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Chapter 14 - The Square of Two

At that moment.

Professor McGonagall stepped forward a few paces, holding a piece of parchment, shielding Dawn from the intense gaze of the sun.

"When I call your name, you will put on the hat, sit on the stool, and wait to be sorted."

She glanced down and called out, "Hannah Abbott!"

A rosy-cheeked girl with two golden braids stumbled out from the line.

Dawn recognized her—she was the daughter of the Leaky Cauldron's owner. He had seen her a few times when visiting the bar, though they had never spoken.

After a brief pause, the Sorting Hat shouted, "Hufflepuff!"

The table on the left immediately burst into cheers and applause for Hannah. Blushing furiously, she jogged over to join them.

"Susan Bones!" Professor McGonagall called the next name.

The sorting proceeded in alphabetical order by surname. Richter, beginning with R, meant that Dawn would be sorted toward the end.

Compared to him, Abel Davis went up fairly early.

The hat barely hesitated before sorting him into Hufflepuff as well.

After that, Hermione was sorted into Gryffindor, just as in the original story.

Harry too. The only difference was that, after Harry's sorting, the hall erupted into cheers so loud it seemed as if the roof might cave in.

Dawn saw—sitting high up, Albus Dumbledore, with his long silver beard, smiled warmly, his once-straight posture relaxing ever so slightly.

After Harry, a few more students were sorted.

Then it was Aemon Carter's turn.

Unexpectedly—

After wearing the hat for quite some time, Aemon suddenly shouted, face flushed with frustration, "I want to go to Ravenclaw!"

The little witches and wizards in the hall were startled by his loud outburst, and the lively atmosphere briefly froze.

"Oh, are you really sure?" the Sorting Hat murmured in Aemon's mind. "I feel you might achieve greater things in Gryffindor... very well, very well, I understand... Ravenclaw!"

This time the applause came a little late.

But once they realized, the Ravenclaw table made up for it with even more enthusiastic cheers. Such a determined choice immediately won Aemon a lot of goodwill among Ravenclaw.

Aemon took off the hat, staggered slightly as he stood, glanced stiffly at Dawn, and then hurried to the Ravenclaw table.

The next few students sorted normally.

The process went quickly, without any more incidents.

Among them, however, Neville Longbottom caught Dawn's attention. The boy who had lost his toad on the train looked anxious and rushed. He even tripped and fell while walking up.

But none of that mattered.

What mattered was that the magic pattern within Neville's body looked extremely strange, very different from the other young wizards.

Dawn narrowed his eyes.

But before he could study it more carefully— Neville was sorted into Gryffindor and disappeared into the thick cloud of magical auras, making it impossible to tell anything further.

Time passed quickly.

The floating candles burned brightly, reflecting off the starry sky displayed on the enchanted ceiling.

Professor McGonagall reached the name that had particularly caught her attention, paused briefly, and called out loudly:

"Dawn Richter!"

Hearing his name, Dawn stepped out from the thinning group of students.

He gave Professor McGonagall a polite nod, used his clumsy Occlumency to seal away any secrets he did not want exposed, and then placed the Sorting Hat on his head.

"Hey, you're Dawn Richter, aren't you?"

The hat had barely touched his head when it started muttering in his mind:

"Did you know? What you said really upset that Aemon boy! He was so determined to go to Ravenclaw! Yet he could have achieved greater things in Gryffindor!"

Hearing this, Dawn raised an eyebrow. "You think he's brave?"

"Oh, absolutely! I have no doubt about it. Deep down, he harbors great courage!"

The Sorting Hat sounded regretful, its crooked tip drooping slightly, but it quickly perked up again.

"Now, let's see... oh, eager to learn! But you don't just crave knowledge—you also thirst for strength... hey, how do you feel about Slytherin?"

"I'd rather not," Dawn frowned and refused.

He had no particular prejudice against the four Houses themselves, but the baggage some of them carried was something he preferred to avoid.

Take Slytherin, for example, where the pureblood atmosphere often led to the exclusion and targeting of Muggle-born wizards.

That alone would have been tolerable, but what was worse, excelling in Slytherin would also bring about Dumbledore's scrutiny and suspicion.

Dawn had no interest in wasting energy on anything unrelated to his research.

"Alright, alright, I'll respect your wish. Then, let's go with Raven—"

"Wait a minute!"

Dawn interrupted the Sorting Hat before it could call out "Ravenclaw." "Sorry, but may I ask you a question first?"

"A question? That's a first!" the Sorting Hat said, surprised. After thinking for a moment, it agreed, "Alright, as long as it doesn't take too much time."

"Then, Mr. Sorting Hat..."

Dawn tilted his eyes up toward the trembling brim of the hat. "Do you consider yourself an alchemical object?"

"Oh, what a strange question! Of course I'm an alchemical object! What else could I be?"

The Sorting Hat chuckled, shaking its whole body with laughter.

"But you possess intelligence!"

Dawn pointed out, "Don't you find that strange? Or rather, have you ever seen another alchemical object like yourself?"

"Intelligence? Oh, child! If you're amazed just because I can talk to you, that only shows you don't know enough about the wizarding world."

The Sorting Hat laughed heartily in his mind. "It's nothing unusual. In this castle, you'll even see ghosts and paintings that can speak to you!"

Dawn refuted, "No, it's not the same."

He tapped his fingers lightly against his thigh, thinking how best to explain. "Hmm... right, do you know anything about mathematics?"

"You mean that Muggle subject? Sorry, I haven't studied it, but I can do basic addition and subtraction!"

"So that means you don't know what a square is?"

"What?" the Sorting Hat didn't catch that.

"Square."

Dawn repeated, explaining, "It's a mathematical concept. For example, the square of 2 is two times two. The square of 3 is three times three."

"New knowledge... but why are you telling me this?" the Sorting Hat asked curiously.

Dawn didn't explain but continued in his mind, "Then, can you tell me what the square of 2 is?"

The Sorting Hat fell silent for a second, then grumbled loudly, "Of course it's 4! Hey, kid! Do you think I'm an idiot?"

It grumbled in annoyance.

"You see, that's the difference between you and a ghost."

Dawn shrugged.

"Ghosts have intelligence, but it's based on the memories from when they were alive. For knowledge they didn't learn when they were alive, they can memorize it but not understand it."

He paused for a moment, then continued:

"For example, if you asked a ghost the same question, even if they had memorized that the square of 2 is two times two, and that two times two equals four—"

"If you asked them directly what the square of 2 was, they still wouldn't be able to answer."

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