The Sixteenth Question

Please answer the following question:

1. In the equation 4 sin X + 3 cos 3X = 2, solve for X when X is in the first quadrant.

2. Which equation does Sin (A + B) equate to? Please choose from options 1 to 4.

sin A + cos B

sin A - cos B

sin A cos B

sin A cos B + cos A sin B

Himeji Mizuki's answer

"1: X = π/6, 2: 4"

Question 1, courtesy of Sunny

Teacher's Comment

Correct answer

Yoshii Akihisa's Answer

"I do not know."

Teacher's Comment:

What happened to that 'I'll just write anything here as an answer' att.i.tude you used to have?

“Practicing how to draw a tree...”

“She was really bad at it to be honest, so bad that I couldn't tell what she was drawing even after looking at it for a while.”

When she was young, Himeji-san was simply practicing how to draw on the blackboard with all her effort. No matter how bad, how clumsy she was at it, no matter how I couldn't tell what she was drawing at all on first glance, she worked so hard back then.

Even if that was meaningless, even foolish to others.

But it really makes...

“It really touched me.”

No matter how bad, how clumsy she was, no matter how she wasn't suited to drawing.

I can tell from her method that she was trying her best to express her 'thanks'. No matter how many times she draws that bad and clumsy piece of a drawing, and erased it again, or whether it would be buried amongst everyone's messages, she didn't mind at all.

She wouldn't gain any merit out of this.

n.o.body would thank her.

She simply wanted to express the 'thanks' in her heart to that person, and practiced for that sake.

Once I found how devoted Himeji-san can be to a certain cause, I started to find myself curious about her.

“Did the feelings in Mizuki's drawing reach that teacher?”

“...No, she didn't managed to do so.”

I was curious as to what happened to that girl after that, so on the graduation day itself, I sneaked into the neighbouring cla.s.sroom to check on that blackboard.

But that blackboard never had the picture of the tree that girl practiced so hard to draw.

“I have a very weak body, and I was hospitalized.”

Once we were in the same cla.s.s, I recalled the words she said when I chatted with her.

“My body's weak, I'm slow witted, I'm clumsy...so that's why I have to work harder.”

I felt that she was 'a little weird' when she could say such a thing after so much effort had been wasted.

But I was wrong. That wasn't the case.

“After we ended up in the same cla.s.s, I visited Himeji-san when she was in the hospital—and I saw her crying as she studied in the ward room.”

How could she possibly have any thoughts after all her efforts had been wasted?

There was no way she could not have felt anything after her efforts were for naught despite so much effort.

She went through lots of hardships, and she was so anguished that she was crying out sadly.

She however gritted her teeth as she continued to do what she could do. That's truly very n.o.ble.

In my eyes, that Himeji-san back then really was someone admirable.

Those efforts will definitely not be wasted, and I believed that what awaited this girl, who worked hard and devoted herself so much, would never be hardship alone. I would never allow that.

Right, that was what I thought.

“And I ended up getting in her way...! She entered cla.s.s F in high school because of her weak body, and I ended up preventing her from getting the fruits of her hard work!”

“Aki...”

Himeji-san never changed even when she entered High school.

She worked as hard as she did back then.

She's as clumsy as she was back then.

And like before—she didn't get any fruits from her hard work.

“And that confession just now...! There wasn't a need to confess to me, but she lied to me because she's scared of hurting me..!”

What did I do for her? I said that I was doing things for her sake, but didn't I end up frustrating her...!?

“Aki.”

I heard Minami's gentle voice.

Before I know it, Minami's hands were gently clasping onto mine.

“I'm sorry. I actually lied just now.”

This sudden line caused me to ask back without thinking,

“...lied...?”

What did she lie about—

“Well, I just said that 'I confessed' already, didn't I? That was a lie to you. I haven't confessed yet.”

Minami said to me 'it's meaningless since I confessed already' when I apologized to her because of the diary, but now she's saying it's a lie.

“Minami, why did you say that—”

“It's going to be the same thing either way. I'm going to confess to you now.”

“Eh...?”

Before I could understand what she was trying to say, Minami places a kiss on my lips, so gently that it never felt like it ended on my lips. She then retreated, and smiled.

“I like you, Aki, ever since the time when we were in our First Years.”

Her smile's so beautiful, and I can't help but be amazed by it.

“Aki, you just said that Mizuki's confession wasn't real, right?”

I remain speechless, and Minami doesn't mind as she continues,

“Do you think my confession to you is a lie too? Do you think I'm pitying you just because you're dejected?”

I can only stand blankly, looking all disoriented because of this sudden happening.

“If you don't believe, I can let you read my diary, you know? I've been writing all about you from the time First Year began.”

Minami's large eyes are staring right at me.

I can tell from her expression that she's not lying that she really—likes me.

Because of this, I kept listening to her quietly.

“Aki, you can't lie when you confess to someone. I'm trying to comfort you now, but if I just wanted to comfort you, I won't confess to you. I confessed to you like this because I really like you.”

We spent about 2 years together ever since we enrolled in Fumitzuki Gakuen, and I know how gentle of a girl Minami is, how she really cares for her friends, how compa.s.sionate she is.

But even so, she won't confess just for the sake of a friend. She can only do so when she truly likes someone.

“But I do find it a little annoying how you fidget around like this, and I really hate you for blaming yourself and regretting your actions.”

After saying that, she stared at me with more conviction.

“—and I really hate you when you said that a girl, who summoned all her courage to confess to you, is lying.”

“...”

Minami's words caused me to feel guilty.

I do feel that she has many mixed feelings within that line she said.

“I still remember the French words you said to me when we were in our First Year, Aki.”

Now that she mentioned the French words I said in our Freshman year, I recalled the time when we just got acquainted.

When she told me later on that 'I mixed up French with German', I was so embarra.s.sed that my face was burning.

“What you did back then was so clumsy and hard to understand, but I'm happy that you had the heart to do so. You worked so hard for me like a clumsy kid.”

Minami smiles as she says this.

“Mizuki definitely thinks this too. You're not good at studying, but you worked so hard for her sake. How can she be troubled when she'll be happy about that instead. You'll feel happy if it's for your sake too, right?”

Minami's words repeat themselves in my heart.

—What will I think if it's me?

I already knew that Himeji-san's clumsy, but she really works hard.

I was really attracted by how she reached to express her own thanks to someone.

It didn't matter whether her efforts paid off. I feel that the way she worked so hard is mesmerizing. That's why I had feelings for her.

As Minami had said, while what I did was clumsy and hard to understand, but she's really happy that I made the effort to do so. Himeji-san's the same too.

Even if there's no good result from it, I do know how charming it is to see someone being so devoted and hardworking.

In that case, Himeji-san and Minami's impression of me is—

“Aki, if you have the time to doubt the confession, why don't you think of something else. Someone came to invite Mizuki to study overseas, right?”

If we're talking about Himeji-san going overseas, I think there's only the option of either 'watching her leave' or 'wanting to make her stay'.

If it's for the sake of her future, I should smile and watch her leave. It's not that it's a permanent farewell though; as long as her parents remain in j.a.pan, there's still a chance that I'll meet her.

If I try to make her stay, I'm just thinking about what I want.

A selfish thought of wanting to be with her, to laugh and cry with her, to be in this school with her every day.

“Aki, do you know that Mizuki's not thinking that you're distracting her. She's worried that 'you'll think you're obstructing her' if you know about her going overseas, and that you'll blame yourself.”

Minami never talked about 'sending her off' or 'making her stay'; she simply dispelled my misunderstanding, and told me the truth so that I won't make any wrong decisions.

If she doesn't think that I'm bothering her, and she doesn't want to leave me, I really hope that Himeji-san can be together with us, as part of our regular gang, enjoying ourselves in school like usual every day.

But we still have a long way to go in our lives later on. If we live normally, we might be able to live for another 60 years or more. And...is it really the right decision to cut down on her future options just to be with her for a few more years?

“You have to think through this well, Aki. You don't want to regret the choice you make after that.”

Minami's eyes stare right at me, showing a reflection of myself.

It's just as Minami had said; I don't have the time to doubt the confession. There's something more important to me than that, I have to choose the correct choice, but I have no idea what to choose at all.

“Haha...I really don't know.”

I don't know which option to choose.

If I follow my original motive of doing things for her sake, I should smile and watch her leave. It's an overseas trip, but we still have chances to meet. Minami came back from Germany, and my parents are overseas, so being overseas isn't a faraway thing for her.

But I really wish to spend time in the same school as her. Maybe this time isn't considered long in our lives, but to me, they're really important.

Also, how do I respond to Minami and Himeji-san's confessions? I really don't know my own feelings either.

I do have feelings for Himeji-san, but I also do find Minami charming as someone of the opposite gender.

Looking at how bad I am at choosing, I really hate myself to a point of wanting to punch myself.

Shall I send Himeji-san away? Shall I reciprocate Minami's feelings? There are reasons why I can't ignore them, but for me to make a decision is too—

“There's no time left.”

The familiar, unexpected voice can be heard from behind me.

After saying those sudden words, I felt a hard hit on my back before I could even turn around, and I fall onto the floor weakly.

“!? What!? What!?”

This sudden happening caused me to feel confused and panicky.

That familiar big guy is standing in front of this shocked me.

“There's no time left, Akihisa. We don't have the time to let you laze around. Go take the replenishment tests for humanities.”

The guy who gave me a hard kick while I'm in my thoughts is my nemesis and bad friend—Sakamoto Yuuji.

In place of me on the floor, Minami walks to Yuuji and says,

“W-wait a moment, Sakamoto. How can we allow him to take the replenishment tests now? Aki has something he has to really think about—”

“Like I care. If he has to think about it, think while taking the test.”

Yuuji randomly answers.

“But Aki doesn't have that intellect...”

Minami looks at me worriedly.

It's true that I'm not good at using my brain, and I can be said to be a buffoon at this. I'm already at my wits end just thinking about something important to both of us, so making me take the replenishment tests at the same time will be beyond my brain capacity. It's too hard for me to do two things at once.

“Listen up, Akihisa.”

But Yuuji stares at me right in the eyes as he says,

“The human brain is divided into the left and right sides. You dare to say that you can't do it even then?”

“...It might be possible in theory...”

“No, Aki, it's because it's divided in two halves that they have different functions, you know.”

Even if it's possible in theory, I can't possibly do such a highly difficult skill.

As I continue to be frustrated, Yuuji continues,

“How you intend to deal with Himeji's overseas schooling and Shimada's confession is up to you.”

Yuuji's right. He's not the person directly involved in all these, and it's just me being frustrated due to my stubbornness.

“But if we lose this summoning war, we'll be forced to take what others don't want. You understand what I mean?”

I try to rack my brain after it had thought of too many things, and was at the point of blowing up, trying my best to understand what he meant.

If we lose, the second years won't be able to get the higher cla.s.s facilities, and Himeji-san won't get the facilities she deserves. From what motives are, and what Himeji-san's parents think—

“Goodness, if you can't understand, I'll make it simple for you.”

Yuuji watches me struggle in my thinking, and showed an evil grin on his wild looking face.

“Are we really that kind enough to let those 3rd years get everything?”

After he gave me such a simple question, I recalled the battles against the 3rd years in this summoning war.

Yuuji lost out in strategic planning.

I was completely beaten by Takashiro-sempai. Himeji-san was sent to the detention room to protect me.

Muttsurini was toyed by Kogure-sempai, Hideyoshi and Minami were completely thrashed by the Toko-Natsu pair.

“...I see. This is really easy to understand.”

No matter how little I think about it, I felt that I had to take revenge for this no matter what.

We're not some kind beings to let everything end without leaving any regrets behind...!

“Since you understand, go back, get your answer, and get a high score to be able to beat that b.a.s.t.a.r.d Takashiro.”

Yuuji makes it sound so easy, but neither of these are easy to do. This guy really can make such reckless requests.

“Don't just say things because they don't concern you, Yuuji.”

“It's simple after all, simpler than just enduring everything and losing.”

I do agree with this wholeheartedly. This fact is so simple to understand, and I don't have a chance of arguing back.

That's why my answer's simple too.

“Understood. I'll get the highest score up till now.”

I have to respond to Yuuji's reckless requests if we're going to end everything.

“Anyway, are you really alright? I don't want to find out that the second years lost once I return from the replenishment tests.”

“Are you kidding me? I don't care how it ends, but I'm not going to lose to those guys no matter what.”

“I do agree with that.”

Right now, how can we let this rest without winning? We must do all we can for the sake of victory.

As I attend the replenishment tests with such thoughts.

“Ah...wait, Aki.”

Minami called out for me as she tugged at my sleeve.

“Hm? What is it?”

“Erm...there's still one other thing.”

Minami looks really emotional as she says this,

“I just said that Mizuki and I won't confess because of pity, and we didn't do it. So Aki, don't do it because of kindness or pity—”

“I understand. I'll think through it properly and get the answer.”

“...Right.”

After saying this to Minami, I race off to the old school building.

I have to serious think about my own matters, Minami's matters, and Himeji-san's matters.

So that I won't leave any regrets behind.

I watch Aki run away, and Sakamoto comes over to talk to me.

“You alright with that, Shimada?”

“...With what?”

“Well...how do I say it? If you never said anything, Himeji will leave, and Akihisa will be left depressed. From your standpoint—”

I immediately answer without waiting for Sakamoto to finish his words.

What's good or not good about it—

“I didn't have a choice either.”

It really can't be helped.

He's stupid, foolish, and doesn't understand other people's feelings.

But he's enthusiastic, kind and straightforward.

He's considerate to others, willing to work hard for other people's sake.

“I—like that Aki.”

The Aki who suspected Mizuki's confession isn't the Aki I like; I couldn't let myself see Aki being like that.

I can't let myself not like the person I like.

“...Shimada”

“What?”

“You're a good girl. That's a waste for Akihisa's level.”

“Thanks. I'll just brag about those words to Shouko then.”

“Hey! That's a foul!”

Sakamoto already confessed before, but it's interesting seeing such a little joke causing him to be so awkward.

“Are you done with your words?”

“...(Stealthily appears).”

Kinos.h.i.ta and Tsuchiya, who had been watching from afar, appears. They probably knew that we had something to say, and deliberately hid themselves. In that case, I'm really grateful for that.

“It's still a little embarra.s.sing thinking about how those words were overheard.”

Once I saw Kinos.h.i.ta and Tsuchiya, they say to me,

“What? Just relax, Shimada.”

“...We almost couldn't hear anything.”

“Ah, really?”

“Yeah...but even if we didn't, we could at least guess what you two were talking about.”

“...A fact everyone knows.”

“Ahahaha. What are you talking about? How can you know without hearing?”

““Your confession to Akihisa—””

“I'll wring your necks if you say anything more.”

How did it get exposed anyway! You guys were clearly eavesdropping on us, right?

“We know you for a while longer than Himeji, so we can easily guess whatever you would say to Akihisa in that situation.”

“(nods)...Hideyoshi can understand what women thinks.”

“Muttsurini, that's not what I'm trying to get at.”

But it's as what they said. After I came back to j.a.pan, other than my family, these guys are the ones I spent the most time with. It's not strange for them to guess what I would do in that case.

“But even if you guess so, it's a form of gentleness not to say it out, right?”

“Don't say that. We'll do our best to help you two, so just a little teasing isn't much here.”

“...We'll do our best for our friends.”

Seriously...I have to hand it to these guys.

So they not only treated Aki as a friend, but me too. They'll also do their best for an outcome everyone can accept.

Great, now I can confess—to that coolest Aki and tell him what I feel.

“...Thanks.”

I shyly whisper, and Kinos.h.i.ta and Tsuchiya smile away. What, those smiles are giving me that, 'that's just like you, Shimada' vibe.

“Speaking of which, what do you intend to do, Yuuji?”

“I'll think of all sorts of things, but we'll need to rely on Akihisa's power for the final bit. Our job is to hang on until he comes back from the replenishment tests.

“Hm...but the 3rd years should have somewhat recovered from the damage caused by our sudden attack. They probably want to settle things now. Can we really hang on for that long?”

That sudden attack just now caused quite some damage to the enemy, but we were worn out more than them, and the balance in power is worsened to a point of being more than 3 times. In this situation, we can't possibly last until the replenishment tests are over.

But,

“We won't lose.”

Sakamoto casually denies such doubts.

“We'll win if you guys will help.”

Win, not lose, not draw. Sakamoto says that we can beat the 3rd years.

That's such a nostalgic feeling.

What he says is completely baseless, but for some reason, I feel that what he says is correct. It's just like when we first entered our Second Year.

“Remember guys, we're—”

“““The strongest!!”””

“That's right.”

After hearing our replies, Sakamoto nods in satisfaction, showing his usual evil grin.