Hirano Fayu stood on Teacher Jiang's right hand, silent and silent, but his gloomy eyes kept staring at Cheng Nuo.

4:0！

They are an island team, and now, they have no way out.

In the last game, the island team must win.

Otherwise, it will be abused by the Chinese team 5:0!

Once this happens, their island nation will lose face.

Hoyu Hirano, as the captain of the island nation team, may be fine for the time being. But once you return to China, you will definitely be forced to shoot every day.

This is not the life that Hoyo Hirano wants. He is tired of the life of filming, and he is so addicted to learning that he can't extricate himself!

"Hirano-kun, come on, defeat this great demon king of Huaguo!" all the island country audience shouted wildly in their hearts.

Hoyu Hirano is the strongest of the six players sent by the island nation to participate in the battle. Therefore, the audience in the island country also has the greatest hopes for him.

They knew that the opponent that Hirano Fayu was facing was Cheng Nuo, that hexagonal warrior!

But it's still ...... They have great confidence in the strength of Hirano Hoyu.

"Let's take a look at the challenges of the two players. ”

Teacher Jiang motioned for everyone to look at the big screen.

On the big screen, the picture flashed, and the five big characters of "Tyson polygon" slowly emerged from the big screen.

That's right, this time Cheng Nuo and Hirano Law Education, the name of the project challenged is called "Tyson Polygon"!

Tyson Polygon, is the brainchild of the climatologist A. H· Thiessen proposed a method for calculating average rainfall based on rainfall from discretely distributed weather stations.

It's not that hard to build it.

To put it simply, first select a discrete point as the target point, and then connect this discrete point with the surrounding discrete points to form one triangle after another to form a triangular network.

Let the discrete point be o. Find a triangle with o as the vertex and set it as A; take another vertex of triangle A except o and set it as a, then another vertex can also be found, that is, f; then the next triangle must be of of, that is, triangle F; another vertex of triangle F is e, then the next triangle is edged by oe; and so on until it returns to the oa side.

Calculate the center of the circumscribed circle of each triangle with this discrete point as the fixed point and connect them.

In this way, the triangle formed is called ...... Tyson polygons. If it is expressed by the formula, it is √∑(Si-S)^2/n,(n=1,2,3,...... ）

Take a chestnut~~

The Water Cube in Kyoto is designed according to the principle of Tyson polygons.

The rules for the challenge of the two players are as follows.

Two spheres, each with 5,000 discrete points on each of them.

Each sphere has 5,000 discrete points, and each discrete point can form a Tyson polygon, which is a total of 5,000 Tyson polygons.

The other sphere is also 5,000 Tyson polygons.

Out of a total of 10,000 Tyson polygons, there are only two Tyson polygons, identical!

What the contestant needs to do is to find these two identical Tyson polygons in the shortest possible time and press the answering machine!

One point will be added for a correct answer, and one point will be added for an incorrect answer.

A total of three innings are played, and the first to score two points wins.

This challenge, at first glance, seems to be very simple, it is an upgraded version of the "find the difference" we usually play, find the same......

However, in fact, this challenge is the most difficult challenge in the five matches between China and the island nation today!

The overall strength of the players is a great consideration.

Calculation, memory, spatial, reasoning, creativity, and observation are all indispensable.

The player is unaware of any position where two discrete points can form the same Tyson polygon.

In other words, they need to try them one by one.

Out of two spheres filled with discrete points, a sphere is randomly selected. Observe the 5000 discrete points on it.

Through observation, calculation, and reasoning, the contestant deduces the Tyson polygon corresponding to a discrete point.

The number of triangles formed by the connection of each discrete point and the surrounding discrete points is different. In simple terms, it may be three triangles, in this case, only the centers of the three triangles corresponding to the three circumscribed circles need to be connected to form a Tyson polygon.

Complex, there may be five or six triangles in a triangulation. When you can't use pen and paper, you can only rely on your brain to calculate, and it's easy to get confused when you calculate.

Most importantly, once you have the shape of this Tyson polygon, you need to memorize it. Compare them with the 5,000 Tyson polygons on another sphere.

If you do a simple calculation, if the two players want to find the answer, they need to judge 5000*50000, a total of 25000000 times!

Horror! Quite scary!

The amount of computation required for this problem is so large that I am afraid that I will not be able to do it in a short time with a computer.

............

The rules, that's it.

The audience in the audience, you look at me, I look at you, all of them are confused.

Discrete points, triangulation, circumscribed circles......

A series of math terminology stunned the audience.

And that Tyson polygon, just listening to the name, is slowly forcing the grid!

Pity......

Although on the big screen, even the pictures and text have been explained for a long time, they are still ...... Didn't understand.

Well, the topic of the big guy, we don't understand it as it should be.

Again, their hearts rise up with their own births, just to give humans the feeling of making up the numbers.

On the stage, when everyone in the audience was still doubting their lives, Cheng Nuo and Hirano Fayu were already sitting on their challenge chairs.

On the desktop in front of the two of them, there is a small screen.

On the left and right sides of the screen, there is a sphere with a diameter of about 3/4 of the height of the screen.

It's just that the two spheres at this time are gray and dark, and 10,000 discrete points have not yet covered them.

"Next, please randomly generate 10,000 discrete points in the background. ”

After Teacher Jiang's voice fell, among the audience, the two spheres on the screen in front of Cheng Nuo and Pingye Fayu began to flicker with a little star. It's like stars in the dark.

At first, it was just a little bit or two of the stars, but gradually, 10,000 white points of light almost completely covered the two spheres.

Wow!

Dense, quite dense!

Originally, the area of the sphere is not large. 5,000 discrete points are marked, and in an instant, from a distance, the sphere is almost completely covered by discrete points. Densely packed with large patches.

Everyone's scalp was numb in an instant!

This is definitely the greatest torment for people with dense phobias.

"I announce, challenge, begin!"

Teacher Jiang raised his voice, and after saying this, he immediately pressed the timer under his hand.

Time...... Begin!

Cheng Nuo and Hirano Fayu immediately looked at the screen.

In the last game of the Chinese team against the island team, the first question, who will be the first to complete, the result will be revealed immediately......