In any school, exams and studying are timeless, unchanging staples. Hogwarts is no exception. No matter how much the castle has changed this semester, it is ultimately a place for imparting knowledge, and as the end of term approaches, the finality of examinations remains constant.

According to Pythagoras's theory that all things are number, everything is mysteriously connected to numbers. Therefore, analyzing mathematics before studying the world is undoubtedly a clearer and simpler path.

Although there is still considerable debate in academic circles on this point, it is undeniable that using mathematical thinking to sort out and find connections between things is indeed a highly efficient and clever method – for example, exploring the connections between learning materials, time patterns, and final exam questions.

Ailina picked up the messy pile of old parchment test papers on the table and carefully spread them out on the floor of the room in chronological order, arranging them into rows of exam paper dragons according to different subject categories.

These test papers all came from the Room of Requirement across the corridor from the "Piano Room," opposite the "Troll Bashing Barnabas the Barmy" tapestry. This is a secret magical room in Hogwarts Castle that doesn't have a fixed form, but changes according to the needs of the seeker – whether it's a toilet, a storage room, a training room, a love room, a study, a dining room, an armory...

However, for Ailina, she didn't need a room for a specific purpose, but rather to find past Hogwarts students' final exam papers that had been intentionally or unintentionally hidden in the Room of Requirement.

Hiding and destroying final exam papers is a very common behavior in any school.

After all, apart from a very small number of top students, not every young wizard is willing to put their final exam papers in their luggage at the end of the semester and take them home to share with their parents and siblings.

Using the constraints of "place to hide things/place to hide exam papers" to review and filter, Ailina accurately found all the papers she wanted from the garbage-like Room of Requirement to verify her conjecture.

"As expected, I knew it..."

Ailina looked at the past exam papers on the floor and said softly.

According to the definition in the introduction, the parallel mapping of a finite set must have a finite solution, and the order-preserving mapping on a compatible complete lattice has a sign-preserving property. In other words, the seemingly infinite set of test questions will inevitably converge on the finite set of textbook knowledge points as the time axis lengthens, that is, the phenomenon of repeated solutions will occur.

Of course, the above part is the way ordinary Muggles recognize and understand the world.

From the perspective of a wizard who doesn't study (nothing) (learn), that is, wherever the professor emphasizes is the scope of the final exam questions, although... this scope is usually approximately equal to the textbook in the hands of the young wizards.

Long before time-traveling, Ailina had done a lot of research and speculation on Hogwarts' education system.

A large part of this was due to the fact that the textbook replacement speed in basic education in the magical world was incredibly slow. The most obvious example is in the original *Harry Potter and the Half-Blood Prince*, where Harry Potter in 1997 used the same textbook in Potions class as Snape in 1976.

Not only the title of the book, but even some basic errors and cumbersome methods have not been revised or re-edited in these thirty years, which is unimaginable in the non-magical world during the same period.

In addition, the *Standard Book of Spells* series and the *Beginner's Guide to Transfiguration* are all works left by wizards hundreds of years ago, and there has been no change in so many years. Compared with Ailina's "great-grandmother's" *History of Magic*, it is considered a rare textbook with more frequent revisions.

Leaving aside the problems that long-term use of the same set of textbooks may cause in education quality, for the professors at Hogwarts, setting exam questions at the end of each semester is also a headache.

You know, unlike those schools in the non-magical world, Hogwarts has a very serious shortage of human resources in terms of educational resources. Each professor has to face at least 5-7 grades of young wizards, which means that they have to take the time to come up with so many sets of test questions corresponding to the number of grades.

"It's not easy. In Hogwarts' dormitory system, you have to find a way to prevent cheating."

Ailina looked forward from last year's final exam questions and found that the content of each year's test papers was different from the previous year. Obviously, the professors at Hogwarts were not lazy enough to use only one set of test papers to cope with the exams.

This did not surprise Ailina.

After all, at Hogwarts, students of all grades live together in the same dormitory according to their respective houses. If the same set of test questions is used every year, it will be easy for older students to leak questions to younger students at the end of the term.

"Hogwarts has seven grades. If you want to ensure the lowest level of question bank secrecy, then that is to say that students in the school will not encounter repeated final exam papers, that is..."

Ailina muttered to herself thoughtfully, squatting on the ground and carefully checking and placing the discarded test papers from the "garbage dump" according to the year. As everyone knows, the simplest method of mathematical induction is exhaustive method.

"1990, 1989, 1988... 1985, 1984, 1983... This is it!"

Looking at the familiar parchment test paper in front of her, Ailina quickly stood up and looked at the test paper that had just been thrown into the "garbage dump" last year, putting the two test papers that were 8 years apart together.

From the first question to the last question, all the content was exactly the same. If the time was covered, people would even think that this was the test paper answered by the same class of students. However, whether it was the age of the paper or the student's name written at the top of the paper, it clearly verified Ailina's conjecture again.

The test papers for most subjects at Hogwarts use a seven-year cycle question bank. In other words, the test paper system used by the students who graduated last year is exactly the same as the test papers that the young wizards who have just entered the school this year are using.

In this way, the seven school years at Hogwarts form a cycle like an ouroboros.

Except for the relatively special Defense Against the Dark Arts class, the professors in charge of the other main courses don't have to rack their brains to come up with new exam questions every year, and they don't have to worry too much about the problem of exam questions being leaked in advance.

She casually grabbed a piece of French crème brûlée and put it in her mouth, feeling the thin, crisp caramel melting little by little on her tongue. The delicate, smooth pudding, with a hint of milky aroma but not too sweet, touched her teeth coldly. Ailina happily squinted her eyes.

"Tsk, I just didn't expect to accidentally find the dark history of two 'acquaintances'..."

…………

The Room of Requirement is located in the corner corridor on the eighth floor of Hogwarts Castle.

Next to the Headmaster's office, the Gryffindor common room, and the Ravenclaw common room, it should be the work of Rowena Ravenclaw, one of the founders. After all, Gryffindor doesn't seem like such a meticulous person.

Perhaps because of the unique geographical location of the Room of Requirement, most of the students who use this place are young wizards from Gryffindor and Ravenclaw, which is in line with the personalities of the students of the two houses.

The impulsive Gryffindor cubs always have some dangerous items they want to destroy and discard.

And the sensitive Ravenclaw girls also have many secrets they want to hide and not be discovered.

The two test papers in Ailina's hands happen to be one from Ravenclaw and one from Gryffindor. What's even more interesting is that the owners of these two first-year Potions final exam papers happen to be people she "knows."

"Bill Weasley, Cho Chang... I didn't expect that these two good students also failed exams. Hmm, what's more interesting is that Ravenclaw's cross-time confrontation against Gryffindor actually won?"

Ailina is naturally familiar with Cho Chang, Harry Potter's first love interest in the original work, a second-year Ravenclaw upperclassman with Chinese heritage. Although from a personal emotional point of view, she has never been very fond of this Chinese upperclassman.

It's not that Ailina is deliberately targeting Cho Chang, but mainly when she learned that Cho Chang not only couldn't speak Chinese, but also grew up in the British magical world, and her values and personal habits were completely those of a British wizard, except for her heritage, she didn't have many Chinese elements. It was the estrangement caused by the disappointment of her expectations.

But as they studied at the same school, there were still some memorable interactions between the two of them.

For example...

In those Quidditch matches against Ravenclaw House this school year, the silver-white devil soaring in the sky effortlessly made the girls on the entire Ravenclaw team cry, so that in the following weeks, every time Ailina passed the Ravenclaw table, she could make several older girls' eyes turn red instantly.

And Cho Chang, who was also a seeker, could be said to be one of the young wizards who cried the loudest.

Except for her own little wings, Ailina has always been as ruthless as the autumn wind sweeping away fallen leaves towards the cabbages outside. Moreover, facing this upperclassman who had a Chinese heritage but didn't have any familiar feeling, it was difficult for her to have too much closeness.

However, Ailina has a completely different attitude towards Bill Weasley.

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Chapter 1!! Yay!!