The following day she passed her midterm with her second 90% after the penalty was applied.
After another study session, she took another test I came up with. This time she didn't get stuck on the first question like the day before despite it being something we hadn't covered. She easily came up with an answer and breezed through the rest of the test.
When she handed over the test I glanced at it and asked her, "Are you sure you want to hand it over? You don't want to go over your answers and double-check them to make sure they're right?"
"You're trying to trick me into second-guessing one of my answers to make me change it so I get it wrong, aren't you?"
"If that's what you think, then so be it."
I placed the pencil down onto the paper and drew an X beside the very first question. When she saw that, she had a face filled with confusion. She didn't get mad, rather, her eyes were filled with curiosity as to why her answer was wrong. She knew it was something we hadn't covered, but she was pretty confident she'd solved it correctly.
"Do you want me to tell you why your answer is wrong?"
"It's not because you just want to bully me when it's actually right, is it?"
"Of course not. If an answer is correct, I will mark it as such without fail. Even if I, the maker of the test, was the one with the wrong answer, if the test taker pointed out the error in my solution, I will make that wrong right, correct my mistake, and mark the test taker's answer as the correct one. Your answer just so happens to be incorrect, and can easily be proven to be as such."
"I see."
"Why not try the question out in the real world to fully convince yourself that your answer is incorrect?"
"Try it out?"
"Yes, it's quite easy, don't you think?"
"Now that you mention it… I guess it really is. Just cut out a circle of radius 1 and a circle of radius 3, right?"
"Yes, that is correct."
She took out a protractor and ruler from her geometry set and did exactly that. She carefully cut them out with a pair of scissors then tested the question out in real life by rotating the smaller circle around the larger circle. When the smaller circle rotated from the top to the three-quarter mark around the larger circle, she froze up.
"Why is it like this?"
"So? What's the answer?"
"Four, right? It revolves four times around the larger circle before it gets back to the start."
"Now, what was your logic when solving this problem?"
"To compare the circumference of each circle. If you unravel the larger circle in a straight line it has a distance of 6π while the smaller circle has a circumference of 2π. So by that logic, it just becomes a matter of the ratio between the two circumferences, right?"
"Wrong."
"I know it's wrong, but why is it wrong?"
"When the answer isn't directly before you try changing your perspective a bit. Why did you believe the distance traveled around the circle when rotating it would be the same as rotating it along a straight line? They are two completely different things. The answer lies in what you don't see."
"What I don't see?"
"Yes."
"What is it I don't see exactly?"
"The true distance being traveled here."
She looked down at the question again one more time and while in deep thought she muttered to herself, "it's in what you don't see?"
She lowered her pencil onto the paper and tapped it up and down on the center of the smaller circle.
After a while, she stopped tapping and raised one brow, hesitant at what she saw in her mind there, but not depicted in the image.
She drew a circle around the middle circle passing through the center of the smaller circle.
When she finally saw it, it looked as though a lightbulb went off in her head.
Unbridled excitement bubbled up in her eyes as she said, "So that's what it was! The center of the smaller circle is traveling along a circular path that has a radius equal to the combined radius of the two circles. So it's a matter of the combined radius divided by the radius of the circle revolving around the other. Is that it?"
"Yes, that is correct. It's really quite a shame, if you had figured it out you would have gotten your reward today."
I'd already skimmed through her other answers and they'd all been correct except for this one.
"Haaaah. Oh well. I learned something valuable."
"Oh? You did?"
"A few things actually. Even if I can't solve a problem with my head, there are other methods that may be available to solve it. Also to double-check my answers if I have time and don't underestimate a question just because it looks easy at first glance. There could be trick questions that I need to keep an eye out for. Is that about what your intentions were with this mean-spirited question?"
"Pretty much. You got the gist of the message."
"Tomorrow… I'll be two days dry. I hope you're prepared for that."
"Please feel free to do your best. As they often say, the third time's the charm."
She headed to bed, not the slightest bit angry. She actually appeared to be in quite a good mood. It was the happiness one had when solving a problem they originally got wrong all on their own. Sure, she'd received some hints, but she figured it out herself in the end.
It was this sort of feeling and experience that I believed would serve as a motivation for her to study properly even without any rewards from me.
The following day she bragged about how the midterm had been a walk in the park. I wasn't too surprised by her saying that as I'd expected her to do just fine after everything I'd taught her. The only thing that did surprise me was how when I returned to her place that day I discovered she'd already started studying on her own even without me there.
It was honestly a surprise. I didn't know what she'd gone over and she didn't tell me either. It seemed she really wanted that reward and had made her war preparations. She wouldn't allow herself to be tricked for the third time in a row.
Seeing that, I could help but want to hug her for being so cute. She'd reached the point where she was trying to learn things that were beyond what was covered in our year through the internet all on her own. It was a small step, but she'd acquired a thirst for knowledge.
When I gave her the test she had a big grin on her face as she let out a small chuckle when she saw the tenth question on the test I slipped in that we hadn't covered together. She knew how to do it despite how I never taught it to her.
It seemed I'd be suffering her payback tonight.
Even after she completed the test, she didn't immediately hand it over as she'd done on every prior occasion. She looked over all her answers to ensure she hadn't made any careless mistakes.
Only when she'd gone through them all did she slide her paper over to me. I let out a small sigh when I scanned through her answers and wrote down her score at the top.
"So you've already resigned yourself to your defeat?"
"I wouldn't consider this a defeat. Rather, it's a great success. Today will be the last reward for the tests I give you, there will not be a reward for tomorrow's study session."
"No more after this?"
"Yeah."
"Well… I suppose it's fine. Knowing that I don't need to worry about holding back for the last two I'm getting."
With those ominous words, she stood up, forcefully pulled me off the couch, and dragged me to her room. She pushed me onto the bed then crawled on top of me. She straddled my waist and pinned my arms down under her knees. She slid her hands under my shirt and pushed it up.
I looked up at her and asked, "Uh… what exactly are you-"
"Shut it. You sure had your fun bullying me for the last two days, didn't you?"
"I wouldn't say it was bullying per se." I averted my eyes to the side.
"You can't even look me in the eyes when saying it, can you?"
I really couldn't. It was rather enjoyable to watch her frustrated face.