First, the coin paradox.

Put two identical coins together, fix one coin and let the other coin revolve around it. So, how many times does the rotating coin have to turn to return to its original position?

Theoretically, the same coin will have the same circumference, so it will turn back to the origin after just one revolution. In the process of doing the experiment, it was observed that it was just half the position of the fixed coin after one lap. By the time I turned back to the original point, I had already turned twice.

This can be said to be a misunderstanding and illusion of the experimental operation process. As shown above, at first, point D is below the coin and connected with the fixed coin, and the rotating coin is above the fixed coin. When the rotating coin rotates under the fixed coin, the point D is still under the coin, but at this time the point I is connected with the fixed coin. When the experiment is done, people will subconsciously think that the rotating coin has turned once (try it, hehe), but it is actually half a turn. On the one hand, I don't know why this brain teaser was once listed as a century problem.

Second, three questions.

The biggest reason why this problem was widely discussed at one time was man-made restrictions. Why do you say that? Let's talk about the problem itself first.

Three closed doors, one of which has a sheep behind it. Now open one of the doors and the probability of seeing the sheep is 1/3. If someone chooses a door first, whether there is a goat or not, this door will not open for the time being, and one of the other two doors without a goat will open. At this time, let the person who chose the door at first make a second choice, continue to open this door or open another door that has not been opened. Then I don't know who came to the conclusion: "The probability of seeing a sheep at this time is 2/3."

This really froze me, because no matter what I think, I think the probability at this time is 1/2, because this situation is not the same as expelling a door and making a choice between two doors. How to get two-thirds of the choices? If you don't struggle, it is an endless cycle that you can't jump out.

Therefore, without a modest heart, I seek omnipotent netizens on the Internet to solve this problem for me.

Netizens are really omnipotent, and even the methods to solve problems are varied. Sure enough, I can't be stupid when I do math problems. I'm too young to study more.

I couldn't understand many explanations, because my knowledge level was limited, so I later found some netizens with grounded words to answer them for me. With the help of everyone, I finally figured it out. At first, I just thought I was too young, but after I figured it out, I realized that I was simply ignorant. This kind of problem can last for hours. I can't think of two-thirds of the reasons, and the conditions of the problem are missing. What is missing? In the second option, there are two options, keep or replace. If we want to get the probability of 2/3, we must have the conditions to choose replacement, which becomes a problem of choosing two out of three.

So why didn't you see this condition at the beginning? Because if this condition existed from the beginning, wouldn't this "big problem" become a problem for primary school students? I see. The problem that cannot be solved should not be a problem of nothing, but a problem of conditions. Don't! This is my problem! I can't find this missing condition for such a long time. How could it not be my problem?