Become a master from now on

Chapter 184 Competition in the League of Legends (ask for a monthly ticket subscription!)
Not a regular question.

Quite interesting!

That's the title.

The weak and pitiful short-legged rabbit Teemo and the aggressive hunter Picheng Policewoman met in a summoner's canyon with no blocking objects and unlimited sizes.

The Piltover policewoman thought she saw a soft persimmon and must kill the short-legged Captain Teemo!
But when they played against each other, they found that their skills had been modified by someone, and they were no longer those in the "League of Legends" game.

It is known that Teemo's starting position grass A0 coincides with the starting position grass B0 of Piltover Policewoman.

After n-1 rounds of the game, Teemo is at point An-1, and the Pittsburgh policewoman is at point Bn-1. In the nth round, the following events happen in sequence.

(1) Teemo has a powerful passive stealth skill, which makes Piltover policewoman unable to see him at any time.And he moves to point A in an invisible way, so that the distance between An-1 and An is exactly 1;

(2) The Piltover Policewoman is not a vegetarian either. She has a second skill yordle trap that can feed back a point of Pn to the Piltover Policewoman, and it can be used at any time. There is no cooldown CD, and there can also be countless traps at the same time. .And it will expose the location range of Captain Teemo, but this range only ensures that the distance between Pn and An is at most 1;

(3) The Piltover policewoman moves to point Bn in a visible way, so that the distance between point Bn-1 and Bn is exactly 1.
Then comes the problem!
Let me ask: no matter how the Piltover policewoman moves, and no matter what points are fed back by the trapping and positioning equipment, the Piltover policewoman can always make the local choose its movement method, so that after the 10th power round, she can ensure that she and Captain Teemo The distance between is at most 100?

"This is really a fairy question..."

If you simply regard it as a game topic, then you are very wrong.

Once you underestimate the problems that arise in IMO events, you will die miserably.

Fang Chao did not write lightly. This involved non-Euclidean geometry, which was very interesting.

Mathematics is relatively simple, nothing more than calculations, but once geometry is involved, the steps are not so easy.

Fang Chao looked up and found that the players from the US team were doing it very quickly, basically without any pause, while the players from Singapore, South Korea, and Canada were also doing it faster. What was also somewhat different was the performance of the Indian players in this aspect. It is also very amazing. It has risen in recent years, which has to be sighing.

In addition, the dozens of yellow people at the competition site aroused Fang Chao's surprise. It seems that not only the American emperor, but also people from other countries are stealing our players, because just judging from the color of their skin, they are Chinese, but The national flag in front of them shows their identities. They are only Chinese, but their identities are from other countries.

Robertson Kenard felt the strange gaze, and his eyes happened to meet Fang Chao's, so he raised his middle finger.

"Selim!!"

Fang Chao cursed.

It's great, the spirit is revived again, and at this moment he feels that he has entered the realm of selflessness!

Maybe you will feel the perfection of seamlessness on this arena.

Review, review, review again!

Fang Chao was not in a hurry to answer immediately. Questions that could appear in IMO competitions must have their own reasons. Even if Fang Chao could get full marks in mathematics every time, he would not dare to be arrogant in such a place.

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

According to the title, we know that Captain Teemo and Piltover Policewoman are both members of "League of Legends".

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

However, I learned from the title, [When they played against each other, they found that their skills had been modified by someone, and they were no longer the ones in the "League of Legends" game. 】

Therefore, they are not Captain Teemo and Piltover Policewoman in the simple sense.

We can set their two heroes as A and B.

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

10 minutes of time wasted.

So angry!

But IMO competitions are just like this. In fact, there is not much difference in everyone's level, because the agreed mathematics content is those, so your thinking, agility, reaction, abstract thinking, etc. become extremely important.

There is a saying that also explains mathematicians.

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

Let Dn=AnBn.

Then Fang Chao verified below that the Piltover policewoman and Captain Teemo could not ensure that the distance between them did not exceed 100 within two hundred rounds.

The calculation formula is: dn+200dn+1/2 possibility.

Assume that after the Nth round, Captain Teemo is at A=An, and the Piltover policewoman is at B=Bn.You might as well let Captain Teemo know the location of the Piltover Policewomen, so that the previous feedback from the yordle trap can be ignored.

Fang Chao stopped writing, and explained with mathematical formulas, words and pictures.

After half an hour, the entire test paper was almost filled with Fang Chao's answers. In order to solve this problem, Fang Chao even used up two erasers.

The person who asked this question is simply a devil!
But Fang Chao is not afraid, and he also has full confidence in this question.

After drinking another bottle of Red Bull, stuffing a little bread into his mouth, Fang Chao felt that his energy had recovered a little bit, and his efficient answering made his physical energy exhausted very quickly, and there was also sweat flowing from his forehead And down.

Fang Chao took out a tissue and wiped his sweat.

In such a competition scene, you are very free. Without electronic equipment, you feel like you are in ancient times.

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

You will or you will, or you will not.

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.

The topic of the competition, if you have no idea, it is difficult to solve such a topic, it is difficult to reach the sky.

(End of this chapter)