Lynn used his magical power as ink to inscribe the formula represented by the grid game, then turned to face the apprentices, who were still in shock from the terrifying exponential growth, and said in a loud voice:
"Why don't you write down this formula?"
Jonie and the others hurriedly opened their pages and, with quill pens in hand, began to copy down the formula they couldn't comprehend. Elok, who stood dazed and stupefied beside them, was the perfect example of what happens when one doesn't study advanced mathematics.
"Professor Lynn..." Elok looked at Lynn, his voice trembling, eyes brimming with tears, on the verge of breaking down.
"Elok, I heard you say earlier that you're good at arithmetic?" Lynn asked.
I am not, I didn't say that, don't spread rumors...
Elok frantically shook his head, wanting to deny it, but Lynn waved his hand dismissively and continued.
"How about this: if you can accurately calculate the total number of copper coins in these thirty-six squares by tomorrow's class, then the bet will be canceled!"
"Of course, you only have one chance to answer!"
Lynn glanced regretfully at the large pile of coins on the table, but he had no intention of taking them.
Firstly, the other party couldn't possibly afford it, and secondly, it would be a bit too terrifying to drain the savings of all the apprentices through a single game.
Who would dare attend his advanced mathematics class in the future?
Elok stared blankly at the floating magical symbols, unable to make sense of the mathematical symbols, doubting whether he could even do basic arithmetic.
Pierce, who had previously envied Elok, now gloated with relief, glad he had hesitated earlier; otherwise, he would have made a fool of himself.
Who would have expected Lynn to suddenly turn and address the crowd again.
"The same goes for all of you!"
"If I remember correctly, Elok told you when borrowing money that 'if he could fill all the squares, he would repay double.'"
"Unfortunately, Elok didn't achieve that, so the promise is invalid. Not only will you not receive more gold coins, but the money you put down will stay with me!" Lynn picked up a few gold and silver coins from the table, speaking with amusement.
Upon hearing this, the classroom filled with wails, and Pierce and the others glared angrily at Elok, realizing he had tricked them.
Lynn raised his voice and pointed to the summation formula floating in the air. "There's a simple way to calculate sums involving exponential operations. If it were me, knowing the last number, I could calculate the total sum in ten seconds!"
"Your homework is to find the pattern and solve the formula I wrote down! Once you have the answer, you can come and retrieve your money."
Lynn surveyed the students, who were now furiously calculating with their quills, and nodded in satisfaction. Only through such personal experiences could they truly appreciate the charm of advanced mathematics!
Moreover, this game also allowed him to gauge the students' mathematical proficiency.
Judging by Elok's performance, they had already mastered the most basic arithmetic rules. Next time, he might start teaching slightly more challenging formulas!
The two-hour advanced mathematics class soon ended.
Although they didn't learn any new magic, the students' enthusiasm remained high, driven by the thought of retrieving their deposits. They couldn't wait to share their classroom experiences with others.
In just one day, Professor Lynn's grid game had become widely known.
To allow more people to experience the allure of exponential growth, Lynn moved the grid to the front of Iyetta Academy, expanding it to seven rows and seven columns, totaling forty-nine squares. He also set up a sign, rewriting the rules of the bet.
If anyone could fill the squares with the corresponding copper coins, he would give away the alchemy recipe used to destroy Harbor Town.
Yes, starting with just one copper coin and doubling the amount for each subsequent square would be enough. After filling the squares, they could even take the money back—he wouldn't keep a single coin!
This offer intrigued not only the wizard apprentices but also a few of the academy's professors.
Could there really be such a good deal?
This alchemy recipe, though requiring extensive preparation to unleash its full power, could prove invaluable in certain situations.
Its power was said to rival that of fifth- or even sixth-circle magic!
In the evening, when most students had left the school or returned to their dormitories, Professor Kevin of Shapeshifting sneaked over to the combined tables to study the grid's rules.
Each square's number had to be double the previous one?
Kevin stroked his chin, pondering, when a familiar voice came from behind him.
"Don't bother calculating. It's absolutely impossible to fill those squares!"
"Do you know how much I have in savings, Professor Philip?" Kevin asked, slightly annoyed. After all, he knew many friends who could lend him money. Since the coins would only be used to fill the squares and could be taken back afterward, he could always borrow a little more.
Could it really be that no amount of wealth in Iyetta Harbor could fill these squares, as the rumors suggested?
Kevin found this notion absurd.
"Do you know how many copper coins are needed for the last square in the seven-by-seven grid?" Philip said with a hint of exasperation. "It's two hundred and eighty-one trillion!"
"Two hundred and eighty-one million copper coins... That's quite a lot..." Kevin said, somewhat surprised, but after a pause, he suddenly realized Philip had said... trillion?
"Wait, are you sure you didn't make a mistake?" Kevin was dumbfounded.
This was the first time he had heard of a unit like trillion.
"Of course not! I personally verified it..." Philip replied irritably. He had been just as shocked when he first heard about it from the students, and it took him nine sheets of paper to complete the calculation because the numbers were simply too long.
Kevin silently began to calculate. Although it was just simple multiplication, the numbers grew increasingly vast with each step, and mental arithmetic soon became insufficient, forcing him to rely on rough estimates.
Based on the pattern from the first few squares, every three to four squares increased the sum by about ten times.
With seventy-nine squares in total, that meant... at least a million billion times!
Kevin gasped in shock. Such growth was terrifying!
Forget Iyetta Harbor—no amount of money from the entire continent could fill those squares!
Fortunately, he had chosen a time when no one was around to attempt this, or he would have made a fool of himself in front of the students.
Kevin breathed a sigh of relief, then noticed that in addition to the rows of squares, the table also bore some strange symbols.
Sn=a1{q^(n-1)}/(q-1)
"What are these symbols? Some kind of magical notation?" Kevin asked, puzzled.
"This seems to be... a geometric series summation formula? I think that's what it's called," Philip replied uncertainly. "Professor Lynn said that as long as you know the final number, you can calculate the total sum of the copper coins in these squares within ten seconds."
"Can such complex calculations really be done in ten seconds?" Kevin frowned.
"Master Heralam seems to have already deciphered the meaning of this advanced mathematics formula!" Philip remarked with admiration. "And in just one afternoon—truly worthy of the title of Grand Sorcerer."
"Did the master tell you what these mathematical symbols mean?" Kevin asked eagerly, finding this advanced mathematics increasingly fascinating after the exponential calculation.
"No, he didn't..." Philip shook his head regretfully. "Master Heralam only asked me to add a small reward to this game. Whoever deciphers the formula's meaning first will receive twenty magic gold coins!"
As he spoke, Philip took out the coins and used magic to affix them to the table.
...
At this moment, the subject of everyone's conversation, the new advanced mathematics professor, Lynn, was leisurely sitting on the sofa in his room, eating the dinner delivered by a fairy while reading the borrowed books *Fundamental Principles of Magic* and *Analysis of Elemental Magic* from the academy's library.
Although life as a professor at Iyetta Academy was incredibly comfortable, with no sense of danger, Lynn refused to become complacent.
Everything in the wizard's land was unfamiliar to him, and if trouble arose, his only reliable asset would be his own strength.
Additionally, as a professor, he needed to thoroughly study some basic magical knowledge.
However, the two books written by legendary wizards were giving Lynn a headache, filled with terms like "Serlu," "Enzeci," and "Koze," which he couldn't quite grasp. He had to painstakingly verify each term based on the descriptions provided in the book.
After three hours of analysis, combining his limited understanding of magic since his arrival, Lynn finally managed to understand the first half of the book.
First, his previous speculation was correct: wizards indeed cast spells by manipulating, influencing, and mimicking elements.
However, a wizard's ability was quite limited. Not all elements could be controlled, and the precision was insufficient, at least not to the extent of shattering molecules or atoms—only simple combinations were possible.
"Hydrogen, oxygen, nitrogen, phosphorus..." Lynn silently considered the four elements he had previously manipulated, forming several hypotheses in his mind.
The first hypothesis was that the difficulty of element manipulation might correlate with the periodic table, with wizards able to control only the short-period elements in the first three columns and not the long-period elements in the fourth through seventh columns.
The second was that the manipulation might be limited by atomic size, with wizards unable to touch larger atoms.