Numbed! by David Lubar Page B

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.
    â€œWelcome 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.
    â€œI’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.
    â€œYou can solve the problem or remain in this infinite loop,” the voice said.
    â€œWhat’s the problem?” I asked.
    â€œA 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?”
    â€œYeah,” 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.
    â€œI’m getting an infinite headache,” Benedict said.
    I shushed him and waited for the rest of the problem.
    â€œInfinite more guests show up. How can you find rooms for all of them without asking any of the current guests to leave?”
    â€œWhat?” 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 .
    â€œWrong,” the voice said.
    Benedict stepped away from the keyboard. “Well, that was the best I could do. Any ideas?”
    â€œNot 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?”
    â€œIt’s big?” Benedict guessed.
    â€œYeah. But it’s more than big. It’s endless.”
    â€œLet’s try that,” Benedict said. He typed: Put all the new people at the end, after the guests who are already there .
    â€œWrong,” 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.”
    â€œForget 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.”
    â€œTwo …” 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.
    â€œOh, 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.
    â€œHuh?” Benedict said, looking over my ­shoulder.
    â€œYou 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