A magical journey that begins in Azkaban

Bathsheda stared at the two of them with suspicion. When she saw that Hermione just opened her school robe to reveal the clothes underneath, she felt a little more at ease.

But she still remained vigilant. After all, the third-grade wizards had entered a new stage.

At Hogwarts, third year is considered a watershed. After two years of magic training, the little wizards have been able to enter Hogsmeade Village and explore the social life of the wizarding world.

They began to become independent, and the identities of wizards and witches became clearer. At this age, they begin to become curious about each other, and dating becomes a regular occurrence. The cafe in Hogsmeade village is full of young people falling in love.

However, Bathsheda's view of wizards remains the same. In her eyes, wizards always had bad motives. She snorted at Rogge, expressing her distrust of the wizard.

In her mind, wizards are the best deceivers. They use sweet words to confuse witches and make them fall into the whirlpool of emotions. Bathsheda hoped that Hermione would be vigilant and not be fooled.

Roger felt Professor Bass's doubtful and displeased eyes, and somewhat understood Harry's feelings towards Snape.

Then, he heard the professor's instruction: "Go and write the runes from 0 to 9."

"Okay." Roger nodded, quickly moved to the blackboard, and began to draw on the blackboard skillfully.

"The invisible beast represents 0, which itself means invisible. The unicorn has a horn, so it represents 1." He explained while drawing, and the runes on the blackboard came to life.

"By analogy, the next is the horned beast with two horns and the three-headed rune snake. Then there is the evil bird, the five-legged monster, the sandmanro, the mamai, the acromantula, and the hydra. .”

"Professor, the drawing is done." Rogge clapped his hands, and the 10 runes on the blackboard were flowing with silver light.

Professor Basi stared at Rogge, and nodded after a long time: "The drawing is very good, and the corresponding words are marked. Five points for Slytherin."

Although she gave Rogge extra points, she didn't mean to let go of the little wizard who didn't listen carefully. So she asked a more complicated question.

"How are each family of runes formed?" the professor asked, trying to expose the fact that he was not paying attention to the lecture.

Rogge recalled carefully. Professor Basi had just talked about this knowledge point. He answered confidently: "There are 24 kinds of runes, and the family is the smallest unit that uses it. And each family is a A structure of three rows and eight columns.”

"So, how many different families can it create?" Professor Ba Si asked immediately, without giving Rogge time to relax.

This question made Rogge fall into silence and began to seriously think about the number of permutations and combinations. Seeing his thoughtful expression, the professor couldn't help but raise the corners of his mouth slightly, showing a proud smile.

The little wizards below also picked up their quills and wrote and drew in their notebooks, trying to calculate the answer.

They fill in 1 rune in the first slot, then the second slot. However, there are so many that even the first row is difficult to count. The other little wizards all looked confused and helpless, and quickly gave up their calculations.

Rogge understood that to calculate the number of rune families, relying on the exhaustive method would not work. If you think about it for a moment, you will know that it would take a lifetime to list this order of magnitude. To get the final answer, clever mathematical methods must be used.

He viewed the rune family as a 3x8 matrix. Well, this matrix has exactly 24 positions, and there is a mysterious relationship with the types of runes.

Assuming that each position in the matrix can be filled with runes at will, it means that there are 24 possibilities for each position.

Three seconds later, when the other little wizards were still talking about it and not knowing how to calculate it, Rogge turned to the blackboard with confidence and wrote the answer: 24^24.

The small number 24 falls on the upper right side of the large number 24. This counting method is read in the Muggle world as: 24 to the 24th power.

"Two 24, one big and one small?" Professor Basi was confused. She seemed to have seen this counting form on a certain manuscript.

The students looked at the blackboard in confusion, full of doubts and did not understand the meaning of power at all. As a result, everyone started talking in low voices.

"Roger isn't lying to the professor, is he?" Someone mocked maliciously.

"I think it's possible. You see, the position of the clan and the number of runes are the same. Could it be that by putting two 24s together, he can get away with it?"

"It's definitely not that simple. Roger won't write randomly."

"Yes, Rogge is so powerful, how could he make it up randomly? The professor will also let him explain."

Amid the noisy discussion, Professor Ba Si knocked on the table to calm everyone down. She gave Roger a look, indicating for explanation.

Rogge looked calm, pointed to the answer on the blackboard and said: "This is a counting method, which means the number of times a number is multiplied by itself."

Professor Ba Si's eyes lit up and asked: "Is it pronounced as 24 to the 24th power?"

Before Rogge could answer, the professor began to explain incessantly: "This form is recorded in the "Elements of Geometry", a manuscript about arithmetic divination in ancient Greece. You may not understand what Rogge means, it can be written …”

As the professor spoke, he began to write 24 on the blackboard, and he stopped after writing a full 24 words.

"So long!"

"You can actually use 2 numbers to represent such a large number. This counting method is so clever!"

Professor Basi knocked on the blackboard and said with unfinished meaning: "This form of counting has a long history and can be traced back to the ancient Egyptian "Reed Papyrus" and the ancient Babylonian "Abelian Table".

"These are mainly courses on arithmetic divination. If you take it as an elective, you can experience the personality of numbers and the magic of destiny from the Pythagoreans in ancient Greece."

"It turns out it's a matter of arithmetic and divination. I don't think I chose it."

"Don't choose. Arithmetic divination is the most terrifying course in the world. You can't learn it at all. How can anyone use numbers to calculate fate!"

"Professor, are the results of Roger's calculation correct?" Hermione asked curiously, becoming very interested in the arithmetic and divination class that had not yet started.

"Theoretically there are so many possibilities, but in reality..." Professor Ba Si signaled that Rogge could go down. She pointed at the string of numbers and explained: "In practical applications, the family composed of runes must be stable."

"For example, if I fill the entire family with an invisible beast represented by 0, theoretically the object carrying it should disappear completely. But according to the records in the ancient wizard manuscripts, if there are no other runes to adjust the balance, after three consecutive burning After 0, the object will be damaged..."

Professor Ba Si began to introduce knowledge enthusiastically and non-stop again, eager to teach everyone the skills of seal carving runes. She held up a clay tablet and demonstrated how ancient wizards used runes to make it as hard as iron.

"It's a pity that ancient magic has disappeared, and the runes have lost their vitality and can only become symbols on paper."

Her first class didn't end until lunch time.

"Oh, five points for Slytherin." Professor Bass pointed at Roger's answer on the blackboard and added before everyone left the classroom.

When get out of class was over, Hermione hurriedly left the classroom without even having time to say hello to Roger. Roger looked at her disappearing back, curiously wondering when he would meet Hermione while eating.

Unfortunately, he didn't see the little witch in the auditorium at all. Daphne told him as Hermione hurried away with her lunch.

"Twelve courses, hiss, it's scary to think about it. Miss Granger, it's so scary!"

Hearing Daphne's sigh, Roger also sighed sympathetically.

Hermione has amazing talents, but unfortunately her family cannot provide her with much help. Everything she gained in the magical world had to be earned through hard work.

In comparison, children from pure-blood families are much happier. You don’t have to force yourself to study hard. As long as your grades are passable and you graduate successfully, your family will arrange everything for them.

For example, Draco, whether he wanted to become a professional Quidditch player or work in the Ministry of Magic, it was all a matter of one sentence. Lucius said hello briefly, and the rest fell into place immediately.

When they work in certain organizations, it is not their own luck, but the other party's honor.

"What should we do if our club recruits new members?" Daphne asked, "Hermione is so busy, how about I come?"

"I'll talk to Hermione during the Care of Magical Creatures class. Then we can invite Theodore and the others to show everyone our club's special products to increase their appeal."

"I hope Theodore has made the weird soda, otherwise he will definitely scare everyone away." The two looked at each other and laughed in unison.

Roger sipped his juice, Hagrid's Magical Creatures lesson must have been a bad one. The school didn't even have a teaching assistant. It was really arrogant.