Super academic master: start with low adjustment scores!

"Question: A hunter and an invisible rabbit play a game on the Euclidean plane.

It is known that the rabbit's starting position A0 coincides with the hunter's starting position B0. After n-1 rounds of the game, the rabbit is at point An-1, and the hunter is at point Bn-1. In the nth round, the following three things happen in sequence...

(1) The rabbit moves to a point An in an invisible way, so that the distance between point An-1 and point An is exactly 1.

(2) A positioning device feeds back a point Pn to the hunter. The only thing this device can guarantee to the hunter is that the distance between point Pn and point An is at most 1.

(3) The hunter moves to a point Bn in a visible way, so that the distance between point Bn-1 and point Bn is exactly 1.

Question: No matter how the rabbit moves, and no matter which points the positioning device feeds back, can the hunter always choose her movement method appropriately so that after 10^9 rounds, she can ensure that the distance between her and the rabbit is at most 100?"

"..."

This is the last question of the three rounds.

It is also a very interesting question.

Of course!

It is just interesting.

As for the difficulty...

For Jiangnan, it is not difficult at all.

It is so easy!

"Isn't this question very simple?"

"As long as you have a certain understanding of common sense thinking, equivalent thinking and extreme thinking, it is easy to get..."

"1: Allow this invisible rabbit to bless magic and manipulate the detector."

"2: Affected by 1, the hunter may have judgment bias in some cases."

"The equivalent statement here allows the creation of some possible situations that are not favorable to the hunter, and see how the hunter and the invisible rabbit deal with it."

"It is worth saying here that you should not understand this question as the rabbit has a winning strategy, because neither the hunter nor the invisible magic rabbit has a winning strategy..."

"..."

Jiangnan spoke very quickly.

It is not an exaggeration to describe it as one-shot.

However...

When he finished his thoughts and looked down at the people below, he only saw 29 confused faces?

Jiangnan: "..."

"I've finished talking."

"You didn't understand, did you?"

"No way? Really? Such a simple question, you don't understand?"

"Fuck, you really didn't understand?"

"This, this, this... you are really too stupid, right?"

"Didn't you all advance to the provincial first place and join the provincial team?"

"Aren't you all the best dozens of people in the province? In the end, you can't even understand this, and you can still participate in the finals?"

"Fuck, are you kidding me?"

"Nimma! ”

“…”

Jiangnan was about to be pissed off.

These people are not just a little bit stupid!

He had finished explaining the question, but they were still looking at him in confusion, just like Bai Xiaochun.

Tsk tsk!

It was really speechless.

At the same time.

The people under the podium were also speechless.

How to describe Jiangnan?

The King of Bullying!

A naked King of Bullying.

There is no other words to say.

You know...

They are also the top academic masters, even academic gods. On weekdays in their respective schools, But they are not less pretentious.

What Long Aotian!

What Versailles!

They played it so skillfully.

But in front of the current Jiangnan, they suddenly felt that they were still too immature.

If you want to know who is the best at pretending, Jiangnan is the third middle school in Jiangcheng.

Who is the best at pretending in ancient and modern times? Once he meets Nanshen, it's all in vain.

Tsk tsk!

They are not on the same level at all!

In the end!

It was still Lin Qianqian who stared at Jiangnan's contemptuous expression and raised her hand weakly and said: "That... Jiangnan classmate, can you say it again? Speak slowly, I don't quite understand. ”

Jiangnan: “…”

Okay!

I’m convinced, completely convinced.

It’s a pity that he had looked up to these people before.

Because everyone present had scored more than 90 points in the first round of the Mathematical Olympiad, and there were even many full marks.

The scores in the second round were not bad either, with a minimum of 90 points, not like Liu Fan, Du Jiang and others, who could not even pass.

But now it seems...

He really overestimated these people.

Yes!

These people are better than Liu Fan and others from No. 1 Middle School.

But they are really that much better.

Not necessarily.

“That... classmate, didn’t you get 90 points in the third round? That means you got half of the points for this question. I explained it in detail, why don’t you understand it?”

Jiangnan frowned, very confused.

It’s okay if the people behind don’t understand.

But Lin Qianqian was sitting in the second row, and she got 10 points out of 20. She shouldn’t have gotten 10 points.Just click and you'll understand?

Lin Qianqian: "..."

Hearing this, her face turned slightly red.

"Then... Jiangnan classmate, I... I used the enumeration method to verify, but because the data is too large, I only listed a part of it and couldn't list it anymore. I can only say that I took a shortcut."

"But your equivalent statement is completely different. You are really verifying, so please tell me again..."

"..."

It has to be said that when it comes to the level of top academic gods like Lin Qianqian, the mentality is not a little bit high.

If it were Liu Fan from Jiangcheng No. 1 Middle School, Du Jiang from No. 2 Middle School, Xia Ji from Chuying and others, seeing Jiangnan so pretentious and hearing Jiangnan despise themselves so much, their first reaction would be dissatisfaction.

But for Lin Qianqian, it's not dissatisfaction, but full of curiosity, really wanting to understand Jiangnan's solution.

When three people walk together, there must be one who can teach me.

In Lin Qianqian's eyes.

At this moment, Jiangnan is no different from a teacher.

She just wants to steal the teacher.

Not only her.

Many people in the audience looked expectant.

In response to this.

Fang Guoping, who was standing aside, nodded.

Although the talents and strengths of these people in mathematics were not as good as Jiangnan.

But this mentality of always being an apprentice and constantly exploring and seeking knowledge was precious.

It seemed that.

This group of students was still very good.

Their future achievements would definitely not be low.

"Okay!"

"I'll say it one last time!"

"Analysis 1: Let's assume that after a certain round, the invisible rabbit is at point A and the hunter is at point B. The distance between the two points is AB=R, where 0 is less than R and less than or equal to 100."

"Consider the position X of the invisible rabbit after N rounds. It is located in the circle w1 with point A as the center and a positive integer N as the radius (including the interior and the boundary)."

"Through language thinking analysis, we can see that the invisible rabbit is dominant, and the detector and the hunter are all around the rabbit."

"Common sense tells us that if the hunter is stupid, then the rabbit can get away from the hunter the farthest by running in a straight line."

"After N rounds, the rabbit escapes to the circumference of circle w, that is, AX=N, and the escape direction is along Vector AX direction. "

"Take point X as the center and 1 as the radius, and make a unit circle w2. Then according to the question, after N rounds..."

"..."

"Analysis 2: Design a hunter to track the enemy..."

"..."

"Analysis 3: After N rounds, the square increment of the distance between the hunter and the invisible rabbit, with vector BA as the x-axis..."

"..."

"Analysis 4: Under the above conditions, the hunter has no better choice than to move forward in a straight line..."

"..."

"I think you all understand all of the above, right?

"Then it's like this... then this... then that... Finally, by comprehensively analyzing 1234 and the graph above, we can clearly see that the answer to this question is no."

"This question is really simple!"

"The integer N is very similar to a loop node. Starting from the node situation, the invisible rabbit will enter a loop mode, just like the reincarnation loop in novels or games."

"If you still don't understand this..."

"Then you are really not a little bit stupid..."

"..."