Floor 3 - Archive (4)

**

The exact midpoint of the Archive’s catalogued collection.
As the Librarian guided me toward it,

“I am curious about your reasoning.”

he suddenly asked.

“Why are you searching for the book positioned at the midpoint?”

He didn’t know?
I shrugged.

“Have you ever heard the story about grains of rice on a chessboard?”
“Yes. It is a famous fable.”

[The Story of the Rice on the Chessboard]

Once upon a time, there was a kingdom whose king loved chess.
One day, the king lost to a wise man and found himself owing an enormous sum as payment for their wager.
Then the wise man said,

-If you would rather not pay me that enormous sum, then give me a single grain of rice. However, each successive square on the chessboard must contain twice as many grains as the one before it.

The wise man’s request was simple.
Place one grain of rice on the first square of the chessboard. Two on the next, four on the next, then eight, sixteen…
That was how he asked to be paid.
After thinking for a moment, the king readily agreed, believing it was nothing.
Just a few grains of rice.
He assumed rice would be far cheaper than paying a massive fortune.
But the kingdom was ruined because it could not afford the amount of rice required.

“A chessboard has sixty-four squares. Starting from a single grain of rice, the final square contains two to the sixty-third power. In other words…”

The Librarian continued.

“9,223,372,036,854,775,808 grains.”

He produced the number instantly like a calculator.

“Over nine quintillion.”

It was an absurd number. The mathematically ignorant king had accepted the request without understanding that and bankrupted himself.
Clearly, it must have been the Kingdom of Idiots ruled by Queen Han Gyeong-ah.

-W-Why?!

An image of Gyeong-ah staring at me in despair flashed through my mind.
Should’ve studied math harder.

“That’s what you call a geometric progression.”
“What does that have to do with the answer?”

The Librarian tilted his head. I almost wondered whether he knew perfectly well and was pretending not to.

“Think about it in reverse.”

One grain had grown into more than nine quintillion after sixty-three doublings. Turn the idea around, and…

“Even a ridiculous number like nine quintillion becomes one if you cut it in half sixty-three times.”

So imagine how few steps it would take with a much smaller number like 151,382. Interest appeared in the Librarian’s eyes.

“Oh. Binary search.”

Binary search.
An algorithm that finds the desired information by repeatedly dividing the search range in half.
Say you were trying to find a hidden number between one and one hundred.
First, you split the range at fifty.
Then you determine whether the answer lies above or below it.
If it’s below fifty, you split again at twenty-five… and if it’s above twenty-five, you split again around thirty-seven.
Keep repeating the process, and you can find the answer in at most seven attempts. That was the basic principle of binary search.

“And I’m applying that exact method here.”
“Indeed… even with approximately 150,000 books, binary search would allow you to narrow them down to a single volume in only eighteen questions.”
“You catch on fast.”
“However, there is a problem.”

The Librarian raised an objection.

“I do not know the answer. Even if you ask binary-search questions, I cannot provide meaningful information.”
I knew he’d say that. I answered dismissively.

“I’ve got a way. Just guide me properly.”
“…Understood.”

The Librarian nodded and led the way without further complaint. Eventually, he stopped in front of a bookshelf.
We had reached our destination.
The exact midpoint according to the Archive’s cataloguing order.

“Here.”

He pointed to one of the books on the shelf.

“This is the 75,691st book catalogued in the Archive.”
“You’re sure?”
“Of course.”

Only after receiving his confirmation did I pull the book from the shelf. It felt heavy in my hand.
The Librarian silently watched what I was doing. He seemed intensely curious about what would come next.
I faced him.

“You don’t know what the answer is.”
“Correct.”
“But you do know that there’s a way to clear the game, don’t you?”

For an instant, his expression stiffened slightly. As though I’d hit the mark, he pressed his lips shut.
The reason was simple.
He’d been giving me annoyingly useful advice all along. One example was:

-There is no need to overthink it. If you identify the key point, the game can be cleared.

At the time, I’d wondered why he was making such a big deal out of stating the obvious. But looking back, it was strange.

“Why would someone who doesn’t know the answer say something like that?”
“…”
“And you said you haven’t lied once during this entire game.”

The Librarian spoke only the truth, including when giving that advice. That created a contradiction.

“How can you know there’s a way to clear the game if you don’t know the answer?”

It was like solving every step of a quiz correctly while somehow not knowing the final answer.
It made no sense.
The premise itself had to be wrong.

“There’s only one way both things can be true.”
“And that would be…?”

I slowly answered.

“You told only the truth, but deliberately left information out.”

He didn’t lie. But that didn’t guarantee his words contained the whole truth. Their meaning depended on how the listener interpreted them.
It was a kind of narrative trick.
He’d hidden information inside the truth itself. The trick lay in his claim that he didn’t know the answer. I’d realized it because of one tiny detail.
I pulled out a book, and the Librarian’s eyes widened.

[Seven Ways to Prepare for Death]

“That is the book I recommended earlier.”
“Yeah… this damn thing actually helped.”

Truthfully, any book would have worked. This trashy book had simply happened to catch my eye while lying on the floor.
I pointed to a stamp printed between the closed pages.

“This.”

The Tower’s logo was stamped clearly there.
It resembled the kind of ownership stamp you’d see in a library or bookstore. It indicated that the book was catalogued in the Archive.
Every catalogued book here probably bore the same stamp.

‘…Except one.’

The Librarian knew the location of every book. Whenever I named one, he guided me to it as though he’d memorized the entire collection.
But there was exactly one exception. He claimed he knew nothing about the answer.
That could mean he didn’t know which book had been designated as the answer… but it could also be interpreted more literally.
My theory was simple.

“The reason you don’t know the answer… is because it isn’t a book catalogued in the Archive.”

He didn’t know the answer.
Put another way, there was exactly one book in the entire Archive about which he possessed no information.
The single uncatalogued volume that had never been formally registered. That had to be the answer.
That was the conclusion I’d reached.
In simple terms, Floor 3 contained 151,382 catalogued books and one uncatalogued volume.

“Well?”

“…”

He remained silent. It didn’t matter whether he answered.
I could verify my theory myself.
I checked the book I’d just removed.

‘He said this was number 75,691.’

The 75,691st book formally catalogued in the Archive.
What mattered was its physical position.
If the uncatalogued volume had been inserted somewhere before this point, then this book wouldn’t physically occupy the 75,691st position.
There would be an offset of exactly one book.

Clap-!

I clapped my hands sharply.

“All right. Here’s the question.”

I gestured toward the gap where I’d just removed the book.

“According to the Archive’s cataloguing order, is this the physical position corresponding to number 75,691?”

Silence stretched between us.
I’d been full of confidence moments earlier, but I couldn’t stop myself from tensing up. I was desperate.
Truthfully, I was cornered.
If this didn’t work, I genuinely had no idea what else to do.
I was standing at the edge of a cliff.

‘Please work…’

I anxiously waited for his answer. And then, for the first time, I saw it.

“No. That location corresponds to the 75,692nd physical position in the Archive.”

A faint smile crossed the face that had remained expressionless the entire time.

**

After that, seventeen more questions passed between us. Using binary search to halve the range again and again, I eventually narrowed it down to a single book.
At last, I stood before it.

“…No doubt about it.”

This was the answer I’d been searching for all this time. My heart pounding, I carefully pulled it from the shelf, and the Librarian immediately spoke up.

“What book is it?”
“Why are you asking me?”
“I have never seen it before either.”

Right. Of course he wouldn’t know…
I was curious too.
What kind of book had the Tower chosen as the answer?

[The One-and-Only Busybody]

A children’s story?
The title didn’t tell me much. When I opened it, every page was completely blank. There wasn’t even anything you could call content… It looked like an ordinary notebook.

“What kind of book is this…?”
“I was somewhat looking forward to it. How disappointing.”

What was there to be disappointed about?
Either way, I’d found the answer. My business here was done.
It was time to end the game.
I immediately closed the book and held it out to him.

“This book is the answer.”
“Is this your selection?”

He glanced at me.

“Once you decide, you cannot take it back. I advise you to think carefully.”

He continued with the formal warning. But after coming this far, I had nothing left to hesitate over.

“What else could it possibly be?”
“I recommend that you consider your choice more carefully. There are still twenty-two hours and thirty minutes remaining. As I have repeatedly stated, once you decide, you will never be able to take it back…”
“Don’t need it.”
“…Understood.”

I practically forced the book into his hands, and he reluctantly accepted it.
He really was talkative.

“By the way, I am impressed. I suspected as much when you arrived on Floor 3 alone, but you are no ordinary person.”
“What is that supposed to mean…?”
“It is a compliment. You need not hide your delight.”
“Getting complimented by someone like you doesn’t make me happy at all.”

The meaningful look in his eyes made me uncomfortable.

“Setting aside the idle chatter, I will now verify whether your selection is correct.”

Floor 3’s game had reached its final stage. All that remained was the result.
The Librarian opened the front of his shirt and slid the book into the hole in his chest.
It was just as unpleasant to watch as before.

“…Could you turn around when you do that?”
“I will correct my behavior.”

The moment he inserted the answer, there was a click, and the entire Archive began to shake.
It was similar to what had happened when the game began.

Rumble-!

The bookshelves shook violently.
The floor bucked like a Disco Pang Pang¹ ride, making it hard to stay on my feet.
Even amid all that, the Librarian stood perfectly straight and spoke.

“I will now announce the result of the Floor 3 game.”

He was really drawing out the suspense when there was no reason to.

“Pass. You pass. Congratulations.”

The system announced the end of the game. The twist was that there was no twist.
I’d still been tense just in case, but the moment I saw the message, my worries melted away.

“Whew…”

It was over.
I’d finally done it.
I’d cleared Floor 3’s game all by myself. I barely had time to celebrate surviving before the Librarian continued in his usual flat tone.

“With this, Floor 3 has been cleared. From this point forward, the floor will be fully open, allowing participants to enter and leave whenever they wish. As it contains a great many books, it should be suitable for passing the time.”

He clapped mechanically, apparently as a gesture of congratulations.

“I will also remain here as the Administrator, so if there is anything you wish to know, please visit at any time.”
“Don’t worry. I’m never coming back.”

I waved him off.
Like hell I was ever coming back here.
I’d nearly spent eternity trapped in this hell of printed words, unable even to die.
The sight of books alone was enough to make me shudder now. A chill ran down my spine. And with that, Floor 3’s game came to an end.

“Then I look forward to seeing you again.”

Just as he had at the beginning of the game, the Librarian pulled the bell from inside his clothes.

Chime-!

The clear, crystalline chime lingered in my ears as I escaped the Archive.

**

**

When I came to, I was inside the elevator.
Just like last time. I’d safely escaped Floor 3.

“I survived…”

Relief swelled in my chest at the realization that I was alive. The doors slowly opened, revealing the Hotel beyond.
And the first thing waiting for me upon my return to Floor 1 was,

“You bastard!”

Kang Se-rim’s affectionately delivered kick.