The second question is also a proof question.

Let x, be a given even number, x is greater than 0, and y*(x-1) is even.

Proof that a,b exists such that (a,x)=(b,x)=1 and a+b=y(modx)

Gee.

Yi Cheng let out two exclamations, and the corners of his mouth rose slightly.

Who came out of this volume, full of patriotic enthusiasm.

The proof of this problem requires the use of a very famous mathematical theorem -

Sun Tzu's theorem.

Also known as the Chinese remainder theorem.

This is one of the few great theorems in the history of Greater China that has been recorded in history and looked up to by everyone in the world.

Together with Euler's theorem, Wilson's theorem, and Fermat's theorem, it is known as the Four Theorems of Number Theory.

This is a mathematical theorem that elementary school students know.

Specifically, you can go to the elementary school math fun problem "Han Xin Point Soldier".

What does it illustrate?

Explanation: Assuming that the integers m1, m2,..., mn are mutually primitive, then for any integer: a1, a2,...,an, the system of equations S has a solution, and can be constructed.

Math problems are not difficult for those who know, but not for those who are difficult.

A theorem that elementary school students know, there is no reason why Yi Cheng would not be.

This question will be solved, so it was quickly solved.

Next, we will start to tackle the next two big questions worth 50 points.

The third question is a geometry problem:

The attached diagram shows two circles, called circle 1 and circle 2 respectively, with a triangle ABC in the middle of the two circles, and the three straight lines where the three sides of triangle ABC are located are tangent to circle 1 and circle 2. E, F, G, H are the four tangent points. The straight line EG intersects FH at the point P.

Verification: PA is perpendicular to BC.

It seems that this time, the questioner prefers proof questions, so 3 of the 4 major questions are proof questions.

Although this question is a bit convoluted, the conditions given are very sufficient.

And there is a very obvious feature in the diagram:

BCDEF5 point collinear.

Yi Cheng shook his head and let out a sigh.

Doesn't this brain-dead questioner tell you that this question is related to Menelaus' theorem?

So he quoted Menelaus' theorem, and he quickly completed the proof.

Another 50 points to hand.

In other words, he has now scored at least 130 points in the second test.

But these two questions are obviously a bit simple, if he can, Ziqi will definitely do too.

I can only pin my hopes on the last big question:

[In the s8 World Finals, the first match between the IG team and FNC.

Between the 18th and 19th minutes, due to FNC's knife sister waves, I don't know what I'm doing, which leads to a wave of being harvested.

At this time, the ratio of the number of heads of the two sides is:

4：9. IG leads.

The economic situation of both sides: FNC: IG is 29.4K: 34.4K

Figure 1 shows the economic growth curve of each player in the first 19 minutes.

Figure 2 shows the spawn and movement speed of creeps and creeps, as well as the amount of gold they provide.

Figure 3 shows the operation error rate of each person and the performance rate of the team's strength

Figure 4 shows the exchange of money for combat power

Figure 5 shows the difference in the growth of each hero's ability

It is assumed that each player is a standard person (i.e., the level and ability of individual operation and the ability to grasp the rhythm of the game are all 1)

At the same time, the actual equipment impact is not taken into account (the combat power can be exchanged for money).

The factor of towers and dragons is not taken into account.

The impact of map attributes is not taken into account.

The future teamfight incidences are as follows:

Figure 6 shows the location of the team battle and the probability of each location.

So, what is the change in FNC's team victory rate in the next 10 minutes? 】

Yi Cheng finished reading the title and the 5 attached pictures below, and was stunned for about 10 seconds.

the !!!

What the hell is this?

Several teenagers who were on the same level as him noticed this.

"Yes, keep up with the times!"

"the chicken! I thought I didn't need much math to play games, but now I find that I don't know how to play games at all. ”

"Shouldn't you have sent the paper down and started reviewing the questions?" A voice complained.

"When I started to review the question, I only saw a bunch of charts, except that the double triangle was a little familiar, who would have thought that it was actually LOL?"

……

"Please refrain from making noise in the exam room." The invigilator reminded.

Everyone was quiet again.

But......

Yi Cheng's palms sweated.

The answer to this question is obvious, he has watched that game before, and in the end IG won.

However, how to calculate the change in the win rate of teamfights requires a little thought.

He closed his eyes and carefully extracted all the math knowledge in his mind.

Now that he is at the level of lv3 mathematics, this kind of problem should not stump him.

It's just that because the question type is relatively new, it has never appeared in the previous high-level competition, so I was a little flustered for a while.

Yi Cheng's heart slowly sank, like a calm lake.

One of the wonderful figures slowly surfaced......

Yi Cheng slowly opened his eyes.

He laughed silently.

What a beautiful little beauty, the key to the answer to the question-

Lanchester's equation.

This is an equation specifically used to describe the variation of warfare and the probability of victory.

Especially when there is only confrontation between the two sides.

In 1914, the Englishman Lanchester discovered the Lanchester equation while studying the best formations for air combat.

Later, this equation was widely used in warfare.

The former head of state of the 10,000-character country studied this equation extremely deeply, which helped them win many battles.

Today, the Lanchester equation is used in many versus games to simulate and describe the damage rate of both sides due to changes in certain elements.

The most famous of these is Warcraft 3.

And after that, COC and the shore of the land......

But...... When Yi Cheng was about to put pen to paper, he suddenly found a problem:

Within the scope of the high union, the Lanchester equation is not included, and if he uses it, then it is an over-the-top behavior.

There is no score for using college knowledge to solve high school problems.

What to do?

After thinking for about three minutes, Yi Cheng laughed.

It doesn't matter if you can't use it.

Because the basis of the Lanchester equation comes from calculus.

Whereas, calculus is within the scope of the syllabus.

Several factors can be assumed here, and the strength curve does not use the ratio of the square of the quantity described in the Lanchester equation, but the economic ratio in Figure 4.

The relationship between the influence of the economic graph and the outcome of the battle is reflected in the previous descriptions of the battles.

This functional equation is easy to get.

Then, a little more complicated is the teamfight incidence in the back.

This is a scatter plot that cannot be described in simple mathematical curves.

So Yi Cheng listed:

Let's assume that the top road points are A1, A2, A3

The middle points are B1, B2, B3

The mob point is ......

Then we can get the probability matrix:

【a1、a2、a3】

【b1、b2、b3】

【c1、c2、c3】

……

He then incorporated his generalized Lanchester equation.

……

Derive the probability matrix for each point:

【A1、A2、A3】

【B1、B2、B3】

【C1、C2、C3】

……

A1=……

Each of these probability terms is a function of time.

After that's done.

Yi Cheng finally let out a long breath.

……

There is still half an hour left before the deadline.

He has exceeded his mandate.

And according to his own review, there is a high probability of a perfect score.

Yi Cheng knocked on the table with his hand, do you want to hand in the paper in advance?

Will it be said that it is too hasty?

His gaze fell on the probability matrix equation that he had finally derived.

After a three-second pause, Yi Cheng decided to calculate what the probability maximum was.

It took 10 minutes.

Yi Cheng pushed the probability matrix from the 19th point all the way back to the 28th minute.

After 28 minutes, the economic curve of the FNC has collapsed, and the probability in the matrix at this time is almost zero.

But—

Yi Cheng's eyes widened in surprise.

In the 23rd minute, the win rate of B2 points can be 0.35?

Yi Cheng was skeptical of this result, and then continued to calculate it, and sure enough, it was still so high.

Mommy.

Although this topic is idealistic, there is a certain deviation from reality.

But he found out from the results the possibility of FNC winning that game -

If these guys don't scatter the money and their support is not timely, there is a 35% probability of winning together.

……

This time, Yi Cheng stopped being nostalgic, put the paper on the table, stood up and left the classroom.

At this time, Yan Ziqi was still fighting.