Chapter 15

Li Zhendong glanced at Zhang Yuan, and was taken aback when he saw that he smiled honey on the phone.

Very good, I'm looking for someone.

A gossip heart is burning.

I glanced at it secretly, isn't it right, you are actually doing a super brain?

Li Zhendong had to pinch his nose, said ill-humoredly: "Is it so hard?"

"It's boring, let’s do the problem for fun. Look at this integration, how beautiful the solution is Ah, there are very few integral formulas that can really calculate analytical solutions."

Entertainment...

Eliminate...

Li Zhendong's blue veins on his forehead are jumping wildly, and he is short of breath. Reminiscent of his college days, Zhang Yuan was like this diligent dog, which caused him to be criticized by his parents.

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

Li Zhendong couldn't help feeling irritable. After graduating from university, this guy not only didn't converge, but instead got worse. Problem solving has become a high level pastime. Is it so awesome? !

"Wait a minute, there is a game that my younger sister can't play. It is a puzzle game. If you are bored, please try it."

Game?

"Let's take a look."

Seeing the other's harboring malicious intentions' eyes, Zhang Yuan became a little bit interested. How difficult can a little child's stuff be?

The little girl took a learning machine and handed it over. There was a small program called "light off game" on it.

The title is this: There is a 4*4 square array of electric lights on the panel. Every time you operate an electric light, it even brings the surrounding up, down, left, and right lights all change state (on Darken, darken and brighten.)

If all these lights are turned off through a series of operations, the game will be cleared.

"This is very simple."

Zhang Yuan clicked on it randomly, all the lights went out, and it passed.

Another image jumped out on the screen, which turned into a 5*5 electric lamp matrix, and several electric lamps in the middle were already off.

"The difficulty has increased."

Zhang Yuan thought for a while, clicked a few times, and passed the level again. This time it took more time than the last time. .

Obviously, as the number of electric lights increases, the game will become more and more difficult.

"My idea is..."

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

Zhang Yuan scratched his head and said with a smile: "Your younger sister has a lot of mathematical thinking Well, this general algorithm, well, let me think about it..."

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

"big brother I am smarter than you "

"Why are you smarter than me?"

Li Zhendong smiled hehe on his mouth and hehe in his heart.

This topic is difficult.

Why is it difficult?

Because he thought for a while, Li Zhendong didn't make it.

So, Brotherly Zhang, who loves to be a topic, slowly think about it, think of murky heavens dark earth, day and night are reversed...

Make good friends ashamed in front of biological younger sister, he Very happily! It's so cool!

"I'll take a shower first. You do it slowly."

The little girl looked at Zhang Yuan expectantly. Anyway, she couldn't do this kind of topic.

However, as the author of the question, I feel very proud.

Zhang Yuan's reaction was beyond their expectations. He was a bit sorry: "No, don't take a shower. It's already untied."

What?

Untied?

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

Zhang Yuan talked eloquently: "According to the title: press the switch once, and all the lights on the top, bottom, left, and right will change the state. So we can get a conclusion: For a certain light, press an odd number The effect of the second switch is the same as the effect of pressing the switch once; the effect of pressing the switch even times is equivalent to not pressing it, which is 0."

Interesting.

"So, if there is a solution to the problem, each lamp should only be operated once at most, or not operated."

"First of all, let’s discuss the N*N matrix, which is actually a The two-element group is 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 is about to burst, and his inspiration is like spring water. Surging!

Wait a minute.

It seems, that's it...

It's a very simple topic.

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 do this to my younger sister!"

Lian Li Zhendong mother all came out and saw that they weren't doing anything, and shook the head again and went back to the kitchen.

"Let’s do it. Junior high school students have studied Simultaneous Equations once more, right?"

Little girl nodded, dual Simultaneous Equations, it is indeed the content of junior high school, the elimination method is , Substitution method can be solved.

Three yuan once, four yuan once is also acceptable.

Zhang Yuan continued: "Assuming that Aij is the number of times to adjust the jth lamp in the i-th column, obviously, according to what I just said, Aij is not 1, or 0."

"Let’s take the simplest 2*2 matrix as an example, set the light off state of at first to 0 and turn on the light to 1."

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

" p>

[1-0]

[0-0]"

"Then you can write four equations:

A11⊕A12⊕ A21=1

A11⊕A12⊕A22=0

& lt;p>A11⊕A21⊕A22=0

A12⊕A21⊕A22=0”

"The solution can be A21=A11=A12=1, A22=0. So just operate the three lights A21, A11, A12 in sequence, the order does not matter."

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