, in a row ......"
One hundred bulbs are arranged in a row. In the first round, you turn them on, and in the second round, you turn off one bulb every other, so that all the even bulb bulbs are turned off.
Next, in the third round, you turn off the light bulb on every two bulbs and turn off the light bulb on (that is to say, change the switch status of all the bulb in multiples of 3 ).
And so on, you change the switch status of all the bulbs that are in multiples of 4, and then change the Switch Status of the bulbs that are in multiples of 5 ......
How many bulb bulbs are on during the 100th round?
Tip: if you are in the N round (N greater than 1 and less than 100), the switch status of the bulb at the multiple position of N changes.
In turn, for example, 8th bulbs, when you are in the 8-factor wheel (I .e., Round 1, 2, 4 and 8), it will change the switch status. So if M has an odd number of factors, the switch status changes odd once.

The best answer for job seekers:

The 10 light bulbs are on, and the 10 light bulbs are all in the middle of the queue.
According to the prompts, we can see that the essence of this problem is to find out how many BITs have an odd number of factors. Each time there is a factor, the light bulb will be switched to the switch state at the round of the factor number.
For example, 1st rounds, because all 100 digits have a factor of 1, all are opened; 2nd rounds, only the bulb bulbs with a factor of 2 that can be divisible by a number are switched off; 3rd rounds, only the bulbs with three elements that can be divisible by three are switched. Similarly, if a light bulb has an odd number of factors, which means that the light bulb is opened and closed for an odd number of times, the light bulb is eventually turned on. If the light bulb has an even number of factors, in the end, it is in the closed state.
For example, 1st bulbs have an odd number of factors, 2nd have an even number (3rd), and 4th have an even number (). Have an odd number (, 4 ), so 4th bulbs are still on.
The final calculation result shows that all the bulbs with the number of BITs are still bright, because these BITs have an odd number of factors, such as, and 16 ......
In less than 100, there are 10 shards, which are 81,100, respectively. The 10-digit bulb will eventually be on.

Question 7:

There is a bucket with 100 white balls and black balls each. People must take the ball out according to the following rules:
1. Get two balls from the bucket each time
2. If there are two balls of the same color, put another black ball;
3. If there are two different colored balls, put another white ball.
Q: What is the probability that only one black ball is left in the last bucket?

The best answer for job seekers:

The last ball is black.
Method 1: In either case, the number of balls in the bucket is constantly decreasing, and the number of balls is always decreasing every time (take two balls and put them in one). In this way, we can speculate that, in the end, only one ball is in the bucket. Of course, white balls and black balls are all possible at this time. When two identical white balls are extracted from the ball, you should add another black ball, and reduce the white ball by two. When two identical black balls are taken out, add another black ball to reduce it. When one of the black and white balls is removed, the black ball is reduced by one. In either case, there are only two ways to reduce the number of white balls each time, either without increasing or decreasing, or reducing two. There is no situation where only one white ball is reduced, from the above results, we can see that the last one must be a black ball.
Method 2: Consider the difference or XOR in mathematics: if there are two balls of the same color, put another black ball. If there are two balls of the same color, then put another white ball, think of the difference or in mathematics: two numbers are the same, the difference or result is 0, two numbers are different, and the difference or result is 1. Because the ball is not at the same time, put another black ball, then assign the black ball to 0, and the white ball to 1. There are 100 white balls and 100 black balls each, 100 0 and 1. The result of the exclusive or exclusive operation is 0, that is, the black ball.