The Optimal Solution to an Inequality

Under Hermione's supervision and Mrs. Granger's gentle persuasion, Lin Yue slowed down and calmly finished her first dinner since arriving at the Granger family's home.

As soon as the Grangers and Hermione set down their knives and forks after dinner, Lin Yue swiftly rose from her seat, skillfully gathered the plates and cutlery from the table, and headed for the kitchen.

Seeing this, Hermione hurriedly stood as well and gave her mother an obedient smile. "The two of us can wash the dishes."

With that, she quickly ran into the kitchen and took over the task of drying the dishes and putting them into the cupboard.

The Grangers exchanged a glance and could not help smiling with gratification. Both girls were such sensible, good children.

The two quietly walked over to the kitchen doorway and looked inside. In the kitchen, Lin Yue washed the dishes beneath the tap at an incredible speed.

Each plate was sparkling clean in less than twenty seconds in her hands. Hermione, holding a dry dishcloth beside her, kept wiping down the plates Lin Yue passed over, but she was still having trouble keeping up.

This round of dishwashing was unbelievably quick. In less than five minutes, Lin Yue and Hermione had worked together to wash every piece of tableware and put it back in the cupboard.

Once the dishes were done, Lin Yue did not pause for even a moment. Reciting Herbology class knowledge over and over in her head, she hurried up to Hermione's room on the second floor.

She opened her trunk, took out parchment, a quill, and ink, then looked at Hermione's desk.

This was Hermione's desk. Hermione still needed it to study. I can't affect someone else because of my presence.

Those words instinctively sprang into Lin Yue's mind. Not affecting others because of one's own existence was a basic virtue, one that had to be upheld.

Taking the parchment, quill, and ink with her, Lin Yue turned around and hurried back downstairs.

Hermione and the Grangers, who were standing at the foot of the stairs and looking up in confusion, wore different expressions when they saw Lin Yue come down carrying those things.

Hermione's face held a sigh of resignation and heartache, as though she had expected this all along. The Grangers, meanwhile, looked utterly incredulous and distressed.

Sitting down at the dining table with her things, Lin Yue spread the parchment out and began writing the essay assigned for Transfiguration.

As she wrote, her mind continuously formulated what came next. She did not pause in the slightest, like the smoothest typewriter. One word followed another, one line after another, as knowledge was constantly retrieved from Lin Yue's mind and written onto the page.

Mr. Granger could not help wanting to say something, but Hermione tugged at the corner of his clothes and shook her head.

"What is it?" Mr. Granger looked down at Hermione, momentarily stunned. As far as he was concerned, what child started doing homework on the very first day of their holiday?

Wasn't the point of a holiday to relax and let children have fun? They only needed to set aside a little time from playing to do their homework, just enough to make sure they did not forget everything they had learned.

So he had wanted to persuade Lin Yue to rest, at least for tonight. Taking a little break on the first evening of returning home for the summer holiday was hardly too much to ask.

Hermione sighed helplessly. "Lin Yue has already started writing. Let her finish this essay before we try to persuade her to rest."

"Otherwise, if we interrupt her train of thought now, she might have an even harder time when she goes back to writing."

Mr. Granger fell silent for a moment, feeling that his daughter had a point. Shaking his head, he went with Mrs. Granger and Hermione to sit on the sofa.

Since Lin Yue was writing her essay, the three of them did not feel it was appropriate to watch television. Besides, after not seeing their daughter/Parents for an entire semester, they all had plenty to say to one another, so the family of three sat together and began chatting.

Mrs. Granger sat in the middle, with Hermione on her right and Mr. Granger on her left. Hermione began vividly recounting all sorts of interesting things she had experienced over the semester to her parents.

Of course, it was an edited version. When she spoke of seeing a dragon hatch, she only described the wondrous sight she had witnessed, never mentioning how they had nearly been caught by a professor afterward. Nor did she mention Harry, who had gone to serve detention in the Forbidden Forest after that and encountered Quirrell, who had been possessed by Voldemort.

Listening to their daughter's descriptions, the Grangers truly felt the wonder and magic of a magical school.

But no one knew a daughter better than her mother. From the words between the lines, Mrs. Granger could still sense what Hermione was concealing.

For one thing, when Hermione mentioned the dragon egg, fear and lingering dread flashed through her eyes. That could not escape Mrs. Granger's notice.

Her child had grown up. She wanted to handle things herself so they would not worry. Mrs. Granger pressed her lips together and reached out to stroke Hermione's head.

Hermione looked up at her mother, only to see the loving expression on her face as she spoke.

"Hermione has grown up," Mrs. Granger said, gently smoothing her hair. "You know to share good news but not bad news now. But remember, Hermione, we will always be a family. Whatever difficulties arise, we should get through them together. Your father and I do not know much about the Wizarding World, and perhaps there is not much we can do to help with what happens there. But if you are ever unhappy there, or if you are ever in danger, come home. Home will always be safe."

"That's right. Your mother and I will always be waiting for you at home. If there are any bad people or bad things, Dad will chase them away for you!" Mr. Granger added cheerfully, waving his fist as he spoke.

Yet his smile never reached his eyes. Deep guilt and worry filled his heart, making it ache in waves.

It was all because he was useless... As Hermione's father, he should have been there where she was, sheltering her from wind and rain until the day she could spread her wings and face the storms herself.

Yet now, he could only stand where he was and watch his daughter walk farther and farther into the unknown, facing all kinds of storms he knew nothing about.

Hermione bit down on her lower lip and reached out to embrace both her mother and father. Only after burying her face in Mrs. Granger's arms did her eyes quietly redden.

Had she not been afraid when facing the Troll? Had she not been afraid when facing the black-robed man in the Forbidden Forest? Had she not been afraid when facing the various trials and unknown dangers in the Forbidden Corridor on the fourth floor?

How could she not have been? She was only an eleven-year-old child. What did it matter if she was smart?

When those things happened, she had wanted to call for her parents and hide her head in their arms, seeking their protection.

But she knew she could not. Her Parents knew nothing of the Wizarding World and were powerless there.

It was not for them to protect her. She had to grow up quickly, becoming the great tree capable of shielding them from the storms of the Wizarding World.

That had been decided from the moment her name was entered into the Hogwarts Book of Admittance.

Thinking back on the past year, she had encountered all kinds of danger. But had not the truly dangerous situations all been blocked by Lin Yue?

While she herself was still as tender as a sapling, Lin Yue had already grown into a towering tree, sheltering the sky above her.

No... not just her. Harry and Ron, and perhaps even more little wizards, had probably long since been gathered beneath Lin Yue's branches and leaves as well.

So she had to study even harder and become a towering tree capable of standing shoulder to shoulder with Lin Yue as soon as possible. While sheltering her own parents, she could also become someone that girl beside her could rely on.

So Lin Yue would not have to push herself so relentlessly anymore. So she could truly enjoy life, instead of being chased by it.

Gently stroking Hermione's back, the Granger family sank into a long silence.

Lin Yue's quill had long since stopped moving as she sat at the dining table writing her essay. Whenever Hermione talked about the interesting things that had happened at Hogwarts, she inevitably mentioned Lin Yue's name. After all, Lin Yue had been far too involved in Hermione's school life.

So the moment Hermione mentioned her full name, Lin Yue had already slipped out of her studying state.

Although Hermione had deliberately lowered her voice because she was afraid of disturbing Lin Yue, she clearly had not expected Lin Yue's hearing to be so good.

Even with her voice deliberately lowered, Lin Yue still heard her.

As she listened to the conversation between Hermione and The Grangers, Lin Yue's brain kept processing its thoughts.

Hermione did not want Aunt and Uncle to worry after learning about what she had encountered at Hogwarts, so she had concealed some things. Having already understood what the feeling of worry was, Lin Yue quickly reached the conclusion of why Hermione had not told the truth.

Hermione must not have concealed it well enough, so Aunt and Uncle had still realized that she had encountered some danger at Hogwarts. That was why they were worried about Hermione. As she listened to what The Grangers said afterward, Lin Yue continued analyzing.

So why did they worry about each other, speculate about each other's thoughts, and then decide to conceal things from one another?

There was not the slightest trace of confusion in Lin Yue's heart. She merely continued thinking and analyzing in a procedural manner.

Yet, like a computer stuck on a program bug, Lin Yue's thoughts stalled at this step and could not move forward at all.

Her brain began throbbing with pain again, because... they were family.

Those two words surfaced intermittently from the depths of Lin Yue's brain, as though it had once been severely damaged by something.

Family... Lin Yue's brain quickly searched for the definition of family, then continued advancing her thoughts.

So, because The Grangers were Hermione's family—Hermione's Parents—they worried about her safety.

Because Hermione was The Grangers' family—their daughter—she did not want them to worry about her.

But why worry? Lin Yue's thought process malfunctioned again at this point.

Did family members worry about each other? Did Parents worry about their own children?

But she had never seen the Parents she had encountered before worry about the children being dragged away by enforcement officers. Only a very small number of Parents shed a few tears, but after analyzing it, she could not determine whether those tears were for themselves being relocated to the Slums or for their children.

Just like her own Parents. Her memory was completely accurate—she remembered that when they watched her being taken away by enforcement officers, their faces had worn extremely relaxed expressions.

If Lin Yue had understood all emotions, she would have known that the extremely relaxed expressions on their faces were called relief and delight.

Although Lin Yue could not figure out why The Grangers, as Parents, worried about their daughter, or why Hermione, as their daughter, did not want her Parents to worry about her—

She understood that worrying felt bad. It made one's heart hurt and one's head muddled.

In her mind appeared the kindness and friendliness The Grangers had shown when they first saw her, along with the image of Mrs. Granger telling her to savor her dinner slowly.

Then she thought of all the moments she had spent with Hermione. She did not want The Grangers—Hermione's Parents—to experience the feeling of worry.

Even more, she did not want anything to happen to Hermione that would make The Grangers worry.

Perhaps it was because of that tiny bit of "selfishness" deep in her brain that Lin Yue had yet to recognize.

Lin Yue formed the simplest, yet most unscientific, inequality in her mind.

Hermione's safety, plus The Grangers' worry for her, was greater than her own safety, plus no one worrying.

Choose the better option. Choose the more worthwhile option. Between Hermione's safety and Lin Yue's own safety, the answer was already obvious.

Hermione's safety should take priority over her own. With no expression on her face and no emotion in her heart, Lin Yue determined the result of the inequality.

Although she had already been doing this before, at this moment, Lin Yue's thoughts had completely clarified this idea.

Although she did not know why this inequality never appeared in her brain when facing other people, since it had now appeared and produced a result—

Lin Yue would seriously follow the optimal solution and ensure Hermione's safety in either the Wizarding World or the Muggle World.

Lowering her head, she picked up her quill again and prepared to resume writing her essay. For some reason, the sound of The Grangers and Hermione breathing as they embraced seemed especially clear to Lin Yue's ears.

Usually, no matter how noisy her surroundings were, she could swiftly enter a studying state. Yet now, those breathing sounds were making it difficult for her to study.

Imagining Hermione embracing The Grangers right now and recalling the things they had said to one another, Lin Yue's nose inexplicably stung, and her eye sockets grew faintly warm.

She blinked her unfocused eyes, and two clear tears fell onto the Parchment.

Nothing had been written in this spot yet. The essay did not need to be rewritten. It would not delay her later study time or slow down her studying efficiency.

With no change in her expression, Lin Yue made her judgment. Her mood completely undisturbed, she raised a hand and wiped at the corners of her eyes. Once her vision became clear again, she first used her sleeve to wipe away the two drops of tears on the Parchment.

Then she immersed herself in studying, her quill smoothly continuing to complete her Transfiguration essay.

Only after Hermione had suppressed the warmth in her eyes and felt that her eye sockets were no longer reddening did she release The Grangers and lift her head from Mrs. Granger's embrace.

"I'll go see whether Lin Yue has finished her essay." Hermione gave her Parents a brilliant smile, then turned and stepped down from the sofa to check on Lin Yue at the dining table.

Lin Yue had just finished her Transfiguration essay and was rolling up the long sheet of Parchment.

Seeing that Lin Yue had already finished, Hermione hurried over to help her tidy up her things. She also began talking to her, lest Lin Yue start writing essays for other classes as soon as she put away this roll of Parchment.

"Lin Yue, why did you come downstairs to do your homework at the dining table? The lighting here isn't good—it'll hurt your eyes. Why didn't you study upstairs?"

She had wanted to ask earlier, but just as she had told her Dad, she was afraid of interrupting Lin Yue's train of thought. So she had not asked, waiting until Lin Yue finished her essay before voicing the question.