Li Zhendong looked at Zhang Yuan and saw him smiling at his phone with a honeyed smile. He was stunned.

Very good, looking for a partner.

A gossip heart burns.

I glanced at it secretly and said, "No, I'm actually doing a super brain?"

Li Zhendong had to pinch his nose and said angrily: "You're working so hard?"

"Bored, do the questions and have fun. Look at this integral, how beautiful the solution is. There are very few integral formulas that can really calculate the analytical solutions."

Have some fun...

pastime……

remove……

Li Zhendong's forehead was leaping and his breathing was rapid. Thinking of his college years, Zhang Yuan was like this diligent dog, which made him criticized many times by his parents.

"Look at him, look at you!" My father's judgment seemed to ring in his ears.

Li Zhendong couldn't help but feel irritated. After graduating from college, this guy not only did not restrain himself, but became more serious. The problem-solving has become a high-level entertainment. Is it so awesome?!

"Wait a minute, my sister has a game that can't be played, a puzzle game. If you are bored, try it."

game?

"Take it and take a look."

Seeing the other party's malicious eyes, Zhang Yuan became a little interested. How difficult can a child's thing be?

The little girl handed over with a learning machine, and there was a mini program called "Downlights Game" on it.

The title is as follows: There is a 4*4 light array on the panel. Each time an electric light is operated, it will all change its state with the upper, lower, left and right lights (light becomes dark, dark becomes bright.)

If you pass a series of operations, all these lights will be turned off, and the game will pass.

"This is very simple."

Zhang Yuan lit it a few casually, and all the lights went out and passed the test.

Another image jumped out on the screen, which turned into a 5*5 light matrix, and several lights in the middle have been turned off.

“The difficulty has increased.”

Zhang Yuan thought for a while, clicked a few times, and passed the test again. This time he used more time than the last time.

Obviously, as the meter of electric light array increases, the game will become more and more difficult.

“My thought is…”

The little girl's eyes flashed and she said timidly: "If there is a large queue of lights and the initial state of the lights is arbitrary. Then, is there a mathematical algorithm to solve this problem instead of randomly making up..."

Zhang Yuan scratched his head and said with a smile: "Your sister has a lot of mathematical thinking. This general algorithm, well, I think about it..."

"Of course, she has more than half of my IQ!"

"Brother~ I'm smarter than you~"

"How come you are smarter than me?"

Li Zhendong smiled and smiled in his heart.

This question is difficult.

Why is it difficult?

Because Li Zhendong thought about it for a while, but he didn't do it.

So, Brother Zhang, who loves to do questions, you think slowly, thinking about it when the sky is dark and the earth is inverted day and night...

He was very happy and relieved to let his good friends embarrass him in front of his own sister!

"I'll take a shower first. Do it slowly."

The little girl looked at Zhang Yuan with anticipation. She definitely couldn't do such a problem anyway.

However, as the questioner, I was extremely proud.

Zhang Yuan's reaction was beyond their expectations. He was a little embarrassed: "No need, don't take a shower first, it's already untied."

What?

Unlocked?

Li Zhendong's eyes were about to pop out, he ran out of the bathroom, and then put on his underwear in shame.

Zhang Yuan talked happily: "According to the question: press the switch once, and the lights on the upper, lower, left and right all change the state. So we can get a conclusion: for a certain light, the effect of pressing the odd number of switches is the same as pressing the one switch; the effect of pressing the even number of switches is equivalent to not pressing, which is 0."

Something interesting.

"So, if the question has an answer, each light will only be operated once at most, or it will not be operated."

"First discuss the n*n matrix. This is actually a binary group, and isomorphic to a full rank matrix. Since the matrix is ​​full rank, there must be a unique solution..."

After hearing these few words just now, Li Zhendong's head was about to explode, and inspiration surged like a spring!

Wait a moment.

It seems that that's it...

It's a very simple question.

Why didn't I think of it?

He shouted unwillingly: "How can you use group theory? How can junior high school students understand group theory? You can't treat my sister like this!"

Even Li Zhendong's mother came out to see it and found that they were not doing anything. She shook her head and returned to the kitchen.

"That's OK. Junior high school students have learned multiple system of equations, right?"

The little girl nodded. The two-part system of equations is indeed the content of junior high school. The method of eliminating the element can be solved by substituting the method.

Three yuan per time and four yuan per time are acceptable.

Zhang Yuan continued: "Suppose aij adjusts the number of times the j lights in the i-th column, it is obvious that according to what I just said, aij is either 1 or 0."

"Let's take the simplest 2*2 matrix as an example, let's say the light off state at the beginning is 0 and the light on is 1."

"We assume that the initial state of the matrix is ​​like this:

【1-0】

【0-0】”

“Then you can write four equations:

a11⊕a12⊕a21=1

a11⊕a12⊕a22=0

a11⊕a21⊕a22=0

a12⊕a21⊕a22=0”

"You can find that a21=a11=a12=1,a22=0. So just operate the three lamps a21, a11, and a12 in sequence, and the order doesn't matter."

"...All n*n matrix problems can be calculated in this way, and there must be solutions. But n*m problems may not necessarily have solutions, because this is the reason..."

Li Zhendong was in tears and looked at his sister's eyes little by little, and even little stars appeared!

Although he knew that his sister would probably not understand...

However, girls of this age are innocent and simple, with only learning in their eyes, and they have no resistance to academic masters!

It’s over, my sister’s admiration for her brother was snatched away by someone else!

I only heard my sister ask again: "Why do you need to add a circle for this plus sign?"

"Because it is a binary domain operation, 1⊕1=0,1⊕0=1,0⊕0=0, it is called exclusive OR operation in the computer field... If you use the ordinary plus sign, you will calculate the negative number."

"Brother Zhang, you know so much!"

"So you have to work harder, otherwise you will be talented but not fulfilled, and smart is useless like your brother..."

Livestock will harm me!

go-die!

"Brother Zhang, please help me with the mathematics of the Olympiad. There are many questions I don't know. My brother won't help me."

"Okay...right."

My sister is underage yet!

Let go of your paws!

"Ahem!" Li Zhendong coughed heavily and warned: "I'll go take a shower, don't mess around, my parents are still at home."

What?

Zhang Yuan scratched his head.

The little girl couldn't help but curl her lips and roll her eyes. She was already in junior high school and knew a lot of things. Even if she was in love, she would not be opposed by her family.
Chapter completed!