The study of French numbers and the introduction to base-17 occupied less than half of the course time.

No matter how talented the young wizards were in knowledge acquisition and numerical sensitivity, it couldn't hide the gaps in their basic mathematical knowledge. After successfully sparking the students' interest, the math class gradually got on track.

Compared to the backward and cumbersome "tallying method," vertical calculation was undoubtedly a concept that needed to be popularized.

However, the prerequisite for vertical calculation was familiarity with numerical notation and the memorization of multiplication tables—which was also the most crucial and challenging starting point in the math curriculum designed by Alexei and Aeliana.

Just as the size of a pyramid's base determines its upper limit, this principle applies equally in many fields.

"Alright," Alexei said, gesturing for the students to turn to the last few pages of their textbooks. "I believe everyone has already seen the multiplication tables at the back. This will be your homework for the first week. Memorize them as thoroughly as possible, and next week in class, I will be quizzing you and assigning grades."

"I don't quite understand, Professor Alexei."

Draco Malfoy raised his hand, frowning as he looked at the textbook in front of him, and said perplexedly.

"There are three tables of completely different sizes on this, but their names are all the same..."

At the back of his copy of "Elementary Mathematics I," there were three multiplication tables attached. Each table was filled with densely packed numbers, and even a cursory glance gave him a feeling of mental numbness, making him feel drowsy.

"Oh, yes, that's exactly what I wanted to talk about next."

Alexei's voice echoed in the classroom, the middle-aged man's tone slightly complex.

"As you can see, there are three multiplication tables of different sizes at the back of your textbooks, namely 9x9, 16x16, and 26x26. You can choose any one of them to memorize according to your actual situation."

"However..."

Alexei paused, his gaze sweeping over the impish silver-haired witch in the front, and continued.

"If you choose the 9x9 multiplication table, your highest grade in this course this year will not exceed 'Satisfactory'. Choosing the 16x16 table will give you the opportunity to earn an 'Outstanding'. As for the 26x26—that's just a challenge, and aside from letting you know that you can be a little better than other wizards, there won't be any additional special rewards."

"Oh, so we can choose any one? Then we're definitely going to..."

Hearing this, Ron Weasley instantly perked up, looking at the small table in the front with a relaxed expression.

As Gryffindor's "chess king," Ron had always adhered to the philosophy of getting by if he could. Anyway, neither his family nor the school, nor even he himself, ever expected him to get many "Outstandings" in the end-of-term exams each semester.

However, before Ron could finish speaking, a neat rustling of pages turning sounded around him.

??

???

Ron looked at the people around him with a puzzled expression. Even Neville, who always seemed a bit slow, had actively turned to the last page, which was the most daunting mathematical matrix, and began to mutter and memorize it softly.

As for Harry and Draco, who were sitting on the other side, it goes without saying that they had long betrayed the ranks of the slackers.

"I say, Harry, Neville, didn't you hear what the professor just said?"

Ron looked at the small table in front of him, then at the one that was about three or four times larger, and his mouth twitched slightly. He nudged Neville Longbottom on his right with his elbow and said softly.

"Even if you want to aim for an 'Outstanding,' you can just choose the 16x16 one. If you ask me, this last 26x26 multiplication table is probably just an option to make us give up. Instead of spending so much effort, you might as well memorize some more spells or something, at least those things seem more useful..."

Just then, Alexei's gaze swept over in this direction, and Ron subconsciously stopped speaking.

"But I just want to try..."

Neville Longbottom looked at the densely packed matrix of numbers in front of him and took a deep breath.

"Grandma always tells me to bring honor to the Longbottom family and not to be laughed at by others... I don't really have much talent in spells, but I still want to try something that I can work hard at with a simple method..."

As he spoke, Neville lowered his head again and continued to recite softly.

"But—"

Ron sighed helplessly. As a child from a pure wizarding family, he really couldn't understand the point of adding extra study burden. What was the point of being good at math? He wasn't planning to work at Gringotts later anyway.

However, if the surrounding classmates and friends all chose this way, Ron could only...

"Excuse me, Professor Alexei, I have another question."

Just then, at the desk in the front of the classroom, Hermione's arm was raised high.

"I really can't understand what the point of that last complicated multiplication table is—if the sixteen-by-sixteen table will be useful when we use Galleons and Sickles, then what about the twenty-six-by-twenty-six table?"

Along with Hermione Granger's voice, the students in the classroom looked up curiously.

Alexei frowned slightly, his gaze first lingering on the white fluffy ball next to the girl, then quickly stood up, walked to this "unplanned" questioner, and asked thoughtfully.

"Excuse me, miss, what is your name?"

"Hermione, Hermione Granger, Gryffindor."

Hermione replied quickly, her bright brown eyes showing no hint of timidity.

"Professor, I've already previewed this year's reference materials during the summer vacation. If it's basic arithmetic, then the 9x9 multiplication table is enough. Even considering magical currency, it doesn't need to be raised so high all at once."

"Because... it helps to understand base-27, my dear Miss Granger."

Alexei glanced at Aeliana, who was slightly nodding beside the girl, thought for a moment, and then explained softly.

"By the way, the reason for asking you to memorize the 16x16 multiplication table is not just to make it easier to calculate change in daily life, but more importantly, it will make it easier for you to understand base-16 vertical calculation in the future."

"The smallest even prime number and the smallest odd prime number, base algorithms with them as the base, will inevitably have their unique value."

"As for when and how it will be used..."

Alexei shook his head, subconsciously looked out the window, and replied with a complex tone.

"It's like the meaning of learning mathematics. To a large extent, it depends on the progress of other fields. It may never be used, or it may be used next month. But from the current situation, at least you have hope..."

……

At the same time.

"Hogwarts Academy City - H Research Zone," in the central report hall.

"In short, the precautions can be summarized into these few items—"

Goblin Douglas pointed to the lines of instructions and clauses on the screen behind him and said calmly.

"Do not move around at will, do not disclose your work content at Hogwarts, do not privately research fields involving magic, and it is best to ask the wizards for their opinions first if you have any questions."

"Apart from these situations, you can freely dispose of your monthly salary and flexibly adjust your respective working hours. Some basic benefits are also written above, so I won't repeat them. Now, let's talk about things beyond benefits..."

Douglas cleared his throat, took out a roll of parchment from his arms, and his expression became serious.

"Mr. K. A. Shementyev, we are very interested in the 'ternary' numerical system you proposed. Therefore, in the next six months, your research content will become the highest priority project in this area—we hope to see your implementation plan within this week, as well as the problems that need our help to solve in the implementation process."

"Mr. Andrei Mendanlov, starting tomorrow, house-elves will come to your residence every morning to guide you to the corresponding greenhouses and vegetable gardens to complete a series of tasks. The specific content will be introduced separately later."

"Arkhipovna..."

"Vinogradov..."

Hogwarts was never a charitable institution, and Tianming Group was even less likely to provide relief to Muggles for no reason.

As the Third-Generation Dark Lord, Aeliana and the others had fully demonstrated the sincerity of the magical world in the past six months.

Now, it was finally her turn to issue "main quests" and ask these most outstanding scholars from the non-magical world for some reasonable labor and knowledge feedback—you should know that in order to complete Aeliana's envisioned "A Certain Scientific Hogwarts," they still needed to unlock quite a few prerequisite "black technologies."

And among them, the two technological breakthroughs that Aeliana was most looking forward to were…

————

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Goo ah! Mama Mia, the kidnapper has been defeated again!