New Year’s Eve.
In Zeyang City, the snow fell steadily.
The light in the stairwell was a little dim. A few unfinished heads of Napa cabbage were piled by Grandma Wang’s door on the first floor. On the second floor, a new set of couplets had just been pasted on Uncle Li’s doorframe, the adhesive still wet.
Chen Zhuo climbed the stairs to the fourth floor.
"Mom, I’m home."
Chen Zhuo changed into his slippers and casually hung his down jacket on the rack behind the door.
Liu Xiuying, wearing a floral apron and holding a spatula, leaned out of the kitchen.
"Where have you been all day? Your hands are red from the cold. There’s a freshly filled hot water bottle on the sofa, go warm them up."
As she spoke, Liu Xiuying flipped the hairtail fish in the wok.
"You were out all afternoon, and the phone’s been ringing off the hook."
Chen Zhuo walked into the living room, picked up the hot water bottle in its old knitted cover from the sofa, and hugged it to his chest.
"Who called?"
Liu Xiuying pointed at the coffee table with her spatula.
"I wrote their numbers on the back of a calendar page over there. There were quite a few calls. They all sounded like teenagers. One boy talked like a machine gun, just rattling on and on—it gave me a headache. Then there was another boy who was so formal, like a senior manager from our old factory giving a report."
Liu Xiuying turned down the heat and continued her rambling account.
"Oh, right, there was a girl, too. Her voice sounded so cold. She asked if you were here, and when I said you were out, she just said, ’Thank you, ma’am,’ and hung up immediately."
Listening to his mom’s descriptions, Chen Zhuo instantly pieced it all together.
He walked over to the coffee table and picked up the torn-off page from an old calendar. On the back, several phone numbers were scrawled in ballpoint pen, some including area codes.
"Okay, I’ll call them back in a bit."
"Don’t call them just yet."
Liu Xiuying came out carrying a plate of freshly fried hairtail fish and placed it on the dining table.
"Go check your room. The postman delivered a letter for you this afternoon. On New Year’s Eve of all days... I can’t imagine who still writes letters."
Chen Zhuo hummed in agreement and turned to enter his bedroom.
An envelope lay quietly on his desk.
It was the cheapest kind of envelope, the paper thin. Its corners were already starting to fray from its journey through the mail.
An eight-jiao stamp was affixed to the top-right corner. The postmark was from Guanlong City.
Chen Zhuo sat down in his chair and turned on his desk lamp.
The characters on the envelope were written with such force they nearly tore through the paper.
It was from He Gui.
He took a small letter opener from his drawer, carefully slit open the envelope, and pulled out a sheet of paper.
Chen Zhuo unfolded the letter.
"Captain.
I’m doing well here at the city’s top high school. You don’t need to worry about me.
The temperature dropped recently, and it gets a little drafty in the dorm, but I’ve put down two mattress pads, so I’m not cold.
The school waived my tuition and housing fees for all three years, and they even give me an extra 150 yuan in meal vouchers every month. I didn’t touch a cent of the prize money from the middle school competition; I sent it all back to my dad. He wrote that he finally paid off the loan he took from the town’s credit union two years ago for my sister’s medical bills.
My dad said a huge weight has been lifted this New Year’s."
I’m eating very well here. The cafeteria even serves free braised pork every Wednesday.
The teachers are great to me. They let me join the training team for the Physics Olympiad. This year, I’ll be joining the second- and third-year students to compete for the provincial first-place prize.
Lately, I’ve been tackling a university-level textbook, *General Physics*, but I’ve run into a problem from a past Russia Olympiad.
It’s an extreme value problem involving a spring-mass oscillator superimposed on a multi-pulley system in a non-inertial frame of reference.
The team’s supervising teacher used calculus to fill two blackboards, but the result was still a very complex approximation.
I feel like it shouldn’t be this complicated. I’ve been thinking about it for days and have filled over a dozen sheets of scratch paper with force diagrams, but I still can’t find a simpler approach.
I’ve copied the problem onto the back. If you’re not too busy with your studies, could you take a look? If you don’t have time, it’s okay. It’s no trouble."
Chen Zhuo turned the letter over.
On the back was a meticulously drawn diagram of the pulley and spring system, created with a pencil and ruler.
Next to it, dense columns of attempted calculations using Newtonian mechanics were crammed in. Many spots were smudged black from an eraser, clearly from being written, erased, and rewritten over and over.
Chen Zhuo looked at the convoluted arrows of the force analysis vectors.
He uncapped his fountain pen and pulled a clean sheet of paper from the drawer.
He didn’t follow He Gui’s train of thought with calculus, nor did he bother drawing complex diagrams of frictional and centripetal forces.
He wrote no dizzying equations, no lengthy explanations.
First line, he wrote a state function.
Second line, he substituted the system’s kinetic and potential energy into a clean, concise equation.
Third line, he drew a small diagram off to the side illustrating the critical point of energy transformation.
Then he added a brief note at the bottom:
"Don’t brute-force the force calculations. Use the Lagrangian equation. Treat the entire system as a whole and find the critical point of energy conservation. Basic Newtonian mechanics can lead you astray in a non-inertial frame. Take it a step further and look into analytical mechanics."
Chen Zhuo blew on the ink to dry it, folded the letter into thirds, and tucked it into a new envelope, which he addressed and stamped.
Just as he placed the envelope on the corner of his desk, the phone in the living room suddenly rang.
"RING RING RING—"
The old landline was very loud.
"Chen Zhuo, get the phone!" Liu Xiuying yelled from the kitchen.
Chen Zhuo walked out of his bedroom and picked up the receiver.

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