Scientific Wizard

Tike was utterly bewildered. He had thought that, with two months of advanced study in Arcane Mathematics and a well-stocked knowledge base, tackling Advanced Arithmetic problems would be a breeze.

But this first problem had him stumped.

If the sequence had stopped at a few hundred or a few thousand, he could have persevered, working his way slowly to an answer. However, the final value was nine hundred and ninety-nine thousand, nine hundred and ninety-nine.

No, there had to be a pattern.

Quickly realizing this, Tike's mind raced back to when Lynn had engaged in an exponential sum game back at Iyeta Harbor. It was a similarly complex calculation, yet through a marvellous exponential formula, Lynn had effortlessly simplified the intricate computation to a level an apprentice could solve with some time.

With this in mind, Tike swiftly grabbed a quill, swiftly jotting down the products of the first ten indices on the paper, then meticulously added them together, analyzing similarities and differences between each value.

"1, 4, 9, 16, 25…"

"5, 14, 30, 76…"

Tike pondered furiously, each number flashing through his mind. He attempted to apply the exponential sum formula learned in his math classes, comparing the derived values to the result, and continuously modifying the formula in search of the correct answer.

No, ten numbers were too few, insufficient to ascertain the pattern…

Tike's quill trembled over the parchment, digits and symbols written, then quickly crossed out, beginning the calculations anew.

Pages upon pages piled up and were discarded, accumulating around his ankles.

Unbeknownst to him, dusk had given way to dawn. Tike had spent the entire afternoon and evening on this problem, eyes bloodshot, yet his spirit heightened. Finally, he stood up, unable to contain his excitement.

"That's it, that's it."

Like a parched wanderer stumbling upon an oasis in the desert, Tike eagerly seized another sheet of paper, meticulously matching the previously derived values with those from the formula.

"They're all correct, my formula is right."

Tike was ecstatic, mimicking Lynn's exponential sum formula, solemnly inscribing one line after another on the paper.

{ Sn = 1/6*[n(n+1)(2n+1)] }

After finishing, Tike sat back down, feeling incredibly content. The sensation of discovering unknown patterns and summarizing them was profoundly captivating.

Eagerly, he glanced at the next problem.

[Five monkeys found a pile of peaches by the seaside, deciding to divide them the next morning. The first monkey, arriving earliest, couldn't split the peaches evenly, so it ate one and divided the rest into five portions, taking its share and leaving. The second monkey, unaware of the first's visit, also ate one peach, divided the remaining, and kept its share. This pattern continued with the third, fourth, and fifth monkeys, each eating one peach, and dividing the remainder into five equal parts. How many peaches were there in total?]

At first glance, Tike sighed in relief; this seemed like a straightforward equation, right?

What jumping frogs, sliding snails… he'd seen those apprentices in Iyeta Harbor solve those types of problems numerous times. All it required was to set a few unknowns and solve the equation.

But as he poised his pen to solve it, Tike abruptly realized something was amiss. Lynn's conditions this time were simply too scarce.

The sole known condition was that these peaches had been divided a total of five times, subtracting one each time, leaving Tike clueless about the quantity divided each time or the peaches left after the last monkey's share.

Tike listed the known conditions, pondered for long, even plucking several strands of hair in frustration, eventually feeling utterly at a loss, a desire rising within him to pummel the question setter.

Could a person even solve this?

Helplessly, Tike had to make a random estimation of the peach quantity, assuming it was the total number, trying to plug it in and slowly seek out the pattern.

This night tormented many a wizard in the same way as Tike. Most wizards stumbled at the first three problems, tearing the paper into pieces in their fury or smashing furniture. However, the true warriors surged forward, relishing this simultaneously painful and delightful sensation.

Meanwhile, while hundreds of wizards cursed and desired to thrash him, Lynn was constructing a new setting within the Magic Web.

The second gathering place was transformed into a library, filled with various arcane mathematics books. Lynn pondered on what bait to use to entice these wizards to linger in the Magic Web for an extended period.

Cracking a formal wizard's mental frequency, thus accessing their computational power, wasn't an easy task.

The "Faceless Gathering" concocted by Herlram had taken a year or two to crack the mental frequency of ten-triple-tier wizards.

Lynn didn't have that luxury of time, hence conceived a way to expedite the process: by keeping these wizards engrossed in solving brain-teasing arcane mathematics problems, depleting their mental energy and hastening the decryption of the genius brain.

Calculus might be a good choice; many of the theories and formulas proposed before had left numerous wizards perplexed. Learning calculus might help them comprehend the derivation process of these formulas and theories.

Of course, the wizards of Greenville weren't entirely clueless about calculus. For instance, their method of approximating pi using the method of inscribed polygons — continually approximating the circumference of a circle — was based on calculus.

Some wizards had even succeeded in deriving an algorithm to calculate the volume of a sphere, akin to the method of Gauss, yielding highly accurate results.

It was a testament that intelligence existed everywhere; however, few wizards were willing to devote themselves seriously to the study of mathematics.

Most preferred elemental or morphological subjects, where learning directly augmented their magical prowess. Only alchemists spent time delving into this esoteric field.

As Lynn contemplated, a sense of impending unease suddenly crept in.

In a flash, Lynn broke free from the Magic Web, eyes snapping open. Nothing stood before him, but an invisible magical barrier enveloped him.

Following that, a faint sound, akin to a blade slicing through cloth, echoed. A peculiar dagger, adorned with intricate runes, materialized, gliding toward his neck.