The heavens begin with Hongquan

"Yellow River flood control and earthwork calculations?"

Yelu Chucai's eyes moved slightly, thoughtfully.

In his opinion, the prince did not ask this question for no reason, and this move must have deep meaning.

After Huang Yaoshi read it once, he put down the paper.

"Are you sure you want to ask this?"

The difficulty of this calculation problem is much simpler than that [Solution to the Generation of Heaven and Earth].

He has always been conceited and unwilling to take advantage of others.

"Master Huang, please."

Wanyankang spread his hands, indicating that the other party could start.

"Shhhhh..."

Huang Yaoshi immediately drew a few lines on the paper.

He had already been given the opportunity to change the topic, but when they insisted, he stopped talking.

"This arithmetic problem can be solved using the [acting paragraph method]."

"The so-called performer is to perform the Tianyuan; the segment is to seek it out in sections. It is also a fragment that you want to calculate. If you know the fragments, you can find out the root cause..."

"Dharma said", "section diagrams", "seeking it according to sections", "meaning"... Various terms kept popping up from Huang Yaoshi's mouth. With the help of graphics, Wan Yankang was really enjoying reading them.

Since the difficulty of this question is simpler than [Solution to the Generation of Heaven and Earth], Yelu Chucai can understand the general idea, which makes him stare at Huang Yaoshi with bright eyes.

He seemed to understand why the Crown Prince must subdue the other party.

Huang Rong and everyone else were about to yawn.

Others do it because they simply cannot understand or understand it. Huang Rong has studied with Huang Yaoshi since she was a child, and because of her clever brain, she understands the "acting method" very well, but she has no interest in it at all and feels bored.

In less than a quarter of an hour, Huang Yaoshi finished the solution.

Wanyankang clapped his hands and praised with a smile.

Huang Yaoshi's "Performance Method" is somewhat similar to the fractal mathematics of later generations.

But it is not just arithmetic. It must be understood in conjunction with the thinking of the "Book of Changes". It is a comprehensive integration of astronomy, geography, and personnel.

Although it may not seem as simple as a tool like fractal mathematics, the way of thinking revealed in it is quite groundbreaking.

"Island Master Huang, it's your turn."

Huang Yaoshi wrote a paragraph neatly.

Yelu Chucai stepped forward, picked up and read aloud.

"Guiguzi asked?"

He looked at Huang Yaoshi with surprise.

"Has Guiguzi ever had such a problem?"

Huang Yaoshi waved his hand and said, "That's not important."

Right.

Yelu Chucai read: "Guiguzi was the teacher of Sun Bin and Pang Juan. One day, he selected two different integers from 2 to 99, told Pang Juan the sum of the two numbers, and told Sun Bin the product of the two numbers. "

Pang Juan said to Sun Bin: "Although I can't be sure what these two numbers are, I'm sure you don't know what these two numbers are either." "

Sun Bin said confidently: "I didn't know it at first, but when you said this, I knew it."

As a result, Pang Juan also laughed and said, "Since you know it, then I also know it."

Q: What are these two numbers? "

???

The topic ended abruptly, and everyone else felt as if they had been struck by lightning.

Gone?

Yelu Chucai asked Huang Yaoshi with his eyes and received a positive reply.

The question is just that long.

The expression on Yelu Chucai's face gradually became stiff, and his eyes were fixed on the topic, as if he was trying to understand its meaning.

Even him, let alone others, seemed to be lonely.

"Sir..."

Yelu Chucai looked at Wanyankang.

He wanted to scold this kind of topic as being deliberately disgusting.

But seeing that Wanyan Kang still looked calm, he suppressed his impulse.

"Prince Wanyan, please."

"No rush, I would like to ask, does Huang Island Master himself have the answer to this [Guiguzi question]?"

"Of course."

"So, how long did it take Island Master Huang to solve this problem?"

"Fifty-seven days exactly."

As soon as this number came out, the expressions of the others suddenly changed and their eyebrows furrowed tightly.

Huang Rong also felt that her father was a bit bullying.

"It took Island Master Huang fifty-seven days, so how long do you think it will take me?"

"At least twenty days."

"Ho ho..."

Wanyankang smiled softly.

The power of the mind quietly stirs up the opponent's desire to win or lose.

"What if I told you that I only need half a day?"

"Impossible!" Huang Yaoshi blurted out, "If you really solve it in half a day, it won't matter if I work for you for ten years!"

Wanyankang's lips curved into a smile.

"A gentleman's words..."

"It's hard to chase a horse!"

"Okay, Jin Qing, please get some paper and pen."

…………

"First of all, to facilitate understanding, I define two words: composite numbers and prime numbers."

Wan Yankang transforms into a math teacher.

In fact, Huang Yaoshi's question itself is a type of number theory.

The concept of composite numbers and prime numbers is not difficult, and Bai Feng, Mo Ya and Hong Yu suddenly became energetic.

They... seem to understand themselves?

After thinking about it and recalling it, I was sure that I understood the "composite numbers and prime numbers" that the prince just explained. The eyes of several people suddenly brightened up. After a long time, they finally understood something.

It's not easy!

But then——

"After knowing the concepts of composite numbers and prime numbers, we can start to derive them."

"Pang Juan knows the sum of two numbers. We assume that the sum is [A] and Sun Bin's product is [B]."

"Pang Juan dares to say that Sun Bin must not know, which means: this sum [A] is not the sum of two prime numbers, otherwise Sun Bin might guess the answer."

Uh……

Bai Feng and Mo Ya continued to look at the sky, while Hong Yu continued to look at the flowers.

On the contrary, Yelu Chucai looked enlightened.

"I see."

"Oh. Jin Qing understands this inference?"

"The Crown Prince has spoken to this extent. I believe that most people can understand."

is it?

Bai Feng and Mo Ya looked at each other.

The two instantly understood each other's eyes, turned their heads in tacit understanding, and followed each other.

As for Hongyu, she seems to have been immersed in the world of flowers, completely in a state of flow, unaware of the outside world.

In order to prove that he really understood, Yelu Chucai even gave examples.

"For example, Pang Juan's sum [A] cannot be 16, otherwise if the two numbers are 5 plus 11, Sun Bin will definitely guess it with the product 55. Another example, the sum cannot be 15, because it may be 2 Add 13, Sun Bin can guess it with 26..." "Therefore, this sentence greatly limits the sum [A] that Pang Juan can get. In principle, he can try from 2 plus 3 to 98 plus 99. , try out all possible sums.”

"But there is no need to go to such trouble, because all even numbers greater than 4 can be written as the sum of two prime numbers, so Pang Juan's sum [A] can only be an odd number."

"In this way, the result is reduced by half!"

Speaking fluently in one breath, Yelu Chucai suddenly felt relaxed.

This is the sense of accomplishment of solving a difficult problem.

Oh~ So that’s it.

Brush brush.

The eyes of Bai Feng, Mo Ya, Hong Yu and others were all focused on Yelu Chucai.

Well, Mr. Yelu’s words are actually what I just wanted to say.

It's a pity that it's a step too late.

Otherwise, you can show your skills in front of the Crown Prince.

Huang Rong's crisp voice sounded: "But there are still many odd sums. How can we write all possible sums quickly and easily?"

She felt like she had a vague clue, but upon closer inspection, her brain was in chaos.

"Uh, this..."

Yelu Chucai couldn't help but look at Wanyankang.

The look in his eyes said "I'm being made trouble, come and save me".

Wanyankang smiled helplessly in his heart and immediately came to his rescue.

"The sum of odd numbers must be an even number + an odd number, so Guiguzi must have chosen two numbers, one odd and one even. And don't forget, these two numbers cannot both be prime numbers."

…………

Huang Rong asked: "So? What does this mean?"

"We assume that all possible sums are [C]." Wanyan Kang said: "We might as well give it a try. If an even number is greater than or equal to 4, it itself is not a prime number. In this way, there is no restriction on the other odd number. , it is impossible to narrow down the range of possible sum numbers [C].”

"However, there is a special number that is both an even number and a prime number..."

Yelu Chucai reacted immediately: "2, it's 2."

完颜康微笑附和，道：“因此，庞涓的和数【甲】总是可以拆分为2+一个奇数。这时奇数就必须是非素数，即9、15、21、25、27、33……这些数字。而可能的和数【丙】就可以简便地写出来，即11、17、23、27、29、35……”

After a pause, Wan Yankang looked at Huang Yaoshi and smiled confidently.

"This is what the first sentence tells us. Pang Juan's sum number [A] can only be one of the above numbers."

Quiet.

Quiet.

A pin drop can be heard.

Bai Feng scolded and reflected on herself in her heart.

The most important thing for me is to do the things that the Crown Prince has ordered me to do well. Why do I think about all this? !

Glancing at Mo Ya from the corner of his eye, he found that his face was expressionless, standing like a javelin, staring at the movements around him, doing his best to protect himself.

"Small words mean great things, small words mean great things..."

Yelu Chucai kept nodding.

Does this guy understand again?

"As Sun Bintong was a student of Guiguzi, what Pang Juan could think of, of course, he could also quickly guess the possible sum [C]. Then, he quickly divided each sum into all possible two numbers in his heart. , and then obtain the corresponding possible products.”

Wan Yankang praised: "We assume that these possible product numbers are [D]. Then, each number of [C] can correspond to a group of [D]."

耶律楚材激昂道：“例如，如果庞涓的和是11，可能的积就是2*9=18、3*8=24、4*7=28、5*6=30。如果庞涓和是17，可能的积就是2*15=30、3*14=42、4*13=52、5*12=60、6*11=66、7*10=70、8*9=72……”

"By analogy, let's compare it with the product Gui Guzi told Sun Bin. Only one can match it. If not it, who else could it be?"

The chatter came down like a river.

happy! Refreshing!

My heart is cold and my heart is flying!

黄蓉一盆凉水浇下来：“但是，我们并不知道孙膑到底拿到的乘积是多少，而只出现一次的乘积有很多。例如2*9=18、3*8=24、4*7=28、4*13=52、4*19=76……都只出现一次，所以我们还是不知道答案。”

When talking.

Her eyes were fixed on Yelu Chucai's expression.

Seeing the other person's smile gradually disappear, the corners of her mouth gradually widened.

——Smile transfer method!

Yelu Chucai looked at Huang Rong displeased.

Why did this yellow-haired girl get into trouble with me?

But in his heart, Yelu Chucai secretly admired Huang Rong's agility. Although people were criticizing me one after another, this just showed that this little girl was talented in arithmetic.

Once again receiving Yelu Chucai's look for help, Wan Yankang spoke.

"It all depends on what Pang Juan says in his third sentence."

"Because, Pang Juan has guessed the answer now. He knows his sum [A]. He only needs to split the sum [A] into two numbers and get the product. If there is and is only one product, it is It can be judged if it is different from everything else in [D].”

Huang Rong immediately changed her focus.

"But we neither know Pang Juan's sum [A] nor Sun Bin's product [B], so what should we do?"

After listening for so long, Huang Yaoshi finally spoke.

"Rong'er, the answer has actually appeared."

"When you compare the numbers of [C] and [D], you will find that only the non-repeating product of the sum of 17 is unique."

"That is 4*13=52."

Huang Rong followed the instructions and immediately started calculating in her mind.

Half a stick of incense time.

she shouted in realization.

"That's right! In all the product groups corresponding to other sums in [C], there are multiple non-repeating products."

“比如，和数11这一组有2*9=18、3*8=24、4*7=28，都是唯一的乘积。再比如，和数23这组有4*19=76、7*16=112，都是唯一的乘积。”

"If these sums were spread out, Pang Juan wouldn't be able to guess it."

"So, the only possible answers are 4 and 13."

The problem was finally solved, and everyone's psychological activities were different.

There are surprises, sadness, and relief...

Huang Yaoshi stood there blankly, but he was actually re-deriving Wan Yankang's thinking in his mind.

The more you deduce, the more you can understand the ingenuity and mystery of this kind of thinking.

Although Huang Rong and Yelu Chucai could both say a few words just now, Huang Yaoshi, who spent fifty-seven days personally, understood that the most essential thing was Wanyankang's unique way of thinking.

Those who are not immersed in this way will not understand Huang Yaoshi's turbulent heart at this moment.

This feeling...how to describe it?

After thinking for a long time, Huang Yaoshi uttered two words.

"Oh my God."

The so-called man's calculation is not as good as God's calculation.

I am an ordinary person and can do calculations in the world; the other party understands the rules of calculations and it is like receiving help from heaven.

"Island Master Huang, do you want to continue?"

"I still have two questions in my hand, "The Strange Calculation of Daily Changes" and "The Yuan Outside the Yuan". Even I have a hard time solving it."

Huang Yaoshi clenched his hands into fists, obviously trying to control his emotions. His eyes flickered, as if he was hesitating about something.

"I……"

His body was still tense, as if he was ready to refute or leave at any moment.

However, he ultimately did not do so.

A trace of unwillingness and stubbornness flashed across Huang Yaoshi's face, but it was quickly replaced by an awkward arrogance.

"you win."

"I will abide by this agreement."

Some people find it an unbearable shame to admit defeat.

Would rather die than admit defeat.

But who is Huang Yaoshi?

In his view, admitting defeat does not mean failure, but an opportunity for growth and progress.

…………(End of chapter)