7.1

Yora, Asahi, Noah, Mica, and Rachel headed to the library to sketch up a study program. The building was finished with auburn wood, but it didn't look old. Black, thick carpets covered the floor, and bookshelves were arranged with about 2 meters of distance between each shelf. The grand, frosted windows let in enough light to make the atmosphere comfortable. The central aisle, about 7 meters wide, had circular tables appearing every 15 or so steps, and each one was surrounded by 4 plump, red chairs. The library was lavish, to say the least.

"This school is insane," Noah said, taken aback by the beauty of the building.

"Yeah, and I can feel how thick the carpet is," Rachel replied.

"You could do cartwheels in here!" Mica exclaimed.

"I can't wait to sneak into here at night and scare a few over-studious people"

Asahi looked at Yora as if he were a child.

Asahi fell behind the group after his eye caught a few interesting-looking books at the back of the library. High fantasy, low fantasy, psychological, thriller - there were enough genres to fill any creative with delight. After a while had passed, and he'd neared the climax of the plot of "Wandering Soul", he heard a pile of books fall on the floor in the isle next to him. Annoyed, he peered through a gap in the shelf. On the other side, he saw a girl in an unfortunate position, sprawled over some chemistry books. She had blonde, wavy hair that touched her collarbones, with frosted blue highlights which contrasted with her light grey eyes. She was wearing her uniform in a rather provocative way, with a few buttons undone and her skirt showing an eyeful of skin. Her nose darted left and right as she looked around her, hoping that no one had made note of her presence. Her embarrassment was evident, so Asahi decided not to interlude.

"She doesn't seem the sort to be reading a book like that: that's second-year university quantum chemistry..." He whispered to himself.

He forgot about her and dove right back into his book, eagerly gripping the pages and turning them as he completed them. After he completed his book, he looked into the central aisle and saw the rest of his group playing an intense game of chess.

"Queen D1 to A4, Checkmate," Noah said, casually.

Rachel's eyes were fixed to a point, as she pondered the move.

"Noah... that was brilliant," She admitted, in defeat.

"Oh damn, I have no idea what happened, but that looked cool!" Micah said, rather excitedly.

"Yeah, I didn't even see that move: there was so much going on in the other corner," Yora remarked.

Asahi decided not to disturb the merrymaking with his presence and carried on looking around the hall. Fortunately, he'd found yet another fantasy to dig his claws into.

As he reached halfway through his book, he heard expensive heels inject into the carpet and slam onto the wooden floors underneath, in a fast, rhythmic beat... no, it was 3 pairs of heels clicking in unison.

"What the fuck are you reading, huh?"

The swaying of bright blue hair struck de ja vu into our protagonist. She seemed to have a different aura about her this time, in contrast to her demeanor when she was sprawled across the floor. Her hands sticking by her hips gave forth a tense, domineering presence. He hadn't quite realised how slender her eyes were, which enhanced her predatory glare.

""The guy who leapt through time", it sounds so fucking bad!" she taunted.

"He probably has no friends, I mean, look at how he's shivering!" the girl behind her remarked.

"You can tell he sits at home probably watching TV all day,"

"It's that obvious?" he replied.

"Shut the fuck up, idiot. People who try to escape reality for no reason disgust me." She snapped in return.

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She seemed to stand by her words, but he felt as though her words were passing right past him. Perhaps he felt no emotional pain when an attractive woman cursed him? He realised that wasn't it, but he wasted no more energy on the thought. As the three girls headed back, he noticed that their bags had the sticker labeled "1F". He'd heard rumours that this class was full of all the talentless individuals. He didn't believe these rumours, though, considering Ari, Yora, Evelyn, and Rachel were in the 2nd lowest class- but he noted to try his best not to come in contact with her again.

7.2

Thus, the day of the examinations rolled by. For the sake of his 4 teammates, Asahi studied hard for his examinations, covering all of psychology, chemistry, and mathematics (the subjects he had opted for when he got accepted into the school). He was an intelligent individual, so he had no problem understanding the material, but he felt a little pressure walking down the hall to his classroom as he heard the whole student body stressing out.

"My mum said she'd disown me if I didn't get above 90!"

"That's not even that bad, I have to get 100 in all of them!"

"Guys, Guys, I heard the exams at this school are as hard as the Putnam!"

The overreacting teenagers' claims become more and more out of touch with reality as the stress consumed them. Asahi plugged in his headphones and walked into the classroom, his heart pulsing a little.

Inside the classroom, everyone was sitting at their desks, frantically flicking through their books and trying to rote memorise every little detail on the pages.

"Yora, don't you think you should study at least a little bit?" Noah said to his desk neighbour.

"Hey, don't worry about it,"

"How can I not be worried! I want to go to that theme park..."

"Oh...that's how it is..."

He'd figured out the little crush Noah had on Rachel.

"W-What?"

"Your face is burning red, Noah,"

"Damn it, I was fully focused as well,"

"Look, how about this - If my average isn't the lowest in the group, I'll pay for 2 tickets to the cinema: for you and Rachel."

"Really?"

"Really. And don't try to purposely fail your exams - I know you're not that smart in the first place,"

"Yeah, Yeah, I get it, but I know you're not that smart either."

"Well, let's just see how it goes."

And so, the first exam, mathematics, took place. As Asahi went through the paper, he was rather impressed: the type of questions being asked didn't rely on rote memorisation at all, but rather on ingenuity, intuitive thinking, and application of taught skills. It was more like an aptitude test than an academic one.

"Among Adrain, Brielle, and Chloe, there is one who always lies, one who does the opposite of the person before him, and one who randomly lies and tells the truth. They make some statements in the following order order:

- Adrian: Brielle is the liar

- Brielle: Chloe is the liar

- Chloe: Adrian is the liar

- Adrian: Brielle is the liar

- Brielle: Adrian is the liar

Who is the liar?"

It took him 15 minutes to solve the question. He looked around the class to see how everyone else was fairing on the exam: and it didn't look promising. He had another 10 questions to solve, but he considered them rather elementary. He passed through them without sweat, apart for the last question.

"At sunrise, a mountaineer climbs a steep slope, arrives at the mountain top late in the afternoon, and spends the night. Exactly at sunrise the following morning, he begins to climb down the mountain again along the same path. Is there a time when he is at the same location at the exact same time on both days? Note that the speeds of the 2 journeys are not specified. Please provide intricate proof of your solution."

"I don't even know what this is asking," he said under his breath. He had 40 minutes until the 2-hour time limit was finished.

"I go up a hill, sit there, and come back..."

He formed some velocity equations and tried to simultaneously solve them, but he could not account for the fact that the 2 speeds were irrelevant to the problem. He ate up his time, forming complex arbitrary equations and using random guesswork.

"I have 5 minutes left man, I give up. I probably only lost those 5 marks anyway, and I imagine there are some people that probably got about 5 marks in total, so I shouldn't feel too bad. That's a huge amount of marks to meet in the mid-"

He stopped amidst his thoughts and laughed to himself. The solution was rather simple, in hindsight. With 3 minutes remaining, he frantically wrote his solution.

"Consider a second mountaineer who is already at the top of the mountain. If both of these mountainers begin escalating and climbing down at the same time, then no matter what their respective velocities, they will have to cross each other at some point along the path. Thus, given the mountaineer starts at the same time on both days, there is a point in time for all combinations of velocities whereby he will be at the exact same position at the exact same time on both days. QED."