The movie is pretty good, even though it looks like a compilation of fun math problems. But it's brilliant and fascinating about mathematics, and the story is tighter. The general idea is that a wealthy mathematician spent nearly 35 years proving Goldbach's conjecture, and just as he was about to complete it, a young man actually announced to the media that he had proved Goldbach's conjecture. Then a few days later, the lad said his certificate was destroyed by the intruder. In fact, the young man didn't prove it at all, just to pursue a lie told by a girl with a high IQ, but while talking, the media forced him to "hand in the papers", so he had no choice but to take advantage of someone entering the dormitory to sabotage, claiming that the proof was sabotaged. Now the mathematician has finally succeeded, but because of the respect of the mathematical community for the "first" status, unless the young man confesses (which is unlikely), the mathematician's achievement will not be successful in his life, even if the young man spends another three years. Just handed in the paper, the mathematician is still second. So, in anger, the mathematician set up a plan to kill the young man. And also designed the so-called "mathematical problem" to invite other people to accompany him, the purpose is to test the young man's mathematical ability. And in order to cover up the fact that he murdered, he also created a suspicion and created another person to act as the "master". And it was designed early in the morning to lure the owner out, and then kill him (with poison gas in the car seat belt). Taking advantage of the "hatred" between another participant and the owner (the participant drove his car and injured the owner's daughter, but the two have not met) to make everyone think that they are innocent people involved. Of course, the organization has exhausted the calculations, but ignored a problem. Everyone is smart, and the three stooges are still Zhuge Liang. So in the end his conspiracy was discovered, and he died in the room with the proof instead. The other three managed to escape through his pre-designed escape. The beauty of the movie lies in a "connection". People who seem to be incompatible are actually connected and contradictory. In the eyes of mathematicians, abstract mathematics is related (like the Goldbach conjecture shown in the film: in 1742 mathematician Christian Goldbach discovered that an even number can be expressed as the sum of two prime numbers. For small even numbers, it couldn't be easier: 18, an even number, equals 7+11, where 7 and 11 are both primes; 24 equals 5+19, 5 and 19 are both prime numbers; 50 equals 13+37, and so on. Even big numbers can be done in the same way, let's try, any number, 7112 equals 5119 plus 1993, is a prime number. But you can't try it with all even numbers, because the numbers are infinite, you have to find a law that applies to all numbers, and finding this law becomes the hardest problem in the history of mathematics), and the same is true of everything in reality. So, taking advantage of A as his own rival, B as A's girlfriend and the girl he brought up, C as a scapegoat he introduced, and C thought the mathematician helped him kill his enemy D. He committed a murder. Of course, there are still many loopholes in the screenwriter. The mathematician showed the invitation letter to his doctor friend at the beginning, and he didn't need to show it to his friend at all. Because the person who sent the invitation was himself. Even if he asks his friends to prove that he is only a participant, not the initiator, or the murderer, the police can also check the source of the invitation letter and investigate through evidence such as letter paper and ink. What's more, the police can also catch him by buying the owner of the hydraulic press. When everyone found out that the so-called invitation was a trap at the beginning, they all knew that the life span of the mathematician referred to by their "code name" happened to be their own age. At that time, they ignored the mathematician's "code name" - Hilbert Very long-lived, beyond his age. More importantly, the mathematician left a way for himself, but it was obvious that he was the oldest and could not smash the blackboard and escape in front of everyone. Also, the young couple had not yet gotten rid of the "breakup" crisis, and then the mathematician saw that they were about to kiss when they entered the door. 5 and 19 are both prime numbers; 50 equals 13+37, and so on. Even big numbers can be done in the same way, let's try, any number, 7112 equals 5119 plus 1993, is a prime number. But you can't try it with all even numbers, because the numbers are infinite, you have to find a law that applies to all numbers, and finding this law becomes the hardest problem in the history of mathematics), and the same is true of everything in reality. So, taking advantage of A as his own rival, B as A's girlfriend and the girl he brought up, C as a scapegoat he introduced, and C thought the mathematician helped him kill his enemy D. He committed a murder. Of course, there are still many loopholes in the screenwriter. The mathematician showed the invitation letter to his doctor friend at the beginning, and he didn't need to show it to his friend at all. Because the person who sent the invitation was himself. Even if he asks his friends to prove that he is only a participant, not the initiator, or the murderer, the police can also check the source of the invitation letter and investigate through evidence such as letter paper and ink. What's more, the police can also catch him by buying the owner of the hydraulic press. When everyone found out that the so-called invitation was a trap at the beginning, they all knew that the life span of the mathematician referred to by their "code name" happened to be their own age. At that time, they ignored the mathematician's "code name" - Hilbert Very long-lived, beyond his age. More importantly, the mathematician left a way for himself, but it was obvious that he was the oldest and could not smash the blackboard and escape in front of everyone. Also, the young couple had not yet gotten rid of the "breakup" crisis, and then the mathematician saw that they were about to kiss when they entered the door. 5 and 19 are both prime numbers; 50 equals 13+37, and so on. Even big numbers can be done in the same way, let's try, any number, 7112 equals 5119 plus 1993, is a prime number. But you can't try it with all even numbers, because the numbers are infinite, you have to find a law that applies to all numbers, and finding this law becomes the hardest problem in the history of mathematics), and the same is true of everything in reality. So, taking advantage of A as his own rival, B as A's girlfriend and the girl he brought up, C as a scapegoat he introduced, and C thought the mathematician helped him kill his enemy D. He committed a murder. Of course, there are still many loopholes in the screenwriter. The mathematician showed the invitation letter to his doctor friend at the beginning, and he didn't need to show it to his friend at all. Because the person who sent the invitation was himself. Even if he asks his friends to prove that he is only a participant, not the initiator, or the murderer, the police can also check the source of the invitation letter and investigate through evidence such as letter paper and ink. What's more, the police can also catch him by buying the owner of the hydraulic press. When everyone found out that the so-called invitation was a trap at the beginning, they all knew that the life span of the mathematician referred to by their "code name" happened to be their own age. At that time, they ignored the mathematician's "code name" - Hilbert Very long-lived, beyond his age. More importantly, the mathematician has left a way for himself, but it is obvious that he is the oldest and cannot be in front of everyone. His face smashed open the blackboard and escaped. Also, the young couple had not yet gotten rid of the "breakup" crisis, and then the mathematician saw that they were about to kiss when they entered the door.
Of course, no matter how good the story is, I think it's the math problems. Although in order to be suitable for the public, the subject should not be too difficult. But the topics are clearly handpicked, so they are all instructive. It can even be said that they not only reflect the essence of mathematics, but also demonstrate many methods of mathematical thinking.
The essence of mathematics is to discover laws. As the title of the invitation letter, it is a list of numbers 5 4 2 9 8 6 7 3 1, asking to find out their regularity. It looks like a few Arabic numerals, but it's actually very difficult. But the answer tells us to sort alphabetically, in other words, it's not the numbers themselves, but the sounds of the numbers. Because the movie is a Spanish movie, it is still sorted by Spanish subtitle pronunciation (Spanish, from 0 to 10: cero, uno, dos, tres, cuatro, cinco, seis, siete, ocho, nueve, diez). Such a problem, no matter how talented mathematicians are, if you don't understand Spanish, you really can't start. However, many primary school students in China now also play this set of "Mathematics Olympiad" questions, arranging numbers in the order of Hanyu Pinyin. Why do you say that such a question shows the essence of mathematics? Because there seems to be no regularity, there is actually a regularity. And we find that there are countless ways to find the law, and when we can't find the way, we feel that there is no law. Smart people and geniuses are all good at discovering patterns, and they will use some different ways of thinking, or from different perspectives.
There is also a very instructive problem in the film, which gives us a deeper understanding of the application of mathematics. It's a question of cracking the password. The title is a large sequence of 0s and 1s (00000000000000001111111111000...). Ask to decipher what this number expresses. This problem seems like a fantasy, because we don't know the password, and the 0s and 1s are not arranged regularly. But the boy found a set of mahjong and used its two sides to represent 0 and 1. Of course, there is another key point, that is, this sequence has a total of 169 numbers. And that number is 13 squared. So the boy used mahjong to form a square matrix of 13 by 13, so that 0 and 1, front and back clearly showed a very clear symbol for us: a skull. The reason why this problem is exquisite is that, first of all, when we solve problems with mathematics, we often need to visualize the problem and connect it with the actual material "image", which is Richard Feynman's concept. It is also the key art of Newton and Einstein's problem-solving explained in my book "Absolute Reason" - turning abstraction into image, and image into abstraction. Secondly, for a thing that seems to have no clue, its hidden law must start from its characteristics, understand its characteristics, and try to understand the research object as much as possible. The more features you master, the more details you understand, and the more eloquence you can master. If you ignore that the sequence has 169 numbers, it is 13 squared. Then there are still many possibilities to arrange the front and back of mahjong, which is too time-consuming (not to mention that in addition to bar-shaped columns, rectangles, squares, and other shapes such as isosceles triangles, circles, etc.) . We must minimize the possibilities. In the end, just like the young man began to think that the spelling was a human face, but he was wrong, and the little girl looked carefully and pointed out that it was a skull. We will also find a question with a different interpretation of the answer itself.
Of course, mathematics can also be aimed at real-world problems. What do we need to solve all kinds of problems in reality? The essence is to find the connection, and the specifics are much more complicated: 1. We must fully grasp the conditions to use the connection; 2. We must clarify the process and the steps, because the results are different in different sequences; 3. We must find a There are many breakthroughs (there may be many in reality, but generally one is enough), and the breakthrough is often common sense; fourth, when there is no ready-made breakthrough, one must create a breakthrough to cut into the problem, which fully reflects the initiative of the person who solves the problem.
Below we illustrate these points in conjunction with the questions in the film (I have reordered the questions in the film for clarity).
Question 1:
A student asks the teacher: How old are your daughters? The teacher replied: Multiply their ages and the result is 36; if you add them up, the result is your house number. The student said: There is one more condition. The teacher replied: Indeed, the eldest daughter can play the piano. How old are these three children?
The question film does not give the thought process, only the answer. We can calculate it ourselves. First, according to the first condition, we can calculate the following possibilities (3 daughters, multiplied by age to get 36) 1*1*36, 1*2*18, 1*3*12, 1*4*9 , 1*6*6, 2*2*9, 2*3*6, 3*3*4. Secondly, according to the second condition, the addition is equal to the house number. This condition is known to the student, but after calculating it, he said "there is one more condition", indicating that there are at least two sets of possible sums that are the same, so that he has no way to do it. get the answer. Among them, there are 1+6+6, 2+2+9 two groups of possible sums are both 13, so we can exclude other groups. Finally, the teacher said that "the eldest daughter can play the piano", obviously only the 2+2+9 group has "one eldest daughter". So the answer is that the eldest daughter is 9 years old, and there are twins who are 2 years old. Obviously, it is the "house number that we don't know" that is easy to mislead us, but in fact, this omission is exactly the condition. In other words, when we look at the missing condition, we often ignore that this also happens to be a condition. Just as Einstein considered the "wrong" conditions, it's not necessary to exclude them, they just happen to be the key.
Question 2:
The shepherd had to cross the river in a boat, he brought a sheep, a wolf and a cabbage. you know? The boat can only carry two things at a time, like a shepherd and a sheep, or a shepherd and that cabbage... You have to figure out how the shepherd should cross the river so that the wolf doesn't eat the sheep or the sheep eat vegetables.
The film does not provide an answer to this question, because everyone opposes such an unrealistic question, because "a shepherd can't lead a wolf". Let's look at the answer first: the first time we took sheep across the river, we came back empty. The second time I took the wolf across the river and brought the sheep back; the third time I brought cabbage across the river and came back empty; the fourth time I brought the sheep across the river. 4 times in total. This question may seem unrealistic, but it is clearly an upgraded version of the problem that putting an elephant in the refrigerator takes several steps. Because, in reality, we often encounter such difficulties in dealing with problems, and we must rely on reasonable arrangements to avoid conflicts.
Question 3:
A confectioner receives 3 opaque candy boxes: one with mints, another with anise, and one with both. The box was labeled mint, anise or a mix, but the confectioner was told all the labels were wrong. How does this person take out the least amount of sugar to verify what's in the box?
This question has not only the answer but also the analysis: you just have to take one from the mixed box, because that box cannot be a mixed box. If it is mint that comes out, then it is mint that writes this mix. That way, the two remaining boxes, the one that says mint is the fennel (it can't be mint), and the one that says fennel is the mix (it can't be either fennel or mint). Obviously, as long as the conditions are fully utilized, a breakthrough can be found. What's more, the breakthrough here is the condition "the label is all wrong".
Question 4:
There is a light bulb in an airtight room (implying that the light inside cannot be peeped through the crack of the door), there are three switches outside the room, only one can turn on the light bulb, but the door is locked. The switch can be turned on or off at will, and when you open the door, you have to say which switch lit the bulb.
This seems like an unsolvable problem, and it seems to be all about luck. However, because at this time someone was scalded by the lamp. Inspired the little girl, she found the answer by using the light bulb to get hot: the trick is the temperature of the light bulb! We turn on switch 1, hold it for a while, then turn it off; turn on switch 2, open the door, if the light bulb is on, 2 is the correct switch; if the light bulb is off and hot, then the previous switch, which is 1, is the correct switch switch; if the bulb is off but cold, 3 is the correct switch. Clearly common sense played a role. Solving problems in reality often requires some accumulation of knowledge, or even some common sense. Because there may be a lot of knowledge involved, it is impossible to get started, so many scientists always rely on their own growth conditions, professional training, and even external cues (such as Richard Feynman's cue from the Frisbee, and the Newton who was smashed by an apple). legend). The next question: Mom is 21 years older than her son. After 6 years, her mother is five times as old as her son. Where is Dad now? Obviously it is not difficult to calculate, 5*(6+X)=21+X+6, X=-3/4. But don't say that the son's age is a negative number, just say that the son's age has nothing to do with where the father is now. In fact, the problem is the same as the light bulb problem. It is related to common sense "pregnancy in September". 3/4 years is 9 months, which means that father and mother must be together to create a human being.
Question 5
In the island of lies, everyone always lies; in the island of truth, everyone tells the truth. A foreigner is lured into a room with two doors, one leading to freedom and the other nothing. The two gates are guarded by a gatekeeper from the Island of Lies and a gatekeeper from the Island of Truth. To find the gate to freedom, foreigners can only ask one of the gatekeepers a question. But he didn't know which one was from the island of lies and which one was from the island of truth. What kind of questions did he have to ask?
There are so many variants of this question that everyone feels deja vu. In fact, the answer is not complicated. You should ask one of them: the other will tell me which door leads to freedom? Because they all say the wrong door, choosing the opposite door is the right answer. The specific explanation is like this, for example, the correct door is A, and the wrong one is B. Because people on the island of lies, people who know the island of honesty will point to A, so they will point to B; and people on the island of honesty who know that people on the island of lies will lie and point to B, so they will point to B as well. Clearly, a problem is created here to make the contradictions "cancel" each other. Because mathematical answers are based on a "non-contradiction" basis. This kind of thinking, which seems simple, is actually the key method for Gödel to arrive at the "incompleteness theorem". This problem, in fact, there is another case in the film, that is, the young man wants to investigate who the host who invited everyone is through the mailbox that sent the invitation. He knew that the address to send the answer back to was 325 mailbox. The post office will not tell you who the owner of the mailbox is because of the non-disclosure agreement. His strategy was this: I went to the post office and claimed that I was the president of the Brown Bear Conservation Association, and I said we only had 325 brown bears left in the mountains. We wanted the mailbox number to be a representative number, the staff said 325 mailboxes were owned, and I insisted on how important that mailbox number was to us and how grateful the only 325 brown bears left were. In this way, he cheated the name of the mailbox owner. Because he didn't directly ask for the name of the mailbox owner, which made the post office people ignore his real purpose; and sympathy made the post office people hope that he could get the 325 mailbox. The contradiction was sent to the person at the post office, so that he would tell the owner of the young man's mailbox and let the young man go to him to get the mailbox. And donated money to brown bears.
This kind of solution is creative and proactive, and it is also a problem that often exists in reality.
Of course, there are other problems in reality, as Fermat talks about in the film: I recently read a study on the most common unattainable human desire, about flying or invisibility, not solving mathematical puzzles subject. If you choose to fly or be invisible, it shows more of your own human choice. Just like what method we use to solve the problem, this is actually more real and meaningful. It's like mathematicians aren't trying to kill lads. Instead, inviting him, having a face-to-face conversation with him, may have solved the problem more perfectly. But it is clear that the mathematician's extreme character caused him to make a wrong choice, because he thought of "suicide" at first, and then thought of "murder".
This is where the real beauty of the movie comes from. This is what we should remember most. 16.10.30
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