He'd give a new definition, and then follow it with an unsolved problem built on that very definition.
What Dark was doing was, without question, sheer hooliganism.
But he didn't feel the least bit troubled by it.
Once Dark had breezily finished explaining the definition of "exponentiation," the two elderly scholars exchanged a glance, then committed the definition firmly to memory.
Definitions that simplified calculation like this weren't unheard of, but judging from Dark's manner, this seemed to be one of the foundational definitions of an entire computational system.
"A definition we've never seen before, and apparently part of a whole system at that — could this be some unique method of calculation taught at St. Marian's Academy?"
Even as Aaron Rhodes turned the thought over rapidly in his mind, he couldn't help asking, "I think I roughly understand your problem now, but what's the point of studying something like this?"
"The point?" Dark leaned back, spinning the Magic Guide Scribe between his fingers, and said with blunt frankness, "To give you a hard time, obviously!"
Aaron Rhodes's expression froze for a moment.
Dark seemed to sense this wasn't quite the right thing to say, so he added, "Or how about we call it a test instead?"
...
Whether it was harassment or a test hardly mattered — since they were the ones asking for a favor, they had no choice but to bear it.
After Aaron Rhodes and Aviva Julius had written down Dark's first question, they asked, "What's the second question?"
The corner of Dark's mouth curled up. "This second question is also a half-finished proof. I'd like the two of you to help me verify it."
"How so?" Rhodes straightened, alert.
Dark said, "We all know that an even number is an integer divisible by two. And a prime number is a number greater than one that cannot be divided evenly by any natural number other than one and itself."
"So then — can every even number no smaller than four be written as the sum of two primes? For instance, four equals two plus two; six equals three plus three; eight equals three plus five..."
Aaron Rhodes couldn't help but frown. "The answer to that should be yes."
Dark asked, "Then how do you prove it?"
"This..." Aaron Rhodes glanced over at Aviva Julius beside him, but she too had fallen silent.
The corner of Dark's mouth lifted. "Well then, that settles it. Once you've worked out the answer, write up the proof and bring it to the Duke's estate. The moment I receive it, I'll have someone release Ignaz Cooper."
Assuming, of course, the man was still alive.
...
Truth be told, Dark had no idea what state Ignaz Cooper was currently in — otherwise he'd have found some excuse to toss him out long ago.
Keeping him around was just wasting perfectly good food, after all.
Having said his piece, Dark rose and returned to the dining table, settling in to wait leisurely for the proper lunch.
Aaron Rhodes and Aviva Julius, meanwhile, lingered only a moment longer before hurrying off.
They needed a quiet place to work out the problem!
The two puzzles Dark had posed were, in fact, both proof problems.
The first, since it introduced the concept of "exponentiation" for the very first time, left them unable to grasp what significance the proof might actually hold.
But the second one... if they could prove that conjecture true, it would undeniably carry tremendous significance.
Even setting aside the matter of rescuing Ignaz Cooper, they would have pursued the problem purely for its own sake.
Only now, there was rather more urgency to it.
...
"Finally got rid of them."
Dark glanced at the two retreating backs and shook his head.
Just then, Trina suddenly drew a hand across her throat in a slicing motion and asked, "Young Master, why not just let me handle it directly?"
Dark took a sip of tea and said gently, "Trina, times have changed. In war, we make people submit through force. In peace, we must learn to make them submit through reason. Look — even those two Elders of the Church of Knowledge were perfectly reasonable, weren't they?"
Trina fell silent for a moment before asking, "Then what should be done about Ignaz Cooper?"
Dark smiled faintly. "Go check on him. If he's still alive, lock him up for another two months. Once I go back to school, let him go."
Something clicked in Trina's mind. "Understood."
"Good, as long as you understand."
Dark drained the last of his tea and turned his gaze toward the window.
...
Outside the window, the Eugenie Trade Circle remained as bustling as ever, showing no sign of slowing down just because lunchtime had arrived.
The hurrying crowds were like gears in some vast machine, turning ceaselessly, pushing the whole era forward.
...
Two in the afternoon.
Once Dark had eaten and drunk his fill, he stayed at the tavern to hear the rest of an adventurer's tale, listened to a bard play a short tune, watched a scuffle break out downstairs between adventurers over some argument, and only then climbed back into the carriage, which set off toward the most prosperous district of the royal capital.
It was a place even minor nobles found difficult to enter, a place where even the most reckless of noble scions dared not cause trouble.
There, one might casually run into a person of towering rank — a powerful minister, a nobleman with deep-rooted connections — and even members of the royal family passed through it often.
Though the current king had only three children — First Prince Charles, Eldest Princess Eliza, and two young princesses — the royal bloodline was hardly limited to just them.
Born to nobility of the highest order, they would never run wild through the commoners' district the way a certain Duke's son did without a second thought.
Their very existence represented the dignity of the royal house itself.
So their lives were generally confined to the noble district — places like the area around the Star Tower.
The place they frequented most, though, was the garden just ahead — known as the "Royal Courtyard," the Flower Garden.
And Dark's destination on this outing was a high-class establishment located within the Flower Garden — "Soul-Stirring"!
Ever since receiving that VIP pass to "Soul-Stirring" on his birthday, Dark had often thought of visiting, but it wasn't until today that the chance finally came.
It wasn't that he had any particular interest in the luxury goods or premium services "Soul-Stirring" offered. It was more... how to put it... that itch of holding a ticket you never get around to using.
He figured he ought to at least go take a look, right?
So here he finally was.
...
The three carriages passed through without a hitch.
No matter how prestigious the Flower Garden was, it still couldn't outrank the Duke's estate.
The gatekeeper on duty, after confirming a glance with the Dragon-taming Guards, quickly stepped aside.
Though the small heads that kept poking out of the windows of the two rear carriages gave them pause, in the end they didn't dare press the matter.
One of the gatekeepers, however, mounted a white horse and, under the pretext of guiding the way, fell in alongside the lead carriage.
Not long after, the carriages came to a stop in the garden fronting the entrance of "Soul-Stirring."
Dark climbed down from the carriage and tilted his head back slightly to take in the sight.
Standing before him was a castle of ancient design, with no text of any kind posted anywhere identifying it as belonging to a place of this particular name.
Had he not known beforehand, he never would have guessed this was a place of commerce.
Most of the men and women passing in and out through the castle gates had attendants trailing at their sides.
"So this is 'Soul-Stirring'?"
Diana leapt down from the carriage, her face bright with curiosity as she studied the castle.
"Should be."
Dark laughed. "Speaking of which, this is my first time here too. I wonder if it'll live up to its name and leave me soul-stirred."
Aurora climbed down right after, asking curiously, "I heard even a single glass of water here costs a hundred Saint Coins. Is that true?"
Dark blinked. "Is it really that expensive? Maybe we should've bought drinks outside and brought them in."
"I..." Aurora instinctively lowered her head, fidgeting with the ruffled hem of her dress, her voice barely above a whisper. "I was just saying."
Dark laughed heartily, then turned to the Magic Guide Spirits climbing down one after another and said, "No running off once we're inside, understood?"
"Got it." The Vampire Young Lady came bouncing over, her eyes full of longing. "When will I get a castle like this of my own?"
Dark glanced at her and said breezily, "Once you become a Magic Guide Master, you'll earn plenty of money for it."
The Vampire Young Lady's eyes lit up. "So when will I get to become a Magic Guide Master?"
Watching her innocent expression, Dark couldn't help but laugh. "Six years, maybe."
"Six years? Isn't that a bit too long?" The Vampire Young Lady's lips immediately puffed out, her just-brightened spirits sinking right back down.
But she quickly shrugged off the disappointment and chirped happily again, "I'm Dark's Magic Guide Spirit, so whatever Dark has, I have too! So, Dark, do we have a castle?"
Dark thought about it and said, "We do have one, actually, but it's not here in the capital. Our Demon family moved into the royal capital later on — back on our original lands there's a castle, currently being looked after by an uncle of mine, I believe."
The Vampire Young Lady's eyes shone even brighter. "Then when can we go see it? Every vampire princess in the storybooks has a castle — I can't be the exception."
Dark's gaze drifted off toward the distance. "Honestly, I've never even been there myself. Maybe next year we can go take a look. But this year, there's just not enough time left."
"Next year, huh..." The Vampire Young Lady's face filled with anticipation.
With that, Dark took the lead and started walking toward the castle gates.
The three maids and the whole group of Magic Guide Spirits hurried to follow.
Such a large procession moving forward together naturally drew plenty of attention.
Among the rows of attendants lined up on either side of the castle entrance, a poised-looking woman in her mid-twenties stepped briskly forward to greet them.
Though this was everyone's first visit here, the Duke's carriage alone served as the best possible pass.
Even if Dark hadn't been carrying that top-tier membership pass, they would still have received the warmest welcome — at most, a new pass would simply be drawn up on the spot.
Not wanting to put them through the trouble, though, Dark simply pulled out his membership pass right away and gave it a little wave.
The attendant let out a visible sigh of relief and said warmly, "Is this the young lord's first visit here?"
Dark answered plainly, "It is my first time. Is there anything in particular we should know?"
The attendant said, "You may call me Jessica. If it pleases you, I'll accompany the young lord and explain the facilities and services of the establishment in detail."
"Miss Jessica, my name is Dark." Dark offered her a gentlemanly smile and extended his hand.
Jessica bowed slightly, the lace at her collar setting off the striking paleness and softness of her skin.
She shook Dark's hand with the utmost respect before saying, "Young Lord Dark's membership is of the highest tier — not only free of any restrictions on access, but also carrying a monthly allowance of one million Saint Coins, free of charge."
"That's ten thousand glasses of water, then?" Dark said, amused.
The corner of Jessica's mouth twitched, her poised composure straining to hold.
Dark smiled faintly. "No need to stand on ceremony. We're here to enjoy ourselves, not to inspect the place. Lead the way."
Jessica nodded quickly. "Of course, young lord!"
...
With that, the group followed Jessica's lead into the castle of "Soul-Stirring."
Though the castle's exterior was ancient in style, its interior décor was thoroughly modern, blending old-world tradition with new-age trends so seamlessly that nothing felt out of place.
The nobles and noblewomen strolling through the corridors carried themselves with impeccable manners.
From time to time, some noble who recognized Dark would step forward to offer greetings, but a simple wave from Dark was enough to send them on their way.
He had no interest in expanding his social circle, and even less interest in the hollow pleasantries nobles liked to exchange with one another.
Jessica proved remarkably skilled at her job.
Under her guidance, Dark and the others thoroughly enjoyed themselves.
The services at "Soul-Stirring" were genuinely comfortable, and the luxury goods on display were every bit as impressive in quality as they were in appearance.
Dark picked out a small gift for everyone present, human and Magic Guide Spirit alike — sharing the goodwill equally all around.
The two maids, overwhelmed by the unexpected favor, wore smiles the entire time.
For them, the value of the gift itself was only part of it — what mattered most was that it came from the young master, which would surely make them the envy of every other maid.
About an hour later, after wandering through the establishment at a leisurely pace, the group finally arrived at the heart of "Soul-Stirring."
The ring-shaped corridor encircling a central arena was remarkably spacious, lined everywhere with high-end sofas and amenities.
Staff moved among the various facilities, attending to every guest's needs with the utmost care.
Some lounged idly on sofas, enjoying professional massages.
Some sat quietly reading while elegant music played in the background.
Some gathered in animated conversation around tables.
...
The establishment used a special magic-guide apparatus to divide the space into a series of seamless sections, allowing every guest to enjoy a private area within an otherwise open space.
Once Dark had walked in, Jessica explained, "This is generally considered the most popular gathering spot among our guests. The arena at the center is often used for exhibition matches — swordsmanship, horsemanship, or Magic Guide duels."
"An exhibition match for Magic Guide duels?" Dark's interest suddenly perked up. "Is there one today?"
Jessica answered without hesitation, "There's one tonight — an exhibition match between a renowned duelist known as the 'Butterfly Princess' and one of the establishment's own professional duelists."
Dark said, "Inviting a well-known Magic Guide duelist can't come cheap, I'd imagine."
A trace of envy crossed Jessica's face. "In the millions."
"Just millions? I would've guessed at least tens of millions... hm?"
Just as Dark was speaking, he suddenly noticed a somewhat familiar face among a crowd of onlookers watching an equestrian performance in the arena.
"Isn't that Senior Jeffrey?"
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