Tokyo: Simulation Begins with the Big Sister Next Door

Mr. Ichigaya replied, “It was the same at first, but after walking 1700 meters home, he had used up 51 dorayaki, leaving 49. Nobita can carry a maximum of 50 dorayaki, so he can carry those 49 dorayaki and walk the remaining 3300 meters in one go.”

Upon hearing this, Hayano Hoshiko's eyes lit up.

"That means he'll need to eat 33 dorayaki for the rest of his journey, and he'll still have 16 left when he gets home!"

Mr. Ichigaya nodded: "That's right, so Kuroda's answer is correct."

"The world of mathematics is truly fascinating," Hayano Hoshiko said, but in her heart she wondered: Is Anze's amazing gaming skills largely due to his excellent math grades?

After all, nothing is more difficult than mathematics.

While the two were talking, Aoyama High School had already gained 20 points and was temporarily in first place.

Then, the host continued to read out the questions, and the competition gradually became more intense.

During the competition, Kuroda Shin was very active, sometimes frowning as he thought about the correct answer to the question, and sometimes quickly pressing the buzzer to try and get a chance to answer.

Meanwhile, sitting next to them, Anze Ryo and Hoshimiya Rin were... in a daze...

Because of what happened last night, there was some awkwardness between them, otherwise they would have started interacting by now.

Besides, for Yasuzawa Ryo now, those questions were nothing more than child's play. Since Kuroda Shin was so eager, he'd give him a chance to shine, while he could relax and wait for the final big question.

Meanwhile, Hoshimiya Rin was also deep in thought.

However, she was pondering something else.

The warmth and pleasant scent emanating from An Zeliang sitting next to her suddenly reminded her that she seemed to have smelled a similar scent on herself after returning to her room that day…

Was I really the one who was harmed back then, or did I just pick up his scent because we were in the same bed?

But who exactly took my clothes off?

At this point, she had no energy to think about the questions. Instead, she was preoccupied with what happened last night and worrying about whether she was pregnant. She didn't even realize that as time passed, only the final, extremely difficult question remained in the competition.

At this moment, the host, holding the microphone, excitedly said:

"Ladies and gentlemen, representatives of the participating teams, the regular questions are over, and now only..."

They've given us a really big question!

His words immediately created a tense atmosphere, since even the rules for the super-difficult questions were still unknown.

Prior to this, Kuroda Shin had consistently delivered outstanding performances, scoring 390 points, which propelled Aoyama High School to third place.

However, the most eye-catching contestant wasn't him, but rather the prodigy Saori Tsukishima. She was the only one on her team answering questions, yet she had already reached 500 points, firmly holding first place.

Meanwhile, all three students from Dongda Affiliated High School performed well, ranking second with 440 points.

The host looked at the scores on the field and said:

"The highest score among the eight participating teams is 500 points, and the lowest score is 260 points. That seems like a big difference. But it's okay, because we still have the super challenging questions!"

"Please look at the big screen, everyone!"

As he spoke, the question stem for a super-difficult problem appeared on the screen.

Given an integer N1, there are N squared cable car stations of different heights on a mountain. There are two cable car companies, A and B, each operating k cable cars. Each car travels from one station to a higher station (without stopping at other stations in between).

Company A's k cable cars have k different starting points and k different ending points. Furthermore, the cable car with a higher starting point also has a higher ending point. Company B's cable cars also meet the same conditions.

We say that two stations are connected by a company if the lower station can be reached from the higher station via one or more of the company's cable cars (no other movement is allowed between the stations in between).

Find the smallest positive integer k such that there must be two stations connected by two companies simultaneously.

The moment the question was posed, the audience erupted in uproar.

Many of the audience members were math teachers from various universities who came to observe the students in this competition. They immediately realized that the difficulty of this question far exceeded that of the previous questions!

This question is too difficult for high school students.

Hayano Hoshiko, an English teacher, looked around at the reactions of those around her with only a blank expression on her face.

"Ichigaya-sensei, is this question difficult? Everyone's faces don't look too good."

Mr. Ichigaya frowned and replied, "This problem would be very difficult even in the International Mathematical Olympiad. I'm not confident I can solve it quickly without using paper and pen."

At this point, the host calmly said, "Everyone has seen the question. Now I will announce the rules for this question."

"The last question is also a buzzer-beater question, and you can't use paper and pen to calculate. However, this question is worth 200 points! If you answer correctly, your team will get 200 points, and if you answer incorrectly, you will lose 200 points! If no team answers within 15 minutes, the question will be invalidated, and the team competition will end there!"

He didn't care that revealing the questions first might give the contestants more time to solve them, or rather, the organizing committee didn't care. This was because the organizing committee had conducted thorough research before creating the questions, concluding that no one could provide the correct answer within the rules.

Of course, it would be even better if someone could make it.

That's how you demonstrate strength!

The eighth-place team is 240 points behind the first-place team, but...

The gap between them and second place is only 180 points. This means this question could potentially turn eighth place into second! If any team from another ranking answers correctly, they would instantly become first!

The gifted student from Dongda Affiliated High School immediately stood up: "Teacher, this kind of question is unfair! Such a high score will directly change the outcome of the competition, so what's the point of all our previous efforts?"

The host gestured for the other person to sit down, then said with a smile, "Student, this is exactly what the organizing committee intended. Your team from Dongda Affiliated High School can give up the opportunity to answer this question. That way, even if other teams answer correctly, you will at worst be third place. At the same time, for the teams that are lagging behind, this is an opportunity to strive for a higher ranking."

"At the same time, I would like to remind everyone again that the scores of the team competition and the individual competition will be included in the individual total score according to the proportion. If the score in the team competition is too low, even if the score in the individual competition is high, the final result may not be ideal."

"Will everyone choose to go all out and aim for a better ranking, or play it safe and preserve their current achievements?"

"Students, please think it over carefully! The timer starts!"

As the host spoke, the contestants, who had been discussing animatedly, fell silent. He was right; the choice was in their own hands.

Hayano Hoshiko, sitting in the audience, said indignantly, "What's going on? 200 points? This is ridiculous! We finally got third place. If any of the next five teams get it right, we'll be relegated to fourth!"

Sitting next to him, Mr. Ichigaya said, "High risk, high reward, or low risk, low reward—this forces students to make a choice. After all, game theory is also a part of mathematics. The person who set this question is quite something; although it's just one question, it's been tested twice!"

As she spoke, Ichigaya-sensei pulled out a pen and paper she always carried with her: "15 minutes, that's a really tight timeframe, even I'm getting nervous. Let me try and see if I can get the right result!"

Besides Mr. Ichigaya, many others around him took out paper and pens and started calculating. After all, many of those present were math teachers or math enthusiasts, and they didn't want to miss out on such a challenge.

However, the contestants on stage were not so fortunate; they were prohibited from using paper and pen and had to perform mental calculations continuously.

Under immense pressure regarding scores and time, both the stage and the audience became extremely quiet.

Saori Tsukishima closed her eyes slightly and quickly drew on her left palm with her right index finger, seemingly making calculations.

Her teammate said unwillingly, "Is there really no other way? Even though we're already in first place, what if the other teams..."

But with math problems, if you don't know how, you really don't know how. No matter how many times you look at them, you can't suddenly figure them out.

All our hopes are pinned on Tsukishima-kun!

Meanwhile, on the other side, Kuroda Shin's forehead was already covered in fine beads of sweat.

He was calculating rapidly, but he grew increasingly desperate. After several minutes of thinking, he still couldn't find a suitable solution.

My current ranking is third, with 390 points. If I answer correctly, my score will become 590 points, but if I answer incorrectly, it will become 190 points...

Such a choice

This is really a headache...

Kuroda Shin looked at Yasuzawa Ryo and Hoshimiya Rin, who were completely out of it, and said:

"You two should think of something too! Why am I the only one trying? Have you even thought about bringing honor to the school? Even if not for the school, you should think about yourselves! If you had done something to secure second place, at the very least you would have gotten third, and we wouldn't be in this mess now!"

"Anze, you were so good at the exams before, how come you couldn't answer a single question now! Honestly! It would have been better if you had been killed by the scumbag killer, then someone else wouldn't have been so useless!"

The "Scumbag Killer" is already a well-known urban legend at Aoyama High School. Because of this legend, Kuroda Shin had many nightmares before, and although he wasn't a scumbag, he was still afraid. Now he was too anxious, which is why he blurted out that he hoped Yasuzawa Ryo would be killed by the Scumbag Killer.

However, the words "scumbag killer" made Anze Liang turn his head slightly and look at Kuroda Shin.

During the match, seeing how enthusiastic Kuroda Shin was, Anze Ryo felt comfortable slacking off and spent his time observing the audience. He finally realized that the quality of the girls in this parallel world was much higher than in his previous life.

Seeing Anze Ryo's expression, Kuroda Shin said with dissatisfaction:

"Are you still hungover? Did you drink again yesterday?"

"The competition has been going on for so long, and neither of you has answered a single question. I got all 300 points by myself. If that's the case, why did you even participate in the competition?"

Immediately afterwards, a barrage of complaints poured out of Kuroda Shin's mouth, and Yasuzawa Ryo felt that what he said made sense.

Although I don't like Kuroda Shin, he wasn't wrong about what he said.

Focus on the person, not the issue.

So An Zeliang looked at the big screen, read the question again, confirmed that it matched his calculations, and then picked up the buzzer and pressed the button.

"Ding!" The buzzer sounded.

"What are you doing!" Kuroda Shin was shocked. "Are you trying to kill me by making me answer the question in such a hurry?!"

The host looked at An Zeliang and said in surprise, "A team actually answered first? Please welcome Aoyama High School to answer the question!"

An Zeliang took the microphone and calmly said, "k equals N squared minus N plus 1."

"Oops, I made a mistake." Ichigaya-sensei said regretfully after hearing Anze Ryo's answer, "It should be N squared plus N minus 1."

Hayano Hoshiko, standing nearby, immediately jumped to her throat: "Ah, if that's the case, wouldn't our team become 190 points?"

Mr. Ichigaya hurriedly waved his hand and said, "Not necessarily, not necessarily. I was also in a hurry to calculate, so maybe I'm wrong."

Although he said that, he was really just trying to comfort Hayano Hoshiko. After all, he had been watching his teammates closely throughout the match, and Yasuzawa Ryo had only glanced at the screen for a moment before giving his result—how could that possibly be correct!

Even mental arithmetic couldn't be done that fast! Impossible!

Kuroda Shin, standing on the stage, felt a chill run down her spine as she looked at Yasuzawa Ryo, who had already given his answer.

"We're doomed! We're doomed! This guy is definitely sabotaging us! He deliberately let me..."

"We lost!"

Kuroda Shin said indignantly, "Are you crazy?! I finally got these 390 points, and now I'm going to be last because of you! Anze! You're such a..."

Before she could finish speaking, Kuroda heard the host's voice: "Correct answer, congratulations to Aoyama High School, 200 points added!"

"He's... he's... a genius!"

Kuroda Shin originally wanted to say that Yasuzawa Ryo was crazy, but the host's voice left him completely bewildered.

He stood up in disbelief and turned to the host: "Excuse me, are you kidding me? How could such a casually given answer be correct?"

At this moment, the answer to the question appeared on the big screen, and it was exactly the same as what An Zeliang had said.

The host looked shocked. "Young man, your team has gained 200 points! Aren't you happy? You're now the first place team in the competition!"

"This student named Anze is simply a genius! He was able to mentally calculate such a problem so quickly... No, he definitely didn't calculate it that quickly. Maybe he has done similar problems often before, which is why he can solve them so skillfully."