Numbed! (4 page)

CHAPTER
2 × 2 × 2

I
t worked. Benedict went sprawling.

“Hey!” he screamed when he got back to his feet. “You tripped me!”

“It was an accident.” I shot to my feet. “I was stretching. You should look where you're going.”

“You should keep your big feet under your desk.”

“They're not as big as your head.”

Benedict let out a roar and tackled me. We went rolling across the floor.

“Boys!” Ms. Fractalli shouted.

Benedict and I sprang apart.

“Go to the office. Both of you.”

“That was fun,” Benedict said when we got into the hall. “Did it look like I really tripped?”

“Totally.”

“Good thing she doesn't know we play like that all the time.”

“Yeah. I hope we didn't scare her too much.” I knew Benedict wouldn't get hurt when I stuck my foot out. We play lots of games that involve pretend pushing, tripping, falling, and shoving. We just don't usually play them in the classroom. “Do you think we're in a lot of trouble?”

“No. We'll just get a lecture,” he said.

He was right. I guess Principal Chumpski could tell that Benedict and I were friends and that the whole thing had been an accident followed by a misunderstanding.

We were warned and released.

We got back to the classroom just in time to miss the whole math lesson. Ms. Fractalli called us to her desk after the bell rang.

“I expected better behavior from you,” she said.

“We're sorry,” I said.

“Really sorry,” Benedict said. “But we made up, and we learned a valuable lesson.”

I kicked his foot to stop him from going too far. Ms. Fractalli seemed satisfied. She smiled, went to her cabinet, and reached into her pocket. The smile turned into a frown. “I seem to have misplaced my key,” she said.

“I'll look.” I hunted for a moment and then lifted the marker. “Found it!”

“Thank you, Logan,” she said. “It's a good thing the principal didn't make you stay in his office. Well, I hope both of you are ready for the math test.”

“We're totally ready. Math is all we've been thinking about,” Benedict said.

Ms. Fractalli gave Benedict a funny look. I dragged him out of the room before he said too much.

After school, we took a bus right to the museum. Dr. Thagoras wasn't in his lab, but Cypher was. The robot rotated its head toward us.

“Uh-oh,” Benedict said. “I don't want to get zapped again.”

Neither did I. I didn't trust the robot. But I knew what it was built to do. If I could keep it busy, it wouldn't hurt us. So I asked it a question. “Cypher, can you tell me about zero?” I remembered there was an exhibit upstairs about that.

That did the trick. Cypher started talking. About five minutes later, Dr. Thagoras walked in. “Ah, it's my two new math fans. You realize you ran out of here yesterday without all the skills you needed?”

“We sort of figured that out,” I said.

“Can you fix us?” Benedict asked.

“I believe so,” Dr. Thagoras said. “You'll have to go into the Repetition Room. It will restore your multiplication and division abilities.”

He led us down the hall to the matheteria. When he opened the door to the Repetition Room, we saw a second door at the other end. “This time, there are two rooms to go through,” he said.

“Why?” Benedict asked.

“Numbers like patterns,” Dr. Thagoras said. “So do mathematicians. In you go.”

We walked through the first room into the second. “Good luck, boys,” Dr. Thagoras said.

The door closed. Math flooded back into our heads in swirling numbers. I looked around. The far wall, opposite the door, and the walls on both sides were covered with multiplication problems. Tons of them.

“This can't be good,” Benedict said.

CHAPTER
9 × 9 × 9 ÷ (9 × 9)

L
ike before, there was a small screen in the door. This time, there was no keypad. But there was a message on the screen:

A counter popped up under the message.

“You're kidding!” Benedict screamed. He spun around, as if trying to find the best place to start or maybe to drill his way out of the room.

“Calm down. It won't give us a test we can't pass.” I noticed there wasn't any pencil or paper. I was pretty sure I wouldn't be able to do most of the problems in my head. I walked to the back wall and looked at the problems in front of me. The first four were right at eye level:

478 × 18 = 8,604

27 × 135 = 3,645

9 × 18726 = 168,534

58 × 72 = 4,176

“Think,” I said to Benedict. “There's no way we can check them all out by doing the math. Not in …” I glanced at the timer, “four minutes and forty seconds. So, how else can we check them?”

“I know I've said this before,” Benedict said, “but WHY ARE YOU ASKING ME?”

I sighed and let my head slump forward. There were numbers on the floor. I saw a huge 9 by the door. Stretching out from that, crossing the floor, I saw:

18

27

36

45

54

It was multiples of nine. There was something familiar about that. I stepped back so I could see all of them. “Look,” I said to Benedict, “do you see what's happening with the numbers?”

He moved next to me and looked down. “Why are you asking—wait! I see it. The numbers on the right go down one at a time.”

“You got it.” I could see it in my mind.

  
9

1
8

2
7

3
6

4
5

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

  9

1
8

2
7

3
6

4
5

“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)

W
hile 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.

36
4,812,328,416

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.

36
4
,812,328,416

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

364,
8
12,328,416

Then I punched in a 2 for the 8.

364,8
12
,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,
32
8,416

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

364,812,32
8
,416

364,812,328,
4
16

364,812,328,4
16

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.