Let's look at a small situation first: A came to two detectives and told an event-he overheard a duel agreement between B and C outside the door, or B murdered a person, and the design clue pointed to C; Either c murdered a person and the design clue points to B.

The two detectives began to assume this possibility. According to what they said, they listed all possible assumptions, and then gradually eliminated unreasonable assumptions.

The first hypothesis: B and C are fooling A, which is a bit farce.

Refutation: B and C have no way of knowing that A will eavesdrop outside the door.

The second hypothesis: A wants to murder someone, designs clues to point to B or C, and makes up stories alone.

Refutation: illogical, it will only bring greater risks to A.

The third hypothesis: ABC conspired to deceive two detectives.

Refutation: meaningless behavior. First of all, if it is a joke, ABC's relationship with the two detectives has not reached this level; Secondly, if it disturbs the police's sight, A's statement reveals some key clues to two detectives, which makes them connect a recent murder with BC. This behavior is illogical.

The fourth hypothesis: A and B conspired to fabricate a story in order to frame C after killing.

Refutation: It doesn't mean that one point in this story is related to the recent murder.

The fifth hypothesis: similar to the fourth one, this time A and C conspired to frame B. ..

The rebuttal is the same as the previous one.

The sixth hypothesis: what A said is true, and B and C did make such a duel agreement.

There is no rebuttal, but it is not certain.

From the above story, we can easily see that this analysis method is like a common reasoning problem: after listing all the possibilities, one by one, there will always be a logical one. This is also the so-called mathematical method. In the above story, this method is used to simplify the above six assumptions, which are actually:

1.b and c are lying;

2.a is lying;

3.ABC is lying;

4. A and B are lying;

5.a and C are lying;

6.ABC is telling the truth.

(According to the situation at that time, there is no such thing as B lying alone and A and C being honest; There is no such thing as C lying alone, while A and B are honest. )

To sum up, these six hypotheses contain all the possibilities in this event, and there seems to be no seventh possibility.

So is this really the case?

The plot of the above story comes from the contemporary French detective novelist Paul? Holt is the seventh solution. In this book, the other of the two detectives (referred to as Dr. Tu for short) thinks there is a seventh possibility. He believes that the previous six hypotheses are only simple mathematical analysis methods, and there is "a crucial factor that any science can't control: the human factor" in the case.

He criticized the previous six assumptions: "These analyses are all based on a criterion, which is correct to some extent, but its limitations are also very dangerous: one thing is either true or false-either A is lying, or A is not lying, and so on ... But please note that it is people who lie, not machines. Sometimes, people only occasionally tell unimportant little lies, and in some cases they will tell a lot of lies. Therefore, there are different levels of liars between absolutely honest people and liars. And everyone lies in different ways and in different nature. Some people just cover up the truth when they are upset, some people lie purely for fun, and some people just lie about certain issues ... "

So Dr. Tu firmly believes that there is a seventh possibility.

This passage by Tu Youyou is actually very incisive. In fact, ABC didn't lie completely, just didn't tell the truth completely. Everyone lied to varying degrees for different purposes.

Then let's sort out the real context of the case: B (Jazz) is the murderer, and his purpose is to plant all the murders on C (Actor). First, B, C, a magician and the victim planned a practical joke. The target of the prank is the victim's landlord and his wife. The original plan was to frighten the landlord and his wife by making the victim suddenly disappear in the corridor through magic. But the victim died "accidentally" on the way, which was actually killed by B, but both C and the magician thought it was an accident. In order to avoid trouble, they threw the victim in the trash can on the street. Then B points the clue to C through a series of layouts.

However, the police could do nothing about the case, and other factors prompted B to implement the second plan. B told C that he suspected that A (the secretary) had stolen the collection at home and liked to eavesdrop outside the door, so B and C planned the opening story and performed a duel agreement in the room. On the other hand, A is actually an honest man, but B somehow instigated A to eavesdrop on the performance and asked A to tell the detective what he overheard on the grounds of avoiding C's murder. Some clues of the last murder case were hidden in this performance, so B succeeded in making two detectives turn their suspicious eyes to C, including B of course.

Finally, B carefully arranged to murder A, disguised as self-defense, and became his alibi in another case; Then pretend to murder the magician and design various clues to point to C, with the ultimate goal of hanging C.

This is the true face of the whole case.

Back to the story at the beginning, it is actually very clear about who ABC is lying in that story. Aside from the whole case, only from this incident: A basically told the truth about what he saw and heard, but he concealed that he had come to tell the detectives that these things were actually instructed by B. On the contrary, he repeatedly stressed in his narrative that the two detectives should not disclose this matter, especially B; B is performing, so he is lying; C is cooperating with B to show A, but it is actually lying.

This list is analyzed from this incident. In fact, it basically conforms to the first of the six hypotheses: B and C conspire to deceive A. This is true from the perspective of detectives and bystanders, but what is the difference from other perspectives?

From C's point of view, in his opinion, it is indeed a conspiracy with B to cheat A, or it conforms to the first of the six hypotheses.

From A's point of view, A will think that he and B conspired to stop C from killing people, which is similar to A and B deceiving C and the fourth hypothesis. Although it is not exactly the same as the detective's reasoning, it is essentially the same.

If there is a new situation from the whole case or from the perspective of B, in fact, B cheated A and C at the same time in the whole case. So in the opening story, what A and C did was in B's plan, two people faithfully carried out B's plan, and the liar was B, so the seventh hypothesis appeared, that is, the seventh answer.

But the conclusion I want to draw is that the seventh answer is really a completely false proposition, which is a flashy smoke bomb thrown by the author.

When listening to A's story, the two detectives didn't really think about all the possibilities in a purely mathematical way. In fact, they have subconsciously (or intentionally) ruled out some possibilities based on some limited information they learned at that time, which is not mentioned in the book at all. These possibilities are written in brackets when I simplified the six assumptions in front, namely:

7.b is lying;

8.c is lying.

? Indeed, according to the known situation at that time, the seventh and eighth hypotheses were almost impossible, but it turned out that the so-called seventh answer was the seventh hypothesis that they didn't mention at all, and the missing two hypotheses could be completely analyzed by mathematical methods, as long as the specific circumstances of the case could be temporarily put aside. It's a pity that they didn't use pure mathematical methods from the beginning.

Admittedly, the case itself is much more complicated than these assumptions, and it is impossible to successfully solve the case by finding all the assumptions. I still agree with Dr. Tu that "there are many different levels of swindlers", so the case itself is more complicated, and "human factors" need to be added to see the true colors of things. But we must not belittle the mathematical method. It is still an indispensable foundation to analyze it first.

It can also be seen from this book that although the author tries to emphasize the importance of "human factors" and is therefore suspected of belittling mathematical methods, the final result is that he still cannot jump out of the box of mathematical methods. Even if the case becomes complicated due to human factors, in essence, it evolved from the most basic mathematical analysis method, just like a seed gradually growing into a towering tree. Without that seed, there would be no tree, and the mathematical method is that seed.

PS: I wish Miss Shilla and the actress a happy life after going to America, despite the hardships.