Numbed!

by David Lubar

45

  “And the other numbers—in the tens place—go up by one.” I could see that too.

  9

  18

  27

  36

  45

  “How does that help?” Benedict asked.

  “I’m not sure. But it means there’s a pattern.” I glanced at the timer. We’d used up a whole minute. I thought about the pattern. And I realized why it seemed familiar. When we first met Cypher, he’d been ranting about numbers. One of the things he’d said was 9 × 8 is 72. Add the 7 to the 2, you get 9 again. In each of the numbers on the floor, the digits added up to 9. I had a feeling that was true no matter how big the numbers got. If it went up on one side and down the same amount on the other, the total had to stay the same when you added the digits.

  “That’s it!” I scanned the walls so fast I got dizzy. “Look at the problems. In each one, there’s a multiple of nine.”

  “Yeah, I see 18—that’s 2 × 9. There’s 27. That’s 3 × 9. There’s even 72.” He moved like he was going to tap the wall by the 72, but I grabbed his wrist.

  “Be careful. We’re supposed to tap the problem with the wrong answer.”

  “Oops. That would be bad. Okay—so how does this help us?”

  I pointed to the first problem: 478 × 18 = 8,604.

  “Cypher was telling us about this. Look—if you add 8 + 6 + 0 + 4 in the answer, you get 18. Add the 1 and the 8 from 18 together, and you get 9. So that problem is correct. You start on the left wall. I’ll start on the right one. Add up the digits in the answer. If you end up with more than one digit, add those digits too. You should always end up with 9, so if you don’t, that’s the one we have to tap.”

  We got to work. I was amazed at how every time I added the digits in the answer, it led me to 9. It might add up to 18 or 27 or a higher number, first, but those digits added up to 9. I realized I could even stop as soon as I knew I had a multiple of 9. After a minute, I discovered another shortcut. If I saw two digits that added to 9, I didn’t even have to add them into the total. I could just cross them off in my mind.

  I started to really zip through the problems. Like this one:

  434 × 18 = 7,812

  I could see at a glance that I could toss out the 7 and the 2 on the outside, since they added to 9. The same with the 8 and the 1 in the middle. If I weren’t in danger of being trapped, I would have really been enjoying this.

  I realized a problem could still be wrong, even if the digits added to 9. They could scramble the digits in the answer. But that seemed like an unfair test. I just had to hope the test was fair. I finished the first wall. “How are you doing?” I asked Benedict.

  “I’m about halfway done,” he said.

  “I’ll do the back wall. Look for pairs you can toss out,” I added.

  If I could keep up my pace, we’d make it. But I was starting to get worried that I hadn’t found the error yet. I hoped I hadn’t missed it by mistake. There wasn’t enough time to go back and double-check anything. I’d just reached the bottom of the back wall when Benedict said, “I got it!”

  “Are you sure?”

  “I think it’s the one. Can you check it?”

  “Yeah.” As I was walking over, I saw that the timer was almost down to zero. “Er—no! Go ahead. Do it. We only have three seconds.”

  Benedict tapped the wall. “I hope I didn’t make a mistake.”

  I looked at the problem.

  72 × 388 = 27,136

  There wasn’t even time for me to add the numbers. But before the lock whirled open, I realized this was the problem we’d been looking for. The answer 27,136 was obviously wrong. The 7 and the 2 on one side added up to 9, and the 3 and the 6 on the other side also added up to 9. So the number in the middle, the 1, should have been a 9 or a 0.

  “I hope the next room is easier,” Benedict said as we walked through the door.

  “Me too.” There was a table in the middle, like in the very first room. But when I saw the walls, which were covered with twice as many math problems as the room we were leaving, I had a feeling it wasn’t going to be easier at all.

  CHAPTER

  4 × 25 ÷ (2 × 5)

  While my eyes were glued to the problems on the walls, Benedict ran over to the table and shouted, “Look—there’s a calculator.”

  “It can’t be.”

  “Sure it can.” He held it up. “This will be easy.”

  I saw that it had all the number keys and an Enter key, but no keys to add, subtract, or multiply. But it did have a Divide key. “That’s no good. Division won’t help us multiply.”

  I turned my attention to the problems on the walls. Each one had a screen and a keypad beneath it. The screens all showed 3:00. So we had to solve all the problems in three minutes. I looked at the ones to my left.

  84 × 25 = ?

  1,236 × 25 = ?

  52 × 25 = ?

  “They all use 25,” I said. “There has to be something special about it.”

  “Wingy Dingy has twenty-five flavors of hot sauce,” Benedict said. “And my Uncle Ralph just turned twenty-five. He had a big party at Wingy Dingy.”

  “I don’t think that’s going to help,” I said. “What else?”

  “I have no idea. We’re going to be stuck here. I wish I’d brought a candy bar. Maybe I have some gum.” Benedict shoved his hand in his pocket. Then his eyes got wide.

  “What?”

  “Quarters!” He pulled several coins from his pocket. “Numbers are one thing, but it’s easy to think about money!”

  “Right. A quarter is worth 25 pennies.” My brain rushed ahead of my mouth as I tried to say what I was thinking. Quarters, pennies, and dollars swirled around in my mind.

  It looked like Benedict was thinking the same thing. “There are four quarters in a dollar,” he said. “And there are one hundred pennies in a dollar.”

  Benedict was right—money was easy to think about. I was so used to looking at four quarters and knowing they were worth a dollar. I needed to try to think about numbers the same way. “Since 4 × 25 is easy to figure out, we just have to see how many fours we have in each problem.” I pointed at the calculator. “That’s division! We can use this.”

  I looked at the first problem: 84 × 25. If I had 84 quarters, how many pennies would that be? I pointed to the calculator. “What’s 84 ÷ 4?”

  While Benedict was tapping the keys, I realized I could do that one in my head, one digit at a time. I started on the left, just as I would on paper: 8 ÷ 4 = 2. Then I moved to the right: 4 ÷ 4 = 1. So 84 divided by 4 was 21. That meant that 84 quarters was worth 21 dollars, which was 2,100 pennies.

  I punched in the answer. The problem vanished from the wall, and the countdown timer on the screen was replaced by a check mark. One down, far too many to go.

  We had 2:13 on the other timers. “We have to split up,” I said. “That’s our only chance. You use the calculator, and do all the ones with big numbers. I’ll do the small ones.” I figured I could do most of the problems in my head.

  Benedict zipped around me, scooting from one problem to another, wiping out the longest ones. Each time, he punched in an answer, he shouted, “Score!”

  I discovered another shortcut as I was speeding along. Instead of dividing the number by 4, I could divide it by 2 twice. It gave me the same answer, and for some of the problems, it was easier to do in my head. It’s like, if you cut a pizza in half and then cut it in half again, you’re really dividing it into four slices.

  I had just finished the last of the easy problems when Benedict cried, “It’s too long!”

  I scanned the room and saw a sea of check marks. We’d answered almost every problem. Benedict was standing by the final one.

  364,812,328,416 × 25 = ?

  I looked at all those numbers. Then I looked at the timer. It was at 0:23. My stomach clenched like it had been divided by 4 a whole bunch of times, or divided by 2 a double whole bunch of times. There was no way I could solve that problem
without a pencil and paper.

  “We’re doomed,” Benedict said. “And this room doesn’t have a bathroom either.”

  I thought about everything we’d been through so far. “It won’t ask us to do things we can’t do. I know it won’t. It’s all been fair. I just wish I had something to write with.”

  “You do,” Benedict said, pointing to the keypad under the problem.

  “But that’s for the answer. No—you’re right.” I realized that the keypad wasn’t just for entering the answer—it was also for writing down the answer, keeping track of each digit. I didn’t need a pencil and paper. But I had to hurry. I only had seventeen seconds left.

  “It’s like when we do long division,” I said. “I just have to start at the left and work my way across.” I looked at the huge number again: 364,812,328,416. It was a lot longer than 84, but it worked the same way. All I had to do was break it up.

  364,812,328,416

  I started all the way to the left with 36. That was easy enough: 36 ÷ 4 = 9. I punched in the 9 and looked at the next digit.

  364,812,328,416

  It was a 4. Piece of cake. I punched in a 1.

  364,812,328,416

  Then I punched in a 2 for the 8.

  364,812,328,416

  The next number was trickier: 12 ÷ 4 = 3, but since I was skipping over the 1, I needed to put in a 0 before the 3. I punched in 03.

  364,812,328,416

  The same for the next pair: 32 ÷ 4 = 8. I punched in 08.

  364,812,328,416

  364,812,328,416

  364,812,328,416

  I raced through the rest, typing 2,104.

  I looked at my answer: 91,203,082,104. I’d solved the problem with six seconds left. I was about to hit Enter when Benedict grabbed my arm.

  “Wait!” he shouted.

  “Are you out of your mind?” I tried to yank my hand free.

  “You forgot the two zeroes at the end. It’s like 100 pennies. Remember?” He let go of my hand.

  “Wow. You’re right.” I quickly tapped 0 twice, then hit Enter.

  364,812,328,416 × 25 = 9,120,308,210,400

  The lock clicked open.

  “Wow,” I said again. “Good going. You saved us.”

  “Hey, when it comes to counting money, I don’t make mistakes,” he said. “Unless I’m numbed.”

  We staggered out. Dr. Thagoras was waiting for us. I wasn’t happy to see that Cypher had joined him. I guess the new wheels allowed him to go where he wanted.

  “Well done,” Dr. Thagoras said. “I was confident you boys would succeed.”

  “I still know more than you do,” Cypher said.

  “Yeah, but you’ll never be alive,” Benedict said. “You’ll never laugh at a joke. You’ll never even feel anything. I feel all kinds of things. Watch this, you hunk of metal.”

  Benedict pinched the back of his own hand really hard. “Ouch! That was a mistake.” He shook his hand and jammed it under his other arm.

  I could swear I heard Cypher chuckle. But I didn’t care. Getting multiplication and division skills crammed back into my head was exhausting. All I really wanted to do was go home and totally empty my mind for a while.

  “You don’t know everything,” Cypher called after us as we headed out.

  “Now, Cypher,” Dr. Thagoras said, “nobody knows everything. Even you should know that.”

  “I know one thing,” Benedict said. “We are totally acing that test tomorrow.”

  At that moment, I didn’t see any way he could possibly be wrong.

  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)

  As 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?”