3

We spent the next few days looking for the blank, white puzzle piece. We searched every nook and cranny in that house, looking everywhere we could imagine.

We knew for sure that the puzzle had been fully accounted for in July when Urakawa-san brought it over to continue putting it together. We had counted every single piece. We were certain that 632 pieces were assembled while 368 remained unplaced. Somewhere in the last three weeks, we had managed to misplace a piece.

At one point, we began assuming that it had gotten stuck in our clothes, catching a ride for a while. I turned all the clothes I had worn that summer inside out, crawled around on my bedroom floor, and searched my house’s laundry room. Urakawa-san carefully followed her typical path that she took walks on and checked the lost and found center of the supermarket she frequented. Of course, it went unsaid that if we really had dropped it somewhere outside, it was game over. Nobody else would care about some random white puzzle piece they stumbled across. It could have already been thrown away or incinerated with other burnable trash, but we kept searching anyway.

Once it was too dark to search, we huddled together in the attic, working more on the puzzle. Of course, we kept to our rule that only one person could work on it at a time. I felt some kind of routine compulsion to keep fitting the white pieces together. I had begun thinking that I needed to do it, for Urakawa-san. At some point, it became second nature.

There was a part of me that didn’t like that compulsion, mostly because I knew it was connected to Urakawa-san’s supposed disappearance. I wanted to finish the thing before she had the chance to disappear, but at the same time, I didn’t want to be motivated by fear. So I tried to beat a different thought into its place. I absolutely will not lose her.

But Urakawa-san only seemed to be getting more and more unstable.

She was substituted the day after putting the Band-Aid on her finger. Then again that night. Then three times the following day. It was like she was hurrying along the preparations so everything could fall into place.

We ended up at a nearby shrine on the third day of our puzzle piece search. We had been there some 10 days prior for a summer festival.

As soon as we met, she led with, “I substituted once this morning.”

That made six substitutions already.

She glanced at the Band-Aid on her finger. It was a wonderful yellow color with a cartoon bear printed on, and it looked freshly applied. I would have preferred her to use any other bandage. It was like she revered it as a symbol of her disappearance. But she wanted that one, and I couldn’t refuse her.

“There is only one left, from seven years ago. The time I appeared before you wearing this bandage. We are out of time.”

We searched together around the area with the goldfish scooping tank we had visited and looked under the bench where we had sat together eating takoyaki. But no matter where we looked, we didn’t find a white puzzle piece.

We sat down on the bench, drinking from plastic bottles of Calpis. Ever since seven years ago, we had an unspoken rule of always drinking Calpis together.

After swallowing, Urakawa-san called my name. “Tsumiki… I believe that you were my hope.”

“Your hope?”

She slowly nodded. “Yes. You gave me encouragement to keep living on. I’ll provide an example. As you know, I get a headache just before I am substituted. Do you know what my first reaction is when I get that headache?”

I clutched my bottle of Calpis a little tighter. “I dunno. It’s not like you do anything special.”

“Only when you are watching. Come now, Tsumiki. What do you really think is the answer?”

Dodging the question hadn’t worked, so I was only left with the option to answer honestly.

“You hide.”

She couldn’t let anyone witness her sudden change of age, after all.

“Exactly. I could not stand the thought of anyone else knowing about the strange phenomena happening to my own body.”

Just listening to her broke my heart. Her first substitution had occurred when she was only a second-year elementary schooler. If anything similar had happened to me, my instinctual reaction would be to run to my family and ask for help. It would be scary, it would be overwhelming, and I couldn’t possibly stand being left alone in it.

“When I realized just how frequently it was happening, I began taking precautions to stay out of the public eye. I walked paths that were less traveled, always keeping my eye out for places to run in and hide. It was my main driving force behind deciding to go back and live alone at that house over the summer.”

There was something about her mannerisms that I had begun to notice recently. Substitutions were the foundation of the way she lived her life.

Right after Urakawa-san experienced a substitution, she would typically go shopping. Or maybe she would visit the hospital, or ride the bus. Or visit a shrine for a festival. At the end of the summer, as she made her trip back to her grandfather’s place, she would only leave after she had just been substituted. It was a natural schedule that came from the fact that substitutions only happened once every few days, never in succession.

Recently, she hasn’t even had that comfort. For the last few days, substitution had evolved into an event that happened multiple times a day.

“I did not want to see anybody. I did not want anybody to see me. With only one exception. You, Tsumiki.”

I couldn’t have imagined a greater honor.

Despite that being my true thoughts, I didn’t have the guts to say it out loud.

Urakawa-san tilted her head, suddenly looking rather childish. “Do you remember the time when we first met?”

Of course I remembered. I could never forget. “Summer vacation, back when we were third-years in elementary school.”

But she shook her head, her bangs swaying back and forth. “For you, that might be so. But not for me. I met you four months prior, some time around spring break. I was substituted into the time of my second year of middle school.”

Of course that was how it worked for her. I had gotten so used to seeing her younger self substituted in front of me I forgot what that entailed on her end.

“I’m sure you can understand how shocked I was. I was suddenly faced by some boy I didn’t know. He was sitting across the table, nonchalantly eating pudding. My first reaction was to curse my future self. I had sworn to remain solitary and secretive, yet I screwed it up so royally.”

Try as I might, I just couldn’t recall very much about the moment in question. My memory had never been as strong as Urakawa-san’s.

“But you spoke to me so calmly. ‘Wow, you’re awful small this time,’ you said.”

I really couldn’t remember. Perhaps I had been too distracted by how good the pudding was.

“I was struggling to find a way to answer you, and you kept going. ‘Hey, there’s some great pudding there in front of you. Go ahead, help yourself. Long as you don’t think your second-year junior high self will get mad when she gets back from substituting, at least.’”

That one managed to pull something from me. I could slightly recall just how adorable the little Urakawa-san’s face was in that moment as she stared at me in confusion.

“I could not even manage to get out a single word, in the end. When I returned back to my normal time, that experience was all I could think about. I was going to grow up and become a second-year in junior high. If I had to wait that long, and that pudding wasn’t delicious, I was really going to let you have it.”

“But it was really delicious, right?”

“It was. If I had to describe how I felt, irritation would be putting it nicely.”

That was interesting to hear. Urakawa-san wasn’t one to get irritated very often.

“I met you three more times before that summer vacation finally came around. We were only together during the daytime, so the chance of any substitution leading to you was somewhat rare. But before I knew it, I was wishing that every substitution would lead me to you.”

“Because it made you feel comfortable?”

“Yes. You created the only space where I could feel truly at ease.”

Despite it all, I couldn’t bring myself to be happy about what she said. It only served to show just how lonely the rest of her life was. “You could’ve come over during winter break, too.”

“I did, occasionally. Winter. Spring. Fall. You never noticed I was here.” She sighed in resignation. “Look, this has nothing to do with vacation time. Did you really think I was actually attending school, when I could be suddenly substituted at any time, in any place? Of course you didn’t. But you were more than happy to smile and play along with all of my lies.”

“That can’t be true.”

“Which part?”

I couldn’t answer her. An unsettled smile flickered on my face as her face remained ever-expressionless. It was a shame to admit, but I just didn’t get her as much as she thought I did. All I wanted was to close that distance, no matter how little. “Well, if I had to describe how that makes me feel, happy would be putting it nicely,” I started.

I was actually special to Urakawa-san. For the longest time, I could never be sure if I meant anything to her. Even after all she had said, I was still having a hard time gauging her.

I took a swig of my Calps. The sweet flavor spread throughout my mouth, leaving a sour aftertaste.

Urakawa-san stood up from the bench and gave a long, exaggerated stretch. I stood up as well, glancing around. I noticed a small room just off from the main stone steps leading to the shrine. It looked like it had gone unused for years.

“Y’know, I snuck in that place once, way back when.” If I was remembering correctly, it was back in elementary school. I was hit by a sudden rainstorm, and while looking for shelter, found that the door to that room was surprisingly unlocked.

“I see—” Urakawa-san suddenly went silent.

I looked over at her, and found her staring intently at the room.

“Tsumiki… I was in there just a few days ago.”

According to Urakawa-san, one of her substitutions a few days prior had landed her inside that room. She had been substituted with the elementary school version of herself, taking shelter from the rain. It was just before she had cut her finger. Putting it all together, I remembered that one of the younger substitute Urakawa-sans did in fact have wet hair.

Whenever Urakawa-san experienced a substitution, any clothes, purses, and items she was holding would also go along with her. I didn’t know the exact specifics, but it wasn’t outside of the realm of possibility that a puzzle piece snagged on her clothes could have hitchhiked alongside her.

We both turned towards the room. We began jogging over there instinctively.

The door was unlocked.

We put our hands on the doorknob, and it opened with a high-pitched creak.

What if there was a puzzle piece inside?

“I’m getting a headache,” Urakawa-san interjected.

I looked carefully at her. I noticed her white blouse with navy blue slacks, her black hair that went down about halfway down her back, and the yellow Band-Aid on her right middle finger. Then, she began to shimmer and fade.

“This is the last one.” With that, she blinked away.

It was her last substitution. It happened before she found the final puzzle piece. She would substitute into the past, speaking to the younger me.

Whether I’ll be able to find the piece that was lost.

The next thing I saw was Urakawa-san from seven years ago, right around the time we met. The girl in her third year of elementary school. Her face was ever-expressionless. Her short haircut brought a wave of nostalgia from within me. But no matter how often I saw her, she always looked lovely.

She looked up at me. “Are you… Tsumiki?”

Yep. I was Tsumiki.

“Why are you staying silent?”

I gently shook my head. “Oh, nothing. I was just so taken by your beauty.”

The elementary schooler Urakawa-san slightly tilted her head. “Tsumiki. I’ve finally met you. The one in my actual time, who’s my age.”

“Mhm.”

“How old am I in the present time?”

“15.”

“Do we have a good relationship?”

“It’s the same as always. I’d say it’s good.”

Her outline began to fade.

“I’m glad to hear that,” Urakawa-san said, smiling. It was the completely natural and innocent smile of an utterly normal girl.

I unconsciously reached my hand towards her. Then, just as unconsciously, I stopped it.

The third-year elementary schooler disappeared, replaced by a first-year high schooler. “I was substituted by my third-year elementary school self, just as expected. I should not experience any more substitutions from here.” She whipped out her memo pad, mumbling, “No need to keep track any more.”

We entered the room.

The puzzle piece was right there, lying on the floor, as if it was meant to be there. It had picked up a bit of dirt and moisture, ending up slightly warped. But it was undeniably our white puzzle piece.

Urakawa-san reached out with her lovely fingers, picking it up and closely examining it.

I opened my mouth, finally saying what I had been holding back for her final substitution.

“I’m in love with you.”

It was the first time I had ever said that basic phrase.

She looked over at me with a light smile. “That was a bit more simple than I was expecting.”

“I thought about it for a long time, and I didn’t want to say anything that could be misinterpreted.”

“I am rather interested in you, too, Tsumiki. You may be somewhat callous to a number of things, but you are nonetheless always kind.”

“Then—”

“But.”

She interrupted me, then stayed silent for a while.

Then, with a quiet shake of her head, she slowly continued, “But seven years has been far too long. I know you too well, Tsumiki.”

But it’s been just as long for me.

Some part of my brain registered that she was continuing. “You wanted to find a way to keep me from disappearing. To somehow only remove my substitutions from the equation of this mysterious phenomenon. You assumed it must be possible, because I never switched places with anyone older than my current self.”

Of course it had to be possible. It just meant that you returned to being a normal girl. That’s the obvious conclusion.

“So you tried to figure out what it was that started the entire chain of events. That’s when you remembered what I told you the day we met.”

I am very unstable. You might say I am like a ghost.

I simply do not feel like I belong anywhere.

“Then, you concluded that you needed to create a place for me to belong. You chose to become the place that I needed.”

She was entirely right. Not a single detail was out of place.

“You are kind, Tsumiki. It doesn’t matter what you think of me, or whether I am truly special to you. You would profess your love for me regardless.”

“You’re wrong. I just want to be with you.”

“That is only a passing fancy. It is wasted on something fated to disappear.”

“You don’t know anything about how I feel deep down.”

“And you do? You truly understand yourself deep down?”

I should have just nodded. Confidently, without a single moment of hesitation, like it was a foregone conclusion.

But I couldn’t do anything.

“Three years ago, I vanished. It was as though I were substituted, but nobody came to replace me. I saw you, in a future that is probably even further away than now.” Urakawa-san’s white fingertips felt at her black hair stretching down her back. “You were holding some girl in your arms. The way you held her… it was as though she were the most precious thing in the world.”

I could hardly believe what I was hearing. “Did you see the girl’s face?”

“No. I couldn’t get a good look. Do you have any idea who it might be?”

“Not at all. The only person it could possibly be is you.”

“But if I existed there, I should have been substituted. It is not possible for two of me to exist at the same time.”

She couldn’t see herself when substituted. It had never worked that way before.

Urakawa-san smiled. It looked bright and cheerful, entirely unlike her.

“The obvious happened, just as it should have. If I’m gone, you can be happy.”

If there was one thing that I had ever believed in, it was that she couldn’t have been more wrong.