Could He Have Just Written Nonsense?

Fang Jiaxue glared at him. "I made it. Hurry up and come eat."

Fang Jiaze didn't move.

He stood where he was, the corner of his mouth twitching slightly as his gaze moved back and forth across the dining table.

"Are you eating or not?"

"Um... Sis, I'm suddenly not that hungry..."

"I'll count to three. Are you eating or not?" Fang Jiaxue put her chopsticks down on the table.

Fang Jiaze shrank back.

"One..."

Fang Jiaze rushed to the table and sat down. He grabbed his chopsticks, picked up a piece of tomato and scrambled egg, and stuffed it into his mouth like a man bravely marching to his death.

Then he froze.

"Something's not right." Fang Jiaze looked at his sister suspiciously.

"What is it?" Fang Jiaxue picked up a piece of green pepper but hadn't brought it to her mouth yet.

"There's no way you made something that tastes like this."

Fang Jiaze turned to look at Qi Hao, who was quietly eating beside him.

"Brother," he said bluntly, "you made this, didn't you?"

Qi Hao was chewing a mouthful of rice. Asked so directly, he could only give a muffled grunt of assent.

Fang Jiaze slapped the table. "I knew it!"

"Is there that much of a difference?" Fang Jiaxue asked, unwilling to concede.

She couldn't beat Qi Hao at math, and now she couldn't beat him at cooking either?

Fang Jiaxue lowered her head, picked up some tomato and scrambled egg, and put it in her mouth.

Then she fell silent.

That taste... really was on a different level from what she usually made.

The eggs were tender, silky, and fluffy, coated in the tomatoes' sweet-and-sour flavor. They melted in her mouth without falling apart so much that they lost their texture. The tomatoes hadn't been cooked to mush; they retained just a little of their bite, with sourness in their sweetness and a savory freshness in their sourness.

It really was delicious!

Fang Jiaze had completely let himself go.

"Brother! This shredded pork is incredible! How did you get this texture? It's so tender and full of flavor! The last time my sister made shredded pork with green peppers, the pork was no different from charcoal!"

"Fang Jiaze, do you have a death wish?" Fang Jiaxue threatened.

"I'm stating a fact!"

Fang Jiaxue raised her chopsticks, and Fang Jiaze immediately shut his mouth and bent over his bowl, shoveling in rice.

But after less than five seconds of silence, he couldn't resist looking up at Qi Hao again. "Brother," he said quietly, "can you come cook at our place often from now on?"

"Do your homework." Fang Jiaxue answered the question for Qi Hao.

Qi Hao hadn't said much the whole time. He just ate quietly, the corners of his mouth occasionally curling up.

The siblings' interactions were so entertaining that butting in would only spoil the natural fun.

The way the two got along was much like how he and his younger sister interacted.

Unfortunately, he hadn't seen his sister for over a month since starting university.

He wondered how the little girl was doing.

Fang Jiaxue had already silently finished a bowl of rice. Then she got up without a word, walked over to the rice cooker, and served herself another bowl.

Fang Jiaze saw this and tactfully kept his mouth shut.

Some things didn't need to be said. Two bowls of rice were the most honest review.

The three of them finished eating.

Fang Jiaze got up of his own accord to clear the dishes.

"I'll wash the dishes." Fang Jiaze carried the bowls toward the kitchen.

Qi Hao was a little surprised. Fang Jiaze didn't seem to be as spoiled as he had imagined.

Still, judging by this, Fang Jiaxue had probably been carrying out a plan to reform her younger brother at home quite often.

Qi Hao sat for a while longer, then prepared to leave. Fang Jiaxue saw him to the door.

Fang Jiaxue closed the door and returned to the living room.

Fang Jiaze was washing dishes in the kitchen, the faucet running noisily.

She had only been sitting for a short while when Fang Jiaze poked half his head out of the kitchen, his hands wet.

"Sis."

"What?"

Fang Jiaze said with a perfectly serious expression, "That's the standard for my future brother-in-law."

The remote control in Fang Jiaxue's hand nearly went flying at him.

"I mean cooking! That's the standard for his cooking!" Fang Jiaze quickly pulled his head back, but his voice still floated out of the kitchen. "If you find someone whose cooking isn't as good as Brother Hao's, I won't accept him!"

"Worry about yourself!" Fang Jiaxue's face felt a little hot, and she raised her voice to cover up her discomfort. "I'm telling you, Fang Jiaze, you'd better bring home a wife who can cook. I'll be relying on you two for three meals a day!"

"What kind of sister are you? Why don't you learn to cook yourself?"

"Can't hear you." Fang Jiaxue picked up the remote, turned on the television, and raised the volume two notches.

After Fang Jiaze finished washing the dishes and went upstairs, Fang Jiaxue turned off the television, took out her phone, and photographed each page of the three problems Qi Hao had solved. She opened QQ and sent them to her best friend, Chen Xiang.

[Fang Jiaxue]: Xiangxiang, I had the tutor who came to help my brother today solve those three problems you gave me.

[Fang Jiaxue]: Tell me honestly, are those three problems actually really easy?

Less than a minute later, Chen Xiang's replies came in a burst like machine-gun fire.

[Xiangxiang]: ???

[Xiangxiang]: Easy?

[Xiangxiang]: Those three are variations I handpicked from a collection of the toughest provincial competition problems over the years!

[Xiangxiang]: Even the top students in our math department at Sichuan University wouldn't stand a chance of figuring them out without an hour or two of working through them on scratch paper! And you're calling them easy?!

Fang Jiaxue's head was spinning a little, and her fingers flew over the keyboard.

[Fang Jiaxue]: But... he finished them in less than half an hour! He barely took a break and wrote down the answers straightaway.

[Fang Jiaxue]: He also said the approach to the problems was rather tricky and that his solutions were different from other people's. He said you could ask him if there was anything you didn't understand.

[Xiangxiang]: Impossible! Absolutely impossible!!!

[Xiangxiang]: To borrow a famous line from Conan, "Shinjitsu wa itsumo hitotsu!"

[Xiangxiang]: He must have seen the original problems and the standard answers before!

[Fang Jiaxue]: But he said his solutions were different...

[Fang Jiaxue]: Just look at the steps he wrote down first.

[Xiangxiang]: Hold on, let me take a careful look first.

Chen Xiang put down her phone, enlarged the three photos she had received, and began studying Qi Hao's solutions.

For the first problem, a number theory question, she first looked at the final result.

The answer was correct.

Then she read through the working from the beginning.

After about three lines, her brows knitted.

Something was wrong.

This wasn't the standard solution.

The standard solution used a very classic set of number theory tools. Basically, every contestant's first instinct on seeing this kind of problem would be to head in that direction.

But Qi Hao hadn't.

Right from the start, he used an approach she had never seen. He first constructed an auxiliary function, then used symmetry to directly reduce the original problem by one dimension, making the subsequent derivation extremely concise.

Chen Xiang stared at those lines of working several times. She felt she could understand why each step was valid, but she couldn't figure out how he had thought to construct it that way.

The second problem, in combinatorics, was even more astonishing.

The standard answer took up two and a half full pages and required three lemmas, building layer upon layer before reaching the final conclusion.

Qi Hao's solution was only a little over half a page long.

He approached it from a completely different angle, skipped the cumbersome lemmas in between, and used a set of inequalities to pin down the conclusion directly.

The working was completely different from the standard answer.

But the answer was correct.

Chen Xiang gave up on the third problem, in numerical analysis, after five minutes. It wasn't that she couldn't understand the question; she couldn't follow Qi Hao's line of reasoning.

Partway through, he used a transformation technique she had never seen. He seemed to turn the numerical analysis problem into an operation on some kind of algebraic structure, then use a property of that structure to reach the conclusion directly.

Chen Xiang leafed through her textbooks and notes but found no similar method.

She put down her phone and sat stunned for several seconds.

"I can't understand it. Could he have just written nonsense?"

Chen Xiang knew the chances of that were slim, but she still wasn't willing to believe that a student majoring in math at a radio and television university was more capable than she was.

According to the Ministry of Education's rankings from a few years ago, Sichuan University's math program ranked eleventh in the country, while the radio and television university's math program was nowhere near as high.

Chen Xiang decided to ask her math professor and get to the bottom of it.

Phone in hand, Chen Xiang knocked on the door of Associate Professor Xu's office in the math department.

Professor Xu was one of the math department's competition coaches at Sichuan University. He had long been responsible for training students for provincial and national competitions and was fairly well known in competition circles.

"Teacher Xu, do you have a moment? I have a few problems I'd like to ask you about."

"Come in."

Professor Xu was typing something at his computer and didn't look up. "What problems?"

Chen Xiang handed him her phone. On the screen were photos of Qi Hao's solutions.

"These three are actual problems from provincial competitions in recent years. I'm not quite sure whether the logic of these solutions is completely rigorous... Could you take a look?"

Professor Xu took the phone and glanced at it casually.

Then his finger stopped on the screen.

After about ten seconds of silence, he enlarged the photos and began reading line by line.

Chen Xiang stood beside him and watched as Professor Xu's slightly furrowed brows gradually relaxed.

Half an hour later, Professor Xu had finished reading all three solutions.

He put down the phone and said, "The way an auxiliary function was used to solve the first problem is very elegant. It's at least a third shorter than the standard answer."

Professor Xu stood up, walked to the whiteboard, picked up a pen, and quickly wrote a few lines. "Look here. At this step, the standard solution requires the law of quadratic reciprocity, but this solution bypasses it directly through symmetry. This kind of construction is rarely seen in number theory competitions. It shows that the person who solved it understands number-theoretic structures on a level beyond simply being able to solve problems."

"And the standard solution to the second problem needs three lemmas to lay the groundwork. But look at this set of inequalities. This isn't a conventional competition technique. Someone who can use this method to solve a competition problem has either read a great many academic papers or has an exceptionally strong mathematical intuition."

He turned around, his gaze showing clear appreciation as he looked at Chen Xiang.

"Chen Xiang, at your level, you shouldn't be wasting time on the provincial competition. You should be competing at the national level."

"Me, compete at the national level?" Chen Xiang pointed at herself.