"The level of this year's competition students is a bit worrying. ”

When Tao Li said this, his eyes never left the classroom for a moment, in fact, he deliberately said this, arrogant soldiers will be defeated, these students have always felt that they have learned mathematics well, and over time they will form the illusion that "no topic can stump me", and they will disdain many basic but important knowledge points, but forget such a simple truth as a tall building on the ground.

A typical representative of the eye hand and the low hand!

As soon as Tao Li's words came out, the students in the classroom had different expressions, some lowered their heads in shame, some looked at Tao Li unwillingly, and some were unconvinced with angry faces.

"Teacher Tao, this question can't explain anything at all, I don't think there seems to be a requirement for this in the syllabus!"

"Yes, I just looked at the syllabus of the math competition, and this question should be a question that exceeds the syllabus, so how do we do it? ”

Soon, several students asked such questions.

Tao Li originally said that he was doing a problem related to number theory, but the problem on the blackboard was not linked to number theory at all, and could only be said to be an algebra problem. Some people have such questions, and Tao Li does not find it strange.

"Strictly speaking, what the two students just said was right, this question is indeed not in the competition syllabus. But what doesn't appear in the syllabus, can't you be examined? Or in other words, can't the questions that are out of the syllabus appear in the competition exam?"

Tao Li didn't explain to the two students about the superscription, but asked with a smile.

Since it is called a mathematics competition, the questions of the exam are naturally different from the usual exams, although most of the test questions will definitely be written according to the syllabus, but even the general exam will appear "beyond the syllabus" phenomenon, not to mention the exam of the National High School Mathematics League, which represents the highest level of high school mathematics!

And in Tao Li's view, in fact, there is no such thing as "over-outline" in the exam, although some questions can not be traced back to the source to find out the corresponding test points at a glance, but they must be expanded and extended around one of the knowledge points, not so much that the topic is beyond the outline, but that their knowledge points are not solid enough and the ability to draw inferences is insufficient.

"The purpose of this question is not to stump everyone and make it impossible for all of you to do it, if there is a question in a test paper that no one can answer, then the test paper itself is a failed test paper! The purpose of the problem is to distinguish the span of test scores, not to make you unable to do it!"

Seeing that everyone didn't speak, Tao Li smiled and continued.

"From the very beginning of entering the lecture hall, I could feel that there were many students who thought very highly of themselves, felt that they had learned mathematics very well, and that they would definitely win prizes as long as they participated in mathematics competitions. So when I asked you if you still have any doubts about number theory, your answer was that there was no doubt, all of them, number theory is very simple. But actually, you don't know anything about mathematics, and I don't dare to say that I am good at mathematics after four years of theoretical mathematics, let alone you?"

"Okay, I've said everything I need to say, now let's get to the point. Zheng Tongya, you talk about your understanding of this problem, it doesn't matter if you get a result or not, what I want is your solution idea. ”

Tao Li felt that he was almost educated, so he changed the conversation and prepared to explain this topic. Since no one took the initiative to answer, he could only name him, except for Zhang Xingchen, he only knew Zheng Tongya.

was named by Tao Li to answer the question, Zheng Tongya did not panic in the slightest, pushed the glasses on the bridge of his nose, and then picked up the scratch paper in front of him and glanced at it, and began to speak in an orderly manner.

"After getting this question, my first thought is to figure out the meaning of this question, that is, to grasp the main point of the question, for this question, my understanding is that when each prisoner takes a plan, it is necessary to make the remaining prisoners have the greatest probability of taking the best plan...... Later, I was also inspired by Zhang Xingchen and began to continue to follow his train of thought......"

When Zheng Tongya and the three of them were discussing below, Tao Li knew about it, and originally thought that the original idea would be put forward by Zheng Tongya, but he didn't expect it to be Zhang Xingchen who thought of it first, which was a bit unexpected by Tao Li.

It seems that his excavation of Zhang Xingchen is not thorough enough!

"The three of us finally came to the conclusion that if the first prisoner was determined to let the other prisoners accompany him to death, then he only needed to grab 96 soybeans when he grabbed them. But we feel that there is another answer to this question, and the premise of this answer is that the first prisoner has compassion and wants more people to live, but we have not yet figured out how to do it. ”

Zheng Tongya said all the results of the discussion between the three of them in one breath, then put down the scratch paper in his hand and looked at Tao Li again.

Tao Li nodded with satisfaction and motioned for him to sit down, "It's not bad, although it wasn't made by an individual, but it was already surprising to be able to come to such a conclusion, the overall idea is not problematic, but the derivation of some details still needs to be further strengthened." The final conclusion is also correct, and Zheng Tongya is right, there are indeed two answers to this question according to different understandings. I'll start with the first answer. ”

This problem, which is considered to be Tao Li's magic hand, is a similar problem he encountered when he read the magazine "Intermediate Mathematics" before, Tao Li thought it was very interesting at the time, so he deliberately copied the problem, and now this problem is adapted by Tao Li based on that problem, and the difficulty has also improved.

After listening to his explanation, many students also have a feeling of being sudden, and their cognition of Tao Li in their hearts has improved several grades in an instant!

"This is the first answer, and it is not difficult to understand, so I will focus on the second answer, and then we will continue to deduce this conclusion......"

After a slight pause, Tao Li continued.

It is said that it is a topic that is beyond the outline, but when Tao Li explained, he still used many knowledge points in the competition, but this question has high requirements for the flexible use of knowledge points, which also verifies Tao Li's point of view, there is no so-called super-outline question.

After Tao Li's explanation, the students present basically grasped the essence of this question, Tao Li explained the knowledge points at the same time, but also did not forget to teach them the content related to exam skills, which benefited the students a lot.

"Alright, that's the end of the question. Now let me ask again, is there anything you don't understand about elementary number theory?"

After finishing this question, Tao Li asked the same question again.