A genius? I just love studying.

Chapter 42: The Divine Answer
"Teacher Yan."

After leaving the classroom, Deng Leyan stopped Yan Zhenhua, who was striding forward, and said, "I want to know why he won the special award."

He is also an old contestant, so he naturally knows the rules. Generally speaking, those who can win special prizes have to have clever answers to certain questions on the basis of getting full marks.

He was a little curious about why Chen Hui won the special award.

Of course, he was more skeptical. He didn't think there were any other clever ways to answer these questions this year. He believed that Chen Hui's special award was probably won because he submitted his paper two hours early.

If that was the case, he would not accept it.

He felt it was unfair!

Yan Zhenhua smiled slightly, probably guessing what Deng Leyan meant. "How did you solve the last question?"

If it were someone else, he might not even bother to pay attention. He still had a lot of things to do today and had no time to waste.

But Deng Leyan is also a talented young man, and one of the only two players to score full marks in the provincial competition, so he should be given some face.

"?"

Deng Leyan frowned slightly. Yan Zhenhua's answer gave him a bad feeling.

Could it be that the guy really came up with some brilliant solution?
He was now even more curious.

"I first constructed several number sequences. For example, an 11-term sequence, S11, could be {1, 1, 1, 1, -9, 1, 1, 1, 1, 1}..."

Deng Leyan began to speak, describing his thoughts as simply as possible, "After constructing a few number sequences, I found a pattern."

"If the number of terms in this sequence can be infinite, then there will exist any S11 (the sum of any 11 terms) > 0, S7 0. Since any S7 0 contradicts the question, the number of terms in this sequence cannot be infinite."

"Then I started to select 15 items to try to deduce, and found that 15 items could meet the problem. At this point, I had found the pattern, and I started to deduce the 17-item sequence directly."

“若17项的数列满足题设，那么有S1-11>0，S1-7 0，又因为S5-11 0……同理，根据S2-12>0可以推出S2-5>0，S9-12>0，根据S3-13>0可以推出……

Finally, we can find that if this sequence has 17 terms, we can infer that the sum of any 4 terms in this sequence is greater than zero, and then we can infer that the sum of any 3 terms is less than zero. Finally, the conclusion that any term is greater than zero obviously contradicts the question, so this sequence cannot be greater than 17 terms.

"Then I tried to construct a 16-term sequence. S16 can be {1, 1, -2.6, 1, 1, 1, -2.6, 1, 1, -2.6, 1, 1, 1, -2.6, 1, 1}, so the maximum value of this sequence is 16."

The difficulty of this question lies in using proof by contradiction to deduce that the sequence cannot be infinite, and then relying on mathematical intuition to find the critical point of 17.

Deng Leyan was a little proud. He spent a lot of time constructing the number series, otherwise he could have handed in the paper early.

But he finally solved it. He was also one of the only two people who solved this problem in this exam. Needless to say, he felt a sense of accomplishment for being able to solve such a difficult problem.

After hearing the answer, Yan Zhenhua nodded.

He had actually seen Deng Leyan's test paper, so he naturally knew his way of answering. This was also the solution to the standard answer given by the test setter.

However, only after letting Deng Leyan tell him his solution could he make the other party understand that there was a reason why the special prize was a special prize.

Deng Leyan looked at Yan Zhenhua. He said the answer so quickly in order to get his own answer as soon as possible.

Yan Zhenhua didn't say much, but turned and walked into the classroom.

Without wasting any time, he went to the podium, picked up the chalk on the desk, and started writing on the blackboard.

a1, a2,…, a7, a8,…, a11
a2, a3,…, a8, a9,…, a12
a3, a4,…, a9, a10,…, a13
a4, a5,…, a10, a11,…, a14
a5, a6,…, a11, a12,…, a15
a6, a7,…, a12, a13,…, a16
a7, a8,…, a13, a14,…, a17
After writing down this matrix, Yan Zhenhua threw the chalk on the podium and walked out of the classroom without saying anything. He believed that Deng Leyan would be able to understand it with his IQ, because this solution was really too elegant, too simple and clear.

Even if the person who sees this solution is an elementary school student, he can understand it.

Yan Zhenhua's return had already attracted considerable attention, and his writing on the blackboard captured even more attention. Everyone was puzzled by this strange matrix.

But Deng Leyan, who was standing at the door, staggered as if struck by lightning.

If his back had not been against the classroom door frame, he might have fallen to the ground.

He got it!

This is Chen Hui’s answer to the last question!
So simple, so elegant!

According to the question, the sum of any 7 items is less than zero, and the sum of any 11 items is greater than zero. It can be seen at a glance from this matrix that when the matrix series is added together, each column has 7 items, so the sum of each column is less than zero, then the sum of the elements of the entire matrix should be less than zero.

But if we add up each row of the matrix, each row has 11 items. According to the question, the sum of any 11 items is greater than zero, so the sum of each row is greater than zero. Then, the sum of the matrix elements should be greater than zero.

The sum cannot be greater than zero and less than zero at the same time.

Therefore, there is no such sequence with 17 terms!

wonderful!
Simply wonderful!

Even as a competitor, Deng Leyan couldn't help but applaud the person who came up with this solution in his heart.

This solution is so simple that even elementary school students can understand it.

But it took him more than half an hour and racked his brains to prove it out, and the difference was immediately apparent.

He solved such a difficult problem in such a simple way. No wonder he got the special prize while I could only get a mediocre full score.

"Fuck me!"

"genius!"

"This is too powerful!"

"How could anyone come up with this?"

Soon, bursts of exclamations broke out in the classroom.

Everyone present was a top student in high school mathematics, so they naturally saw the subtlety of this matrix very quickly.

What's more, there were many competition coaches in the classroom, so they could naturally see it at a glance.

But at this moment, they all stared at the blackboard with their eyes wide open, their hearts in turmoil.

Many of them were former CMO gold medal winners, but after knowing the last big question, they did not think of this solution!
After a tingling sensation on their scalps, they couldn't help but look at Chen Hui who was reading quietly.

From the reaction of Deng Leyan who was standing at the door, it was not difficult for them to guess who came up with this answer.

At this time, Chen Hui had already finished writing his speech and continued studying.

It took him less than two minutes to write the speech. This kind of thing was not worth wasting time on. He was very clear-headed and believed that only mathematical ability was the most real thing.

If he is not good at mathematics, no one will applaud him even if he speaks eloquently.

But if he can win the CMO gold medal, even if what he says is shit, there will be people cheering for him.

When I enter the pass, there will be great scholars to debate for me!
(End of this chapter)