Numbed! (6 page)

“Last one's up ahead,” I said.

“We're ready.”

“I hope so.” I was proud of how well we'd done, but I had a feeling the final problem might be four times harder than any of the others.

We walked along the second half of our second pass through the Mobius loop. We were now looking at the bottom half of the second door. We'd already done the problem on the top half during our first pass through the loop, when we'd been walking on the ceiling.

There was a screen. But there was no ­problem. Instead of a keypad, there was a whole keyboard. I hadn't noticed that before, in the darkness.

“Welcome to infinity,” a familiar voice said. “You have this much time to solve the problem.”

Numbers started streaming across the screen, flowing faster and faster until they were a blur.

“I'm starting to not like this,” Benedict said.

I didn't like it, either. I sort of knew what infinity was, but I didn't think I really understood it.

“You can solve the problem or remain in this infinite loop,” the voice said.

“What's the problem?” I asked.

“A hotel has infinite rooms, each of which can hold only one guest. Every room is filled. So the hotel also has infinite guests. Do you understand, so far?”

“Yeah,” I said. That didn't seem too hard to imagine, as long as I didn't think about it too closely. The rooms went on and on forever.

“I'm getting an infinite headache,” Benedict said.

I shushed him and waited for the rest of the problem.

“Infinite more guests show up. How can you find rooms for all of them without asking any of the current guests to leave?”

“What?” I asked.

The voice repeated the question. Then it added, “Take your time. You are allowed to make infinite guesses.”

Benedict stepped past me and typed:
Build more rooms
.

“Wrong,” the voice said.

Benedict stepped away from the keyboard. “Well, that was the best I could do. Any ideas?”

“Not yet. But we've solved every problem. And we've done it using things we've known. We have to be able to do this one. What do we know about infinity?”

“It's big?” Benedict guessed.

“Yeah. But it's more than big. It's endless.”

“Let's try that,” Benedict said. He typed:
Put all the new people at the end, after the guests who are already there
.

“Wrong,” the voice said. “There is no end to an infinite number of rooms already filled with an infinite number of guests. Nice try. Go on. You have infinite guesses remaining.”

“Forget it!' Benedict said. “This is a trap. Dr. Thagoras and his robot want the two of us to stay here forever. I never did trust the two of them.”

“Two …” I said. I thought about everything I'd learned or discovered about numbers and patterns and binary robots. “I have an idea.” I wanted to think about it for a minute, because I wasn't sure how to write it out.

“Oh, man,” Benedict said. “Having infinite time is worse than having a limit. The other way, it's over quickly. That's why they yank loose teeth. This way, you can suffer forever.”

I went to the keyboard. Even though I was still sort of fuzzy about infinity, I felt I had a good idea of how to solve this problem. There was someone in every room. If we moved everyone up to the next room, putting the person in room #1 into room #2, putting the person in room #2 into room #3, and so on, it would just empty the first room. That wouldn't give us infinite rooms. But if we moved everyone at once, that would do the trick.

I typed my answer:
Move each current guest into a room with twice as large a room number.

“Huh?” Benedict said, looking over my ­shoulder.

“You put the person in room #1 into room #2, the person in room #2 goes into #4, the person in #3 goes into #6, and so on. You free up infinite rooms.”

I could actually picture it. The infinite current guests would go into infinite even-­numbered rooms. The infinite new guests would get the infinite odd-numbered rooms.

Guest in room: 1 2 3 4 5 …

Goes into room: 2 4 6 8 10 …

Freeing up room: 1 3 5 7 9 …

“That would never work,” Benedict said.

Before I could argue my point, the voice said, “Correct.”

The door swung open. We walked through and saw the very start of our footstep trail right in front of us. “We did it,” I said to Benedict. “We finished the Mobius loop.”

“Yeah, we did.” Benedict looked like he couldn't believe it. “What are the odds of that?”

I shook my head. “I don't even want to think about it.” I opened the outer door.

“Congratulations!” Dr. Thagoras said. “That should fix the problem for good, unless you find another way to get numbed.”

“Thanks,” I said. “I don't think you have to worry about that. We aren't planning to have any more conversations with robots.”

Benedict walked over to Cypher. “Hold on. I have one more thing to say to you.” He poked the robot in the chest. “Numbers are—”

“No!” I shouted.

“Awesome,” Benedict said. “I love numbers.” He leaned over and gave Cypher a hug.

Cypher said, “One plus one is two.”

I dragged Benedict away from his new pal, and we headed out of the museum.

“Now, we just have to survive one more thing,” he said.

“What's that?” I asked.

“Getting our math tests back tomorrow. That's not going to be fun.”

“Not fun at all,” I said. I could already imagine the look of disappointment in Ms. Fractalli's eyes.

CHAPTER
52 ÷ 4

^“
Y
ou really better watch where she puts her key,” Benedict said when we got to the classroom. “We're going to need every little bit of help we can get.”

“For sure. And she's not the only one who isn't going to be happy.” I looked around at a room full of classmates who were probably already trying to decide whether to go for hot fudge or butterscotch. “Everyone's going to be angry with us when they figure out who ruined the average.”

My hopes drooped even lower when Ms. Fractalli walked into the classroom. She unlocked the cabinet, but then she took the old lock off and put another one in its place. The new one looked like some kind of combination lock with a row of buttons on the front.

“That's the end of that,” I said to Benedict.

“All we can do is wait for our doom,” he said.

We waited all morning, wondering when she'd tell everyone the bad news. But she didn't say a word.

Finally, when the class headed out to recess and lunch, Ms. Fractalli said, “Logan, Benedict, I need to speak with you.”

Oh no. I looked over at Benedict, who was looking at me. I think we both gulped, trying to swallow. We walked up to Ms. Fractalli's desk.

“I don't understand your tests,” she said. “You both did perfectly on the first part and terribly on the last. The word problems counted for half the grade. Your scores dragged the whole class down below 85 percent. Can you explain this?”

Again, I looked at Benedict and he looked at me. I waited. He was really good at coming up with excuses.

“No explanation?” she asked. “I'd love to give you another chance, but I can't without a good reason.”

“My mind sort of went blank,” I said. “I lost my math skills. But I think they came back.”

“Mine too,” Benedict said.

“I guess I'll have to wait until the next test to find out,” Ms. Fractalli said.

She got up from her desk and went to the closet. I turned toward the door. “We're doomed,” I said to Benedict.

“Everyone is going to be angry,” he said. “We might have to move. I have an uncle in Argentina. I've heard they have good steaks down there. You can come. He has lots of room.”

Behind me, I heard a rattling sound. I looked over my shoulder. Ms. Fractalli was yanking at her new lock.

“What's wrong?” I asked.

“I was afraid I'd lose the piece of paper with the instructions, the way I was always losing the key, so I put it in my purse,” she said. “Then I locked my purse in the cabinet, as I always do.”

“You didn't memorize the combination?” I asked.

She shrugged. “I didn't get a chance to memorize it or even look at it. I was up pretty late grading the tests.”

“Let me see.” I liked playing with locks.

“It's hopeless,” she said. “There are too many combinations.”

I lifted up the lock and looked at it. There were five buttons on front, labeled A, B, C, D, E. “How does it work?” I asked.

“I'm supposed to push some of them in,” she said. “But I don't know which ones or how many.”

“I can get a saw,” Benedict said. “Yeah—a power saw. Or those giant pliers they use on cars. Wait! Better idea! We could go to the high school and get some hydrochloric acid from the chemistry lab. That will eat right through it.”

He kept talking, but I stopped listening. The lock had all of my attention. I knew there were letters on it. But it reminded me of the kind of number problems we'd solved at the museum.

“It's binary!” I shouted as the answer hit me.

“Cool,” Benedict said. He stopped talking and looked over my shoulder. “Yeah, you're right.”

I turned toward Ms. Fractalli. “If there was just one button, you'd only have two choices. Right?” I pushed down the button with A on it and then popped it back up.

“And two buttons would only give you four choices,” Benedict said.

“For sure,” I said. It was definitely like the binary numbers we'd learned about. “And three buttons would be … ”

“Eight!” Benedict said. “Like Dr. Thagoras's light switches.”

I held up my right hand and stuck out one finger at a time, doubling the number with each new finger.

Pinkie.

“Two.”

Ring finger.

“Four”

Middle finger.

“Eight.”

Benedict and Ms. Fractalli joined in.

Index finger.

“Sixteen!”

Thumb—my whole hand was spread wide.

“Thirty-two!”

“That's not a lot at all,” Ms. Fractalli said. “I should have realized it right away.”

“Sometimes, we all forget our math skills,” I said. I thought about those pennies that doubled every week for a year. It's a good thing the lock didn't have fifty-two buttons. Or even ten.

I started pushing the five buttons, going through the thirty-two possible combinations:

up-up-up-up-up

up-up-up-up-down

up-up-up-down-up

up-up-up-down-down

up-up-down-up-up

up-up-down-up-down

up-up-down-down-up

up-up-down-down-down

I tugged on the lock after each combination. I hoped I wasn't missing something. It seemed too easy. But then, after more than twenty attempts, I tried

down-up-down-up-down.

The lock pulled open.

“I did it!” I shouted.

“Logan, that was wonderful,” Ms. Fractalli said.

I noticed that the A, C, and E were pushed down. “Ace,” I said. “I'll bet you'll never forget that combination.”

“And I'll never forget how you two helped me,” she said.

“That's the power of two,” I said.

She looked at the clock. “How'd you boys like another chance at the last part of the test?”

If anyone had ever told me I'd be cheering at a chance to take a math test, I never would have believed it. But I was sure cheering then.

“Ready?” I asked Benedict as we walked back to our desks with new copies of the test.

“Let's ace this,” he said.

“Shhh,” I said. “That combination is a secret.”

But when Ms. Fractalli graded our tests, that's exactly what we did. Benedict and I aced it, saving our grades and the ice cream party.

And wouldn't you know it, when the time came for the party, we both ended up getting brain freeze again. But at least, this time, we didn't get numbed.

David Lubar
has written a fairly large, though finite, number of books, including
Punished!
and
Hidden Talents
. He's always enjoyed math, but he never dared write a book about it until now. The chance to send Logan and Benedict on another adventure was just too tempting for him to resist. He lives in Nazareth, Pennsylvania, with his wife and various felines.

Jacket art by Jeffrey Ebbeler

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