Wandering Spaceship in Deep Space - Chapter 15

Chapter 15: Release Your Hands Off My Sister!

Translator: Henyee Translations Editor: Henyee Translations

Li Zhendong was stunned when he glanced at his friend and noticed that Zhang Yuan had a honey-like smile on his face as he looked at his phone.

‘Good, it seems like he has found a partner.’

Following which, his gossiping mentality flared up.

When Li Zhendong secretly took a glimpse at his friend’s phone, his expression immediately turned weird, ‘Wait a minute, he’s playing Super Brain?’

Li Zhendong could not help but rub his nose and say in an irritated tone, “Why are you being so hardworking?”

“I’m bored, so I’m doing these questions as a pastime. Take a look at this integral. The solution for it is so beautiful. There are only a few integral solutions that can obtain an exact answer.”

Doing questions as a pastime…

As a pastime…

Pastime…

Bulging veins popped up on Li Zhendong’s forehead and his breathing suddenly became hurried. He recalled his university days when Zhang Yuan was an extremely diligent student and because of that, he had suffered no lack of scolding from his parents.

“Take a look at him, then at yourself!” His father’s words seemed to be ringing in his ears right now.

Li Zhendong could not help but get irritated. After they had graduated, Zhang Yuan did not restrain his studious habit but instead, turned for the worst! ‘Resolving questions has now become a fun way to pass time? Is there someone as crazy as you?’

“Hold on, my sister has a game she can’t solve. It’s a puzzle game and since you’re bored, give it a try.”

‘A game?’

“Let me take a look at it.”

When Zhang Yuan saw his friend’s gaze that was laced with bad intentions, he became even more interested in the game. How difficult could a child’s game be?

The little girl promptly grabbed her learning device and came over. There was a mini program named ‘Turn Off The Lights’ displayed on the screen.

The question was as such: There’s a 4 by 4 matrix panel on the screen and every time a panel is touched, the surrounding top, bottom, left and right light panels will change their state (Lit panels would turn unlit and unlit panels would turn lit.)

To get through the puzzle, all the panels must be unlit after a series of actions.

“This is quite simple.”

Zhang Yuan casually pressed a few panels and all the light panels were unlit, thus clearing the stage.

Another image popped up on the screen and it was now a 5 by 5 matrix. Moreover, some of the panels were already unlit.

“Oh, the difficulty increases.”

Zhang Yuan pondered for a moment before pressing a few panels and cleared the stage. He took more time to complete this stage compared to the previous stage.

Clearly, with the increase of panels, the game difficulty would also subsequently increase.

“Erm… I have this thought,” the little girl’s eyes flickered with a glint as she said timidly, “if there is a large matrix and the initial state of the lights is randomized, instead of pressing each panel by random, is there a type of mathematical algorithm to solve this problem?”

Zhang Yuan scratched his head and smiled. “Your sister seems to be good at mathematical logic. As for a mathematical algorithm, let me think about it…”

“Of course, she possesses half of my IQ!”

“Brother~ I’m smarter than you~”

“In which aspect are you smarter than me?”

Li Zhendong was smiling on the surface and feeling gleeful deep down.

That question was very difficult.

And why was it difficult you might ask?

It was because he couldn’t solve it even after thinking about it for quite some time!

‘Therefore, my beloved Brother Zhang who loves solving questions so much, you can slowly think about it until the sky turns dim…’

Letting a good friend disgrace himself in front of his sister made him feel happy and allowed him to vent his anger!

“I’ll take a shower first. You can slowly think about it.”

The little girl looked at Zhang Yuan expectantly, as she was incapable of coming up with the solution for such a question.

However, as the person who came up with the question, she felt rather proud.

Zhang Yuan’s response was beyond their expectations, to the extent he himself was slightly embarrassed. “There’s no need. Don’t take a shower first, I’ve already solved it.”

‘What’

‘You solved it?’

Li Zhendong’s eyes were about to pop out as he ran out the bathroom and in a crestfallen manner, he slipped on his underwear.

Zhang Yuan explained with confidence and composure, “As stated in the question, in the case where the surrounding panels will change their states when the center panel is pressed, we can obtain the conclusion that for some panels, pressing an odd number of times is equivalent to turning on the lights. And for another set of panels, pressing an even number of times equals to turning it off, we can essentially regard this as zero.”

‘Hooo, it’s a little interesting,’ Li Zhendong thought.

“Therefore, for example the question has an explanation which states that every panel can only be pressed once or none at all.”

“We should first see the matrix as n by n. This is, in fact, a binary and isomorphic to a matrix of full rank. Since the matrix is a full rank, there will definitely be a solution.”

When Li Zhendong heard Zhang Yuan’s simple explanation, he felt his mind about to explode as a sense of inspiration surged out like a spring!

‘Wait a moment, was the question always that easy…? Why hadn’t I thought of the answer?’

He shouted indignantly, “How can you use group theory? How can junior middle school students possibly understand group theory? You cannot treat my sister like that!”

Even Li Zhendong’s mother came out to look at the commotion. When she realized it was nothing serious, she shook her head and returned to the kitchen.

“Alright then… I believe junior middle school students have learned multiple linear equations?”

The little girl nodded. Two-variable linear equations were indeed taught in middle school and it can be solved by using the elimination or the substitution method.

Three-variable linear equations and four-variable linear equations were also in her range.

Zhang Yuan continued his explanation, “We shall assume that AIJ = adjusting the I column’s number J panel. Based on what I just said, AIJ is either a 0 or 1.”

“We’ll use the simplest 2 by 2 matrix as an example. For example, the unlit state is 0 and the lit state as 1. Assuming that the initial state of the matrix is as follows…”

1-0

0-0

“We can then come up with four equations.”

A11⊕A12⊕A21=1

A11⊕A12⊕A22=0

A11⊕A21⊕A22=0

A12⊕A21⊕A22=0″

“By solving these equations, we will obtain A21=A11=A12=1 and A22=0. Therefore, we will get the desired results as long as we press A21, A11 and A12 on three panels, the sequence doesn’t matter.”

“All n by n matrix questions can be calculated like that and as such, there will always be a solution. However, n by m questions might not necessarily have an answer and the reason is because…”

Li Zhendong had the urge to cry but no tears came out. He looked on helplessly as his sister’s gaze started to fill with admiration. He could even almost faintly see speckles of starlight appearing in her pupils!

Even though he clearly knew that his sister would most probably not understand Zhang Yuan’s explanation…

But the problem was, children at her age were very pure and their mind was only filled with studying, and thus they had no resistance to smart students!

He’s dead meat. The admiration a sister had for her brother had been snatched away by his good friend!

He only heard his sister asking another question. “Why did you add a circle to this plus operator?”

“Because it is a binary field operation, 1⊕1=0, 1⊕0=1, 0⊕0=0. It is also known as the XOR operation in cryptography… If we use the normal plus operator, we will get a negative number.”

“Brother Zhang, you really know a lot!”

“Therefore, you have to work hard. Otherwise, you’ll end up like your brother who has the talent but doesn’t fully utilize it. It’s useless to be only smart…”

‘B*stard, you’re even badmouthing me!’

‘Go die!’

“Brother Zhang, help me with my Math Olympiad questions. I have many questions I can’t solve but my brother doesn’t want to help…”

“Ah… sure.”

‘My sister is still underage, you better get your hands off her!!’

*Cough* Li Zhendong coughed loudly and warned, “I’ll be taking a shower. You better not mess around. My parents are still home.”

‘What the?’

Zhang Yuan scratched his head in confusion.

The little girl could not help but click her tongue and roll her eyes. She was already in middle school and was well informed about many things. Even if she were to fall in love and date, her family members would not oppose it.

She really felt that her brother was really mentally retarded. In comparison, Brother Zhang Yuan appeared a lot more normal.