Nonoha was disoriented. Her head was fuzzy, the air was fuzzy, her memories of the past indefinite amount of time were fuzzy. It was a strange feeling, to have fuzzy memories.
Nonoha realized that she laying in her bed. Someone was with her, sitting by her, their hand resting on her back. Kaito.
Nonoha sat up and the room came into focus. "Kaito—what—" Suddenly, it all came rushing back, the ring, the puzzle, everything. "Kaito! I—I—" She began sobbing. "I almost killed you! Didn't I—I did—"
"Nonoha, it's okay." Kaito wrapped his arms around her and pulled her towards him. "It wasn't you, it was the ring."
"It was me! I put it on, I chose to do that—"
"It was the Orpheus order."
"No! I could have—could have—refused, but I didn't—I chose to put it on." Nonoha wiped one of her tears and attempted to compose herself. "The last thing I thought before I put it on was that I'd be able to solve puzzles, it was selfish, I just wanted to be able to solve puzzles and I put it on and I endangered both of us."
"You… want to solve puzzles?" He asked with a tone of voice as if it was the craziest thing in the world.
"Of course I want to solve puzzles!" She pushed herself away. "Moron! Why do you think I hang out with you?"
"Nonoha, you're just feeling the after-effects of the ring—"
"No! Kaito, don't dismiss me like that! I want to talk about this. Please. It almost got one of us killed." Kaito looked confused, but he was listening. "I've always felt like this. I remember always feeling like this. Do you think the Orpheus ring would have worked if I didn't want to solve puzzles at all?"
"I thought… I thought you just liked watching me solve puzzles."
"What? That's stupid! Who would want to just watch someone solve puzzles?"
(But it's not like I've done anything my entire life to suggest otherwise, Nonoha thought to herself.)
"It's what you said!"
"What? When?"
"Remember? When we were kids, and I told you that you would need to solve puzzles by yourself, and you ate so much you got sick, and then you told me you didn't want to be by yourself, you just wanted to watch—"
"I was a kid! I don't know what I was thinking, but I didn't mean that! I wanted—I just wanted—I wanted to solve puzzles with you, Kaito, that's all I wanted. Just be with you and solve puzzles."
"Oh."
They sat in silence for a while. Nonoha felt embarrassed, as if we she had just confessed… well, she had confessed something, but she felt like she had confessed that.
Finally, Kaito broke the awkward silence. "Well, let's do a puzzle together, then." His face lit up with the usual boyish smile he wore whenever he thought about puzzles. "Right now." He reached into his backpack on the floor and pulled out a standard 3x3x3 Rubik's cube.
"Kaito, I couldn't even do that smaller one you gave me when we were kids."
"We'll solve it together. Now close your eyes while I mix it up, or you'll just reverse what I did."
"Okay." Nonoha closed her eyes while Kaito spun the faces of the Rubik's cube. "Done." Nonoha opened her eyes to see a jumbled cube. Kaito spun it around so she could see the whole thing.
"Okay, now I'm going to give you a hint." He made a sequence of moves on the cube, then handed the cube to Nonoha.
"Uh—what—"
"Do you see what I just showed you?"
Nonoha thought about the moves Kaito had made. She could see them clearly in her head. She could see the cube that Kaito had originally unveiled as if it were right next to the one she was looking at now. There was something about them… they were almost the same. Only three pieces were different. Three corner pieces had swapped places.
Oh. If Nonoha could swap 3 corner pieces, she could get all the corner pieces in the right place, relative to the center tiles. She just had to apply that same sequence of moves a bunch of times in the right places, getting one piece into place at a time.
Right face counter-clockwise.
Bottom face counter-clockwise.
Right face clockwise.
Top face clockwise.
Right face counter-clockwise.
Bottom face clockwise.
Right face clockwise.
Top face clockwise.
Right face counter-clockwise.
Bottom face counter-clockwise.
Right face clockwise.
Top face 180 degrees.
Right face counter-clockwise.
Bottom face clockwise.
Right face clockwise.
This rotated three of the corners on the top face. She did this many times, in various orientations until all eight corners were in the right position.
Almost.
When she was done, two corners were still in the wrong place and they needed to be exchanged with each other. But her procedure only let her swap three at a time. She couldn't move one of these two without moving a third as well, and undoing her progress.
So clearly, this was a case where she would just have to backtrack, mess some of her work up and then put it all back together later, but she couldn't see a way to do it, no way to combine a set of these 3-swap operations to swap just two.
She was about to ask for Kaito's help again, but then she saw it. She simply rotated one face, the face that had the two swapped corners. Suddenly, there were three swapped corners. Then she applied Kaito's sequence again to rotate them, and now all the corners were in the right place.
"Kaito, I did—I did something!"
The corners still weren't right. They occupied the correct physical space, but they didn't have the right orientation. When Kaito solved a Rubik's cube, he always solved one entire face first, then made his way to the other side of the cube. This wasn't progress in the same way. Still, it was something.
"Good job! Here." He held out his hand for the cube, and Nonoha passed it back. Kaito did another sequence of moves and handed it back to Nonoha. A different pattern this time, with a different consequence.
Right face counter-clockwise.
Bottom face counter-clockwise.
Right face clockwise.
Bottom face 180 degrees.
Front face clockwise.
Bottom face counter-clockwise.
Front face counter-clockwise.
Top face clockwise.
Front face clockwise.
Bottom face clockwise.
Front face counter-clockwise.
Bottom face 180 degrees.
Right face counter-clockwise.
Bottom face clockwise.
Right face clockwise.
Top face counter-clockwise.
This one kept all the pieces in the same place, but rotated two of the corners, one clockwise and another counter-clockwise. Nonoha used this to get all the corners turned the right away. She didn't get stuck at the end this time, with just one one corner turned wrong—which was good, because she couldn't have used the same trick this time.
Now all the corners were in the right spot and rotated correctly. Now each face of the cube displayed an X. Only the edge pieces needed fixing, now.
Kaito smiled. "Great!" He held out his hand, as if to take the cube. Nonoha started to hand it to him, but then she paused. "Wait. Let me think for a second."
After executing the sequences so many times, she began to get a feel for how they worked.
For example, the sequence that rotated two corners worked as follows. First, she executed a long sequence of steps which rotated one corner piece in the top face, while completely messing up much of the rest of the cube—but leaving the top face completely intact, other than the one rotated piece. Then she rotated the entire top face. Now a different corner was in the same place as that corner she had rotated. Then, she executed the long sequence of steps in reverse. This rotated this other corner piece in the opposite direction, while repairing the rest of the cube that got jumbled. Then she rotated the top face back. The result was that these two corners had rotated and nothing else had moved.
The procedure to swap three corner pieces worked by a similar principle.
But one she saw this, she saw—
The procedure could be applied to the edge pieces as well!
Excited, Nonoha swapped all the edge pieces into place and then flipped them.
She again didn't run into any problems, needing to swap just two edge pieces, or needing to flip just one.
A completed cube sat in her hands.
"Kaito! I did it! Kaito! Look!"
"Congratulations!" He looked so happy. It wasn't the usual way he looked at her. He usually looked at her with care, with affection, but never the abundant joy he was showing now. Nonoha didn't think she had seen him look at her like that since… she had solved the wooden blocks puzzle when they were kids.
She hadn't felt that way since then, either.
Nonoha wrapped her arms around Kaito. "I get it! You didn't show me the quick tricks, you showed me those long, methodical sequences so I could infer the pattern and make my own!"
"That's right. I can show you the quick tricks later."
Nonoha smiled. "I'd like that. You're a great teacher, Kaito."
"Nonoha, from now on, I want to solve all the puzzles with you."
"Me too, Kaito."
