Chapter 15: Chapter 15 Let Go of Your Claws!
Editor: Henyee Translations
Li Zhendong glanced at Zhang Yuan, saw him smiling sweetly at his phone, and was montarily stunned.
Okay, got a girlfriend now.
His nosy mind burned with curiosity.
He took a quick peek, but no, he was actually doing Super Brain?
Li Zhendong had to pinch his nose and said irritably, “Working so hard, huh?”
“Boredom, just solving problems for fun. Look at this integration, what a beautiful thod, it’s rare to find integrals that can actually be solved analytically.”
...
Just for fun…
Fun…
Ju…
Li Zhendong’s forehead pulsed with veins, and his breathing quickened. Recalling his university days, Zhang Yuan was just as hardworking, causing him to be frequently criticized by his parents.
“Look at him, then look at you!” His father’s judgnt seed to echo in his ears.
Li Zhendong couldn’t help feeling agitated; after graduating from university, this guy only ramped up his efforts instead of restraining himself. Solving problems had beco a sophisticated leisure, that impressive?!
“Wait, my sister can’t get through a ga, a puzzle ga, why not give it a try if you’re bored.”
Ga?
“Let have a look.”
Seeing the mischievous look in his eyes, Zhang Yuan grew a bit interested. What difficulty could a child’s ga hold?
A little girl handed over a learning machine, on which there was a small program called “Lights Out.”
The objective was this: A 4×4 grid of lights was lit up on the panel, and every ti one light was operated, it, along with its surrounding lights above, below, left, and right, would all change state (on to off, off to on).
If you could turn all the lights off through a series of operations, the ga would be cleared.
“This is pretty simple.”
Zhang Yuan tapped a few tis, turned off all the lights, and cleared the level.
The screen then switched to another image, this ti becoming a 5×5 grid of lights, with a few lights already turned off in the middle.
“The difficulty has increased.”
Zhang Yuan thought for a mont, tapped a few more tis, and cleared it again, but this ti took a bit longer than the previous attempt.
Obviously, as the grid of lights increased, the ga beca more challenging.
“My thought is…”
The little girl’s eyes sparkled as she timidly said, “If there’s a very large grid of lights and their initial state is arbitrary, is there a mathematical algorithm to solve this problem, rather than randomly tapping?”
Zhang Yuan scratched his head and laughed, “Your sister has a way with math, this general algorithm, um, let think…”
“Of course, she has half my intelligence!”
“Brother~ I’m smarter than you~”
“In what way are you smarter than ?”
Li Zhendong smiled externally and internally.
This problem was hard.
Why was it difficult?
Because Li Zhendong thought for a while and couldn’t figure it out.
So, puzzle-loving Brother Zhang, take your ti, think yourself into exhaustion, day and night…
He was very pleased! Extrely so!
“I’ll go take a shower first. You take your ti with it.”
The little girl looked at Zhang Yuan expectantly; after all, she definitely couldn’t solve this kind of problem.
Yet as the person who posed the question, there was also an unusual pride in her heart.
Zhang Yuan’s response took them by surprise; he felt a bit embarrassed, “No need, don’t shower yet, I’ve already solved it.”
What?
Solved it?
Li Zhendong’s eyes nearly popped out as he dashed out of the bathroom, then sheepishly put his clothes back on.
Zhang Yuan spoke eloquently, “According to the problem, when you press a switch once, the light itself and those around it all change state. So, we can draw a conclusion: for a given light, pressing the switch an odd number of tis is the sa as pressing it once; pressing it an even number of tis is equivalent to not pressing it at all, or zero.”
Interesting.
“So, if the problem has a solution, each light only needs to be operated on at most once, or not at all.”
“Let’s first discuss an N*N matrix, which 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 listening to just a few sentences, Li Zhendong’s head was about to explode, inspiration bubbling like a spring!
Wait.
It seems like… that’s it…
Such a simple problem.
How did I not think of that?
He shouted unwillingly, “How can you use group theory? How can a middle schooler understand group theory? You can’t do this to my sister!”
Even Li Zhendong’s mother ca out to check, seeing they were not up to anything, shook her head, and returned to the kitchen.
“Alright then. Middle schoolers have learned systems of linear equations, right?”
The little girl nodded, indeed binary system equations are part of middle school content, they can be solved by elimination thod or substitution thod.
Even problems with three variables or four variables are manageable.
Zhang Yuan continued, “Assu Aij is the number of tis the j-th light in the i-th row is adjusted. Obviously, according to what I just said, Aij is either 1 or 0.”
“Let’s take the simplest 2×2 matrix as an example, assuming the initial state is off for zero and on for one.”
“Let’s assu the matrix’s initial state is like this:
[1-0]
[0-0]”
“Then we can write four equations:
A11⊕A12⊕A21=1
A11⊕A12⊕A22=0
A11⊕A21⊕A22=0
A12⊕A21⊕A22=0”
“By solving, we get A21=A11=A12=1, A22=0. So just toggle these three lights in order, A21, A11, A12, it doesn’t matter what order.”
“Every N*N matrix problem can be calculated this way, and there’s always a solution. But an N*M problem may not have a solution, and here’s why…”
Li Zhendong watched helplessly as admiration filled his sister’s eyes, practically seeing stars!
Even though he knew she probably wouldn’t understand…
But, but, at this age, girls are innocent and pure, their eyes focused on learning, they have no resistance to intellectual brilliance!
It’s over; his sister’s admiration for her brother has been stolen!
Then he heard his sister ask, “Why does this plus sign have a circle around it?”
“Because it’s a binary field operation, 1⊕1=0, 1⊕0=1, 0⊕0=0, in computing it’s called XOR operation… If you use a regular plus sign, it would result in a negative number.”
“Brother Zhang, you know so much!”
“So you have to work a little harder, otherwise, like your brother, having talent that’s unfulfilled ans being smart is useless…”
Bastard, still putting down!
Go die!
“Brother Zhang, help with those Math Olympiad problems, a lot of them I don’t understand. My brother won’t help .”
“Sure… all right.”
My sister is still a minor!
Let go of your paws!
“Ahem!” Li Zhendong coughed heavily, warning, “I’m going to take a shower, don’t ss around, my parents are ho.”
What?
Zhang Yuan scratched his head.
The little girl couldn’t help but roll her eyes. She was already in middle school and knew a lot; even dating wouldn’t be opposed by family.
She felt her own brother was a bit brainless, while Brother Zhang seed more normal…
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