Numbed! (5 page)

CHAPTER
1 + 2 + 3 + 5

I
felt great that evening. After dinner, I helped Kaylee with her math homework. It was cute watching her draw a circle around the bigger number in each pair. Her homework involved a lot more coloring than mine.

The next day, when it was time for math, Ms. Fractalli wrote 85 on the board. “This is the lowest average I will accept,” she told us. “I'd be much happier if it comes out closer to this.” She wrote 100. “But if the average score is at least 85, you will get ice cream sundaes.”

I looked over my shoulder at Benedict, pointed at my chest, and mouthed the words
one hundred
.

Benedict tapped his chest and mouthed
110
.

I gave him a puzzled look. “Extra credit,” he whispered.

I didn't know whether there'd be any extra credit problems, but I knew I was ready to blast through whatever our teacher threw at us. I was a flawless math machine, a fearsome number cruncher, and a tireless human calculator. Nothing could stand in my way.

I was so eager to start that I almost snatched the test right out of Ms. Fractalli's hand when she reached my desk. I already had my pencil clutched and ready.

Zip! I blew through the addition problems.

Zap! I knocked off all the subtraction.

Zim! I destroyed the multiplication.

Zoom! I shattered the division.

Huh? I stared at the next section.

After the regular arithmetic problems, I found myself facing this:

Tyler has seven pets. Some are chickens, and some are hamsters. If Tyler's pets have a total of eighteen legs, how many chickens does he have?

Uh … What … ?

I looked at the clock. My math skills and the shortcuts I'd figured out had let me knock off the first part of the test in record time, even after I'd double-checked each answer. But I had absolutely no idea how to solve this problem. I couldn't even start to think about it. I was pretty sure, before I'd been numbed, I would have been able to figure it out. But something was missing from my mind.

I read the next problem.

Maria has five shirts, two pairs of pants, and three pairs of shoes. How many possible outfits can she put together?

I let out a small moan. I should have been able to figure this out. But like with the first problem, I couldn't even think about any way to come up with a solution.

The next problem was no better:

Oliver has 50 feet of fence. He wants to make a rectangular garden. One side will be 12 feet long. How many square feet will the garden have?

It might as well have asked me to guess Oliver's middle name or his favorite kind of pie. I was totally clueless. I read the rest of the problems. I had no idea how to do any of them. I risked a glance back at Benedict. He was staring at his test like the paper had turned into a kidney.

The bell rang. We handed in our tests. “Did you get stuck?” I asked Benedict as we walked away from Ms. Fractalli's desk.

“It was way worse than being stuck. I was totally numbed.”

What was going on?
I glanced at the board, with the 85 on it. I tried to guess whether my total failure and Benedict's with the word problems would bring the class average below that number. It made me feel worse when I realized I didn't even know how to figure that out.

Ms. Fractalli was walking toward her locker. “If we ever needed to get on her good side, this is the time,” I whispered to Benedict.

I waited until Ms. Fractalli realized she didn't have her key. Then I hunted around and found it where she'd left it, between two pages in the big dictionary.

“What's going on?” Benedict asked me as we left the school. “I thought we weren't numbed anymore.”

“I don't know. But I hope Dr. Thagoras does. We'd better get to the museum right now.”

CHAPTER
(2 × 3) + (3 × 2)

A
s soon as we reached his lab, I told Dr. Thagoras about the test.

“Oh, dear,” he said. “I was afraid of that.”

“Afraid of what?” I asked.

“There's a lot more to mathematics than just arithmetic,” he said. “I was hoping you hadn't lost anything except your ability to perform basic calculations, but it appears you were very deeply and thoroughly numbed.”

“I told you,” Cypher said. “You don't know everything.”

“Be nice,” Dr. Thagoras warned the robot.

“What else is there?” Benedict asked.

“My word, that's an excellent question.” Dr. Thagoras scrunched his forehead for a moment. His eyes darted back and forth as if he were watching a grandfather clock. Then he started listing things. “There are dozens of concepts and skills. Reasoning, estimation, rounding, exponents, logarithms, and lots more. Then there are the fields of math. Algebra, calculus, set theory, geometry, trigonometry, game theory, statistics, topology. It's almost endless.” He chuckled and then added, “I was about to say it is infinite. But that is such a misused concept.”

I stared at him for a moment before I spoke. “I'll never get all of that back, will I? Part of me will be numbed forever?”

“There might be one chance,” Dr. Thagoras said. “You need to do something that allows you to grasp all of math, inside and out …”

“What are you talking about?” I asked.

He pointed to the wall behind him. “The ring on the outside was built before I started working here, so I don't know a whole lot about it. It's hollow. It was intended as an exhibit, but people found it far too confusing. I think you have to travel the Mobius loop, all the way around the inside of the ring.” He got up from his stool and rushed down the hall. “This way.”

We followed him back to the matheteria. He pointed at the far end, to the door marked Maintenance.

“What's this about a loop?” Benedict asked.

“I assume you failed to watch the video in the lobby.” Dr. Thagoras thumped the door. “As you may have noticed, the outer ring has a single twist in it. This makes it into a unique shape. If you put your hand on a wall and started walking, you'd have to go all the way around twice before you got back to where you started.”

“I don't get it,” Benedict said.

“Try it yourself with a strip of paper, sometime,” Dr. Thagoras said. “Give one end a half twist. Then tape the ends together in a loop. That's called a Mobius strip.”

Unlike Benedict, I had seen part of the video. But I still didn't see how a twisted strip of paper was going to help get us out of this mess.

Dr. Thagoras opened the door. Blue light spilled into the room.

“Wait.” I looked over at the Give and Take and Repetition doors. When we'd gone into those rooms, we'd been in danger of getting trapped. Those had just been small rooms. This was a whole loop. “What's the risk this time?”

“I'm not sure,” Dr. Thagoras said. “Nobody has ever done this.”

“Trapped,” Cypher said. “You'll be trapped forever.” He laughed again.

“He's joking, right?” I asked.

“He's not programmed to joke,” Dr. Thagoras said.

“Maybe we should just go home,” Benedict said. “I mean, we can do arithmetic. That should be good enough.”

“Remember when you thought we didn't need any math at all?” I said. “That didn't work out very well for us, did it?”

“I guess not,” he said.

“Giving up now won't work either,” I said. “We have to go.”

“You're right,” he said. “But why worry? There's nothing that can stump the two of us.” He turned toward the open door and said, “Bring it on, Mobius. We're ready for you.”

I started to go inside and then looked back. “Any idea how many problems there will be?”

“Well, you had one problem the first time and then two the next time,” Dr. Thagoras said. “What do you think comes next?”

“Three?” I guessed.

“Possibly. But I think four might be more probable,” he said. “Remember, numbers like patterns. Starting with 1, you double it to get 2, and when you double 2, you get 4.”

“It's a good thing this is the last time,” I said. “I wouldn't want to go into a place with eight problems.”

Benedict and I entered the loop. “I hope there aren't any more timers,” he said.

Dr Thagoras closed the door behind us. Numbers and symbols flooded back into my brain, along with other things I couldn't identify. Some were just squiggles. Others looked like Greek letters. Suddenly, I knew how to solve those problems from the math test about pets, clothing, fences, and all of that stuff. Too bad I wouldn't get a second chance.

We were in a low, narrow corridor. It seemed pretty square—the floor was as wide as the walls were high. I guess we were inside the ring. There was a steel door blocking the path to the left, so we headed to the right. There was just enough light to see where we were going.

“Do you understand this twice-around thing he told us about?” Benedict asked.

I thought about the video, with the guy drawing a line on the side of the strip. It still didn't make much sense. “Not really. I hope it isn't on the test.” I looked down as I walked. “Cool.” My footsteps left green glowing marks on the floor, showing me where I'd been.

There was a slight tilt to the walls and the floor. The farther we walked, the more we leaned sideways. After a while, everything tilted so much, the left wall became the floor and the ceiling became the left wall.

That's when we reached the first problem. There was a door ahead of us, with a keypad and a screen. Actually, there were two screens. One was lit. The other, above it, was upside down and dark. I read the question on the lit screen:

The keypad had two keys, labeled Cube and Sphere. We'd learned about area in math and had started to learn about volume. “Do you know how to figure out the volume of a sphere?” I asked Benedict.

“It's something with pi, right?” Benedict said.

“Yeah. But there has to be another way to figure this out.” I pictured the cube. It didn't matter whether it was one inch or a million inches. I just had to picture a sphere the same size.

“Got it!” I said as the image in my mind gave me the answer.

“Me too,” Benedict said.

I tapped Cube. The sphere would fit inside the cube, so it had to have less volume. I saw another way to think about it. If I started with a 50-inch-tall cube, I'd have to carve parts of it away to make a 50-inch-tall sphere.

“That was easy. We're one-fourth finished,” Benedict said.

“Right. But if we miss any of the four, we're ­totally finished.” I opened the door and kept walking. Once again, our right wall gradually became our floor. As soon as we got to the point where the floor felt level, we reached the next door.

And once again, there were two screens. I saw a problem on the lower screen and a keypad below it, with numbers, an Enter key, and a % key.

Benedict read the problem out loud:

“How are we supposed to figure that out?” I said.

Benedict pulled a coin from his pocket. “I'll start tossing. You keep track until we hit 5,000. It's a good thing there's no time limit.”

“I don't think that's how we find a solution,” I said.

Benedict flipped the coin and let it land in his open palm. “I guess you're right. Besides, it's not the same coin as in the problem.”

“That's it!” I grabbed his wrist and pointed at the coin. “You're right—it
isn't
the same coin.”

He stared at his palm. “It doesn't matter which coin we toss, does it?”

“It's a brand-new toss. That's the answer. It has nothing to do with what happened before. Five thousand tosses, five million, it's the same. All we need to know is the chance of heads on the next toss.”

Benedict turned the coin over. “Two sides. Two ways it can land. So it's one out of two.”

“Yeah, 50 percent. Go ahead. You do it.”

Benedict put in the answer. “That's two,” he said. “We're at 50 percent.”

“Just like the coin.” I opened the door and walked through.

“Wow,” Benedict said. “Look at that.” He pointed at the ceiling.

“Yeah, wow.” I saw footprints up there, leading away. We'd started our loop on the other side of this door. Except the ceiling had become the floor as we moved through the twist. One more loop and we'd be back at this door for the final problem. I was beginning to understand what was so special about this Mobius loop.

Once again, we went halfway around before we came to the next door. Actually, I realized, it was the lower half of the first door we'd come to in the loop. The part that had been the ceiling then, halfway through our first time around, was now the floor, halfway through our second time around. Every time we went halfway around the loop, the walls and floor made a quarter turn.

The keypad under the lit screen had two buttons. One was marked with an A. The other had a B. I read the problem on the screen:

“That sounds like an easy choice,” Benedict said. “I mean, one penny to start. How much could that end up being?”

“It could be a trick,” I said.

“Or a double trick,” Benedict said. “They make it sound wrong so you'll think it's right, but it's really wrong.”

“It could be a triple trick,” I said. “Or even a quadruple one.”

“Oh, no, I hadn't thought of that.” Benedict backed away from the door.

I didn't really think it could be a triple trick, but I couldn't resist seeing how Benedict would react. “Come on—let's stop guessing and figure it out.”

I wondered how hard it would be to keep track of doubling the money and also adding in the total for each week. “I'll do the doubling, and you add it. Okay?”

“Go for it.”

“Week one, 1 cent.”

“One,” Benedict said.

“Week two, add another 2 cents.”

“And 1 + 2 = 3,” Benedict said. “This is easy.”

“Week three, add 4 cents.”

“Then 3 + 4 = 7.”

“Week four, add 8 cents.”

“Then 7 + 8 = 15. It's almost a month, and it's nowhere near a dollar, yet,” Benedict said. “And the other way, we'd get $365. That has to be the right answer.”

“Hold on. I want to be sure. Where was I? Oh yeah. Week five, add 16 cents.”

“That's … I lost track,” Benedict said. “Let's start over.”

“No. I don't think we have to. I guess 15 cents isn't very much, after four weeks. But it's still
fifteen times
more than we started with. I think the amount is going to grow so big that the answer will be obvious, even if we don't bother adding the totals. Let's start doubling, and see what we get.”

I held up my fingers, one at a time, to help me keep track: “1, 2, 4, 8, 16, 32, 64, 128.” I looked at my hands. We'd finally passed a dollar on the eighth week. I kept going.

“Then 256.” I paused for a second, wondering whether I could do the next one in my head. But I saw that I could ignore the 6 at first and just double the 250. That was easy—250 doubled was 500. Double the 6 and add it back in, and the result was 512.

I kept going. “Next is 512.” I had all ten fingers up now. I nodded at Benedict, who took over with his fingers as I counted. But I didn't think we'd need to go much further. We were already up to $5.12 on the tenth week.

“Then 1,024. That's $10.24. Then 2,048. That's $20.48.”

“Wow, that's already way more than $7 a week, which you'd get if you took a dollar a day,” Benedict said. “We're only at the twelfth week, and we're not even adding up the total from each week. You're right—it's going to get huge.”

I could have stopped right there, but I was curious. Rounding the $20.48 to $20, just to make the math easier, the weekly payment would grow to $40, $80, $160, and so on. And that was just the fifteenth week. I had no idea how much it would be at the end of a year, but I had a feeling it would take a long time to even write the number.

“I guess it really was a double trick,” I said.

“Yeah, the trick is to try to double your money as often as you can,” Benedict said.

I pressed B on the keypad.

The door swung open.