Numbed! by David Lubar Page A

A WHOLE YEAR
B.  1 PENNY THE FIRST WEEK,
    2 PENNIES THE SECOND WEEK,
4 PENNIES THE THIRD WEEK,
AND SO ON, DOUBLING THE AMOUNT
EACH WEEK FOR A YEAR
    â€œThat sounds like an easy choice,” Benedict said. “I mean, one penny to start. How much could that end up being?”
    â€œIt could be a trick,” I said.
    â€œOr a double trick,” Benedict said. “They make it sound wrong so you’ll think it’s right, but it’s really wrong.”
    â€œIt could be a triple trick,” I said. “Or even a quadruple one.”
    â€œOh, 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?”
    â€œGo for it.”
    â€œWeek one, 1 cent.”
    â€œOne,” Benedict said.
    â€œWeek two, add another 2 cents.”
    â€œAnd 1 + 2 = 3,” Benedict said. “This is easy.”
    â€œWeek three, add 4 cents.”
    â€œThen 3 + 4 = 7.”
    â€œWeek four, add 8 cents.”
    â€œThen 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.”
    â€œHold on. I want to be sure. Where was I? Oh yeah. Week five, add 16 cents.”
    â€œThat’s … I lost track,” Benedict said. “Let’s start over.”
    â€œNo. 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.
    â€œThen 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.
    â€œThen 1,024. That’s $10.24. Then 2,048. That’s $20.48.”
    â€œWow, 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.
    â€œI guess it really was a double trick,” I said.
    â€œYeah, 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.
    â€œLast one’s up ahead,” I said.
    â€œWe’re ready.”
    â€œI 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