This is not a regular question.

Quite interesting!

The title is like this.

Timo, a poor short-legged rabbit, meets the aggressive Hunter Policewoman Picheng in an unobstructed summoner's canyon of infinite size.

The policewoman in Picheng thought that she had seen a soft persimmon and must kill Captain Timo of the little short-legged team!

But when they play each other, they find that their skills have not been modified by anyone, and they are no longer the ones in League of Legends.

It is known that Timo's starting position, Grass A0, coincides with Leather City Policewoman's starting position, Grass B0.

After the n-1 turn of the game, Teemo is at point AN-1 and the Phi City Policewoman is at point BN-1, and in the nth turn, the following events occur in sequence.

(1) Timo has a powerful passive stealth ability that makes it impossible for the Leather City Policewoman to see him at any time. He moves invisibly to point A, so that the distance between An-1 and An is exactly 1;

(2) The Phi Cheng Policewoman is not a vegetarian, she has a two-skill yodel trap that can feed back a point PN to the Leather City Policewoman, and it can be used at any time, no cooldown CD, and there can also be countless traps at the same time. It will also reveal the range of Captain Teemo's position, but this range only ensures that the distance between PN and AN is at most 1;

(3) The policewoman of Picheng moves to the point bn in a visible way, so that the distance between the point bn-1 and the bn is exactly 1.

And then the question arises!

Question: No matter how the Phi Cheng policewoman moves, and no matter what points the trapping and positioning device feeds back, the Leather City policewoman is always able to make the local choice of her movement, so that after 10 to the ninth power, she can ensure that the distance between her and Captain Teemo is at most 100

"This is really a fairy question......

If you think of it as a game topic, you're wrong.

If you underestimate the problems that come up in the IMO event, you will die a miserable death.

Fang Chao did not write easily, which involved non-Euclidean geometry, which was interesting and tight.

Mathematics is relatively simple, nothing more than operations, but when it comes to geometry, the steps are not so easy.

Fang Chao looked up and found that the players of the American team did it very quickly, basically without any pause, while the Singaporean, South Korean, and Canadian players also did it relatively quickly, and the difference is that the performance of the Indian players in this regard is also very amazing, and they have risen in recent years, which has to be emotional.

In addition, dozens of yellow people at the competition site caused Fang Chao's surprise, it seems that not only the US imperialists, but also people from other countries are also stealing our country's players, because just from the color of their skin, they are Chinese, but the national flag in front of them shows their identity, they are just Chinese, and their identity is another country.

Robertson Kenard felt a strange gaze, just as his eyes met Fang Chao's, so he raised a middle finger.

"Selinwood!!"

Fang Chao scolded.

It's so good, his spirit is rejuvenated again, and at this time he feels that he has entered the realm of selflessness!

Maybe you will feel the perfection of perfection on this field.

Review, review, re-examine!

Fang Chao was not in a hurry to answer immediately, the questions that could appear in the IMO event would definitely have its reason, even if Fang Chao could get a full score in mathematics every time, he didn't dare to be arrogant in such a place.

This is a collection of the world's top mathematical geniuses, and his strength is still weak, and he is nothing at all.

According to the title, it is known that Captain Temo and the Leather City Policewoman are both members of "League of Legends".

And their Q, W, E, R skills are very remarkable, can kill people invisibly, on the battlefield of the League of Legends, each of them has achieved a lot of results, carrying tens of thousands of lives, some corpses lie under the crystal tower, some corpses were killed by super soldiers, and some corpses are in the grass, but in every corner of the League of Legends, there have basically been too many corpses lying down.

But from the title, I learned that when they fought each other, they found that their skills were not modified by anyone, and they were no longer those in the League of Legends game. 】

So, they are not Captain Teemo and the Pittsburgh policewoman in the simple sense.

We can set the two heroes to A and B.

Fang Chao thought about it for about ten minutes and then gave up how to verify that the distance between A and B does not exceed 100, because as long as the distance between A and B cannot be guaranteed to exceed 100, then this question can be concluded.

Ten minutes wasted.

I'm so angry!

But that's the case with the IMO competition, everyone's level is not too different, because that's what the agreed math content is, so your thinking, agility, reactions, abstract thinking, etc. become extremely important.

There is a saying that also says mathematicians.

All mathematicians who have left their names in history are essentially insane.

Let dn=anbn.

Fang Chao then verified below that the Phi City Policewoman and Captain Teemo could not guarantee that the distance between them would not exceed 100 in two hundred rounds.

It is calculated as follows: dn + 200 dn + 1/2 possible.

Let's say that after the nth round, Captain Teemo is at a=an and Picheng policewoman is at b=bn. It would be useful to let Captain Timo know the location of the Pitts, as the information from the Yodel Trap would be negligible.

Fang Chao writes and writes, and uses mathematical formulas to explain and explain with words and pictures.

After half an hour, the entire test paper was almost full of Fang Chao's solution answers, and in order to solve this question, Fang Chao even scrapped two erasers.

The person who asked this question is simply the devil!

But Fang Chao was not afraid, and he also had full confidence in this question.

Dried another bottle of Red Bull and went down, stuffed a little bread into his mouth, Fang Chao felt that his spirit had recovered a little, and the efficient answering of the question made his physical energy deplete very quickly, and there was also sweat flowing down his forehead.

Fang Chao took out a tissue and wiped his sweat.

In such a competition scene, you are very free, and without electronic devices, you are like being in ancient times.

But mathematics, as Professor Karen Uhlenbeck said, what you see with your eyes can deceive, and what you hear with your ears deceives, but mathematics does not.

You will be will, and you will not be no.

On the field, as long as you don't stare at other people's test papers and copy them all, no one will care about you too much.

If you don't have your own ideas, it's difficult to get to the top of the sky if you want to solve such a problem.