The Rampage of Haruhi Suzumiya (18 page)

If Koizumi was worried in any way, he was doing a good job of hiding it.

“I am positive that this is the key to our escape. Most likely courtesy of Nagato.”

I checked to see if it said
COPYRIGHT
©
BY YUKI NAGATO
on the panel anywhere. It didn’t.

“This is merely conjecture, but I believe that Nagato’s power is limited in this space. Now that her link with the Data Overmind has been severed, she can only rely on her innate abilities. That would explain the haphazard means of escape.”

You’re making a lot of sense for mere conjecture.

“Yes, I suppose. The ‘Agency’ has made contact with other interfaces aside from Nagato, so I happen to have access to certain information.”

I was interested in hearing about these other aliens, but there wasn’t time for that right now. We needed to deal with this weird puzzle first. I was looking between the symbols on the panel and the numbered blocks in the wooden box when I remembered something Nagato had said in her flat voice.

“This space is putting strain on me.”

I didn’t know the identity of the person who had led us into this mansion in the middle of a blizzard, but I wasn’t going to forgive whoever was responsible for Nagato’s getting a fever and passing out. I wasn’t about to go along with that little puke’s plans. I was ready to do whatever it took to get out of this place and back to Tsuruya’s vacation home. Accompanied by every single SOS Brigade member, no exceptions.

Nagato had done her job. I couldn’t see or hear her handiwork, but I was certain that she’d been fighting this invisible “enemy” from the second we stepped into this alternate space. That was probably why she looked more out of it than usual. As a result, she was able to create this small opening as she collapsed. Now it was our turn to open the door.

“Let’s bust out of this joint.”

Koizumi responded to my proclamation with an easy smile.

“Of course, that was the plan. This place may be comfortable, but I wouldn’t want to stay here forever. Utopia and dystopia are merely two sides of the same coin.”

“Koizumi.”

My voice was so serious that I surprised myself.

“Can you use your ESP to open a hole? The situation’s looking bad. With Nagato the way she is now, you’re the only one who can do something about this.”

“You are overestimating my abilities.”

Koizumi was still smiling, despite our current predicament.

“I do not recall ever saying that I am an omnipotent esper. My powers only come into play under certain conditions. You should be aware of that fact by—”

I didn’t bother listening to the rest of his sentence. I grabbed Koizumi by the collar and pulled him over to me.

“I didn’t ask for your excuses.”

I glared at Koizumi and that cynical smile of his.

“Don’t you specialize in alternate space? Asahina can’t be depended on, and Haruhi’s out of the question. There must be something you can do, like with the cave cricket. Or is your ‘Agency’ made up of a bunch of useless losers?”

I would also be a useless loser in this case. There was nothing I could do. I couldn’t even keep my cool, which probably placed me below Koizumi. The only idea I could come up with was to beat the crap out of Koizumi, and then have him beat the crap out of me. Since I wouldn’t be able to beat the crap out of myself without holding back.

“What are you doing?”

A sharp, irritated voice stabbed into my back.

“Kyon, what’s going on with those ice bags? You were taking forever so I came down to check on you and what? You’re sparring with Koizumi? What are you trying to do?”

Haruhi was standing at full height with her hands on her hips. The look on her face reminded me of an old man in my neighborhood who managed to catch a chronic persimmon thief red-handed.

“Could you be more considerate of Yuki? There isn’t any time for you to play around!”

If Haruhi was interpreting this exchange between Koizumi and me as “playing around,” her mind was clearly elsewhere. I released my grip on Koizumi and picked up the ice bag from the spot on the floor where it had fallen while I wasn’t paying attention.

Haruhi quickly took the bag from me.

“What is this?”

Her gaze shifted to the odd equation on the door. Koizumi straightened his collar as he replied.

“Indeed, the two of us were wondering the same thing. Do you have any ideas?”

“Isn’t that Euler?”

I was thrown off by Haruhi’s instant response. Koizumi continued.

“You mean Leonhard Euler? The mathematician?”

“I don’t know his first name.”

Koizumi looked back at the puzzle panel on the door for a few seconds.

“I see.”

He snapped for dramatic effect.

“Euler’s polyhedron theorem. This must be a variation of that. Suzumiya, I am amazed that you were able to recognize this.”

“I might be wrong. But the
D
is probably where you put the number of dimensions. I’m guessing.”

Let’s not worry about whether you’re right or wrong. I have a much more obvious question that needs to be answered first. Who is Euler and what did he do? What is a polyhedron theorem? Did we learn about this in math? Though I was hesitant to ask all of these questions, since I was always half-asleep during math class.

“No, this usually doesn’t come up in high school math courses. However, I’m sure that you’ve heard of the Seven Bridges of Königsberg.”

That I know. That was one of the puzzles math teacher Yoshizaki mentioned during class. You have two islands connected to the mainland by a number of bridges and you have to cross all of them once and only once? I remember that there isn’t a solution.

“Yes.” Koizumi nodded. “The problem was originally formed on a flat plane, but Euler proved that it also applied to a three-dimensional plane. He formed a number of famous theorems, and this is one of them.”

Koizumi explained.

“His theorem states that when you look at a convex polyhedron and take the number of vertices plus the number of faces minus the number of edges, you will always end up with two.”

“…”

Koizumi must have recognized my desire to abandon anything related to math as he smiled wryly and slid one arm behind his back.

“Then I shall use a simple diagram to explain.”

He took out a black felt-tip pen. Where’d that come from? Had he been carrying that around on him? Or did he use the same method I had used to obtain the ice bag?

Koizumi knelt down on the floor and began to cheerfully draw on the red carpet. Neither Haruhi nor I even moved to stop him.

In this mansion drawing on the furniture, floors, or walls was clearly not a problem.

Eventually, he produced a picture of a dice-like cube.

“I’m sure that you can see this is a regular hexahedron. There are a total of eight vertices. It has six faces, as the name would tell you. And there are twelve edges. Eight plus six minus twelve equals two…yes?”

Koizumi must have felt that wasn’t enough, as he drew a new diagram.

“Now we have a square pyramid. Count and you’ll find there are five vertices, five faces, and eight edges. Five plus five minus eight will also yield an answer of two. You could apply this formula to any polyhedron up to a hectohedron with a hundred faces and the answer will always be two. This would be Euler’s polyhedron theorem.”

“I see. I understand now. But why did Haruhi mention the number of dimensions?”

“That is also quite simple. This polyhedron theorem is not limited to three-dimensional objects, as it can also apply to two-dimensional planes. However, in that case vertices plus faces minus edges will consistently yield an answer of one. This form of the theorem can be applied to the Seven Bridges of Königsberg.”

A new doodle appeared on the carpet.

“As you can see, this is a pentagram. A star that can be drawn in one stroke.”

I did the counting myself this time. There were one, two…ten vertices. It had…six faces. The number of edges would be the highest at, uh, a total of fifteen. Which would give you the equation ten plus six minus fifteen, and the answer was—one.

By the time I finished running those calculations in my head, Koizumi had finished drawing a fourth diagram. This one looked like a failed attempt at the Big Dipper.

“The theorem also applies to such irregular figures.”

I was starting to get sick of this, but I did the math anyway. Uh...seven vertices, one face, and seven edges? I see, you still get one.

Koizumi smiled brightly as he replaced the cap on the felt pen.

“In other words, the answer for a three-dimensional object will equal two and the answer for a two-dimensional plane will equal one. With that in mind, let us return to the formula before us.”

He used the pen to point to the panel on the door.

“
X – y = (D – 1) – z.
Let us assume that
x
refers to the number of vertices. We can then assume that
y
, the variable being subtracted, is the number of edges. The
z
, or number of faces, is more difficult to discern, as it was shifted to the right side of the equation and consequently had its sign reversed. As for the
(D – 1)
, the difference should equal two for a polyhedron and one for a flat plane, which means that
D
would be three when dealing in three dimensions and two when dealing with two dimensions. Thus, the
D
refers to the number of dimensions.
D
for ‘Dimension.’ ”

I listened to him in silence and concentrated on thinking. Yeah, I think I more or less understand now. I see. So this is the theorem thing Herr Euler came up with.

“So?”

I posed this question.

“What’s the answer to this math quiz? Which numerical blocks do we use for
x
,
y
, and
z
?”

“Well.”

Back came Koizumi’s answer.

“I don’t know. Not without the original polyhedron or plane as a reference.”

There’s no point, then. Where are we supposed to find the original figure?

Koizumi merely shrugged, which only added to my irritation.

However, that was when something happened.