Iowa
Jones
Fine Eye Times
475 Second Street
Big City, PU 11248-1632
March 24, 2008
Calculus Student
Franklin &
Marshall College
Lancaster, PA
17604
Dear Calculus Student,
I know you don’t even know who I am, but I hope for Will’s sake
that you can help us out of a big jam! I’m afraid that Eve might
have kidnapped Will and locked him in an underground chamber! You’ve
got to help me figure out how to get him out!
I’m Iowa Jones, by the way. I only met Will about a month ago,
but there was something about him that just drew us together. I
was sitting on a bench outside of Vellen Enterprises, trying to figure
out where I could look for a new job. (Eve had just fired me for
letting it slip in front of a customer that our tanks are parabolic
instead of hemispherical). Bill saw me sitting there and stopped
to cheer me up, which was hard for him because he was pretty depressed
about how Eve had been treating him, too.
As we talked, we began putting together bits and pieces of a giant
puzzle, and we came to realize that for about a year now, Eve has been
hatching a vile scheme to take over the world, one shoe at a
time! It began when Will started working for his
grandfather. You remember he moved from department to department
when he started there. In one of those departments, Will
developed a new kind of rubber that can be used in boat shoes.
Unknown to him at the time, these rubber soles became a huge
phenomenon. You might have heard of these: Blezz Shoes sold
them under the jingle:
Xeno’s Boat Shoes: Get your own pair o’
docksiders!
For a while, everywhere you went, you’d hear people humming about
Xeno’s pair o’ docks. They were amazing!
What made them so amazing -- and ironically, what has me stumped right
now -- is that the rubber soles are astonishingly elastic, with an 81%
bounce coefficient. (That means that if you drop a shoe without
anything in it, it will bounce back to 81% of the height you dropped it
from. If you don’t think that’s amazing, try it with your own
shoes). These shoes put a real spring into everybody’s step for
as long as the shoes were on the market.
But then Eve happened.
Eve stole the rubber recipe for from Blezz by using an elaborate ruse
(she sold Blezz Shoes a rubber-making machine
and then bought it back full of their rubber). She had me hack
into their computers to destroy their own records of how to make the
material. And then she devised a scheme to bankrupt the company
by convincing them to invest in storage tanks
that were smaller than required by industry standards.
Why did she do all this? As I said, she has an evil scheme to
take over the world -- I don’t want to put your own life at risk by
telling you all the nefarious details. We should have realized,
though, that Will was in danger, because the only remaining rubber
recipe outside of her control was in his head! We underestimated
her, and we were totally unprepared when her henchmen broke into his
apartment and abducted him.
I’ve been able to hack back into the Eve L. Vellen system, so I know
where she’s keeping him: he’s strapped to the wall about half-way
up one of her vacant parabolic tanks! I also figured out the code
that I will need to enter into the computer to unlock the doors and let
him out. There are two parts to this code: a simple
password to enter the system that monitors the release mechanism, and a
longer sequence of code that actually accomplishes the
release. So I’m almost all the ready to free him!
But here’s the problem. There’s an elaborate security device that
Eve installed, hoping to thwart rescue attempts like mine. This
is how it goes.
I enter the first part of the security code, which is just a simple
password. That password not only lets me enter into the system,
however; it also automatically releases one of Xeno’s shoes from the
top of the tank, and the shoe falls 100 feet to the bottom of the tank,
where there’s a delicate sensor. From there, the shoe bounces up
and down, with each bounce 81% as high as the previous one.
Exactly 1 minute after I enter the password, the second shoe drops,
and it too starts bouncing. And then exactly 2 minutes after I
enter that first password, if I haven’t already entered the second
sequence of code, the system automatically releases a deadly poison
that will kill Will within seconds!
So, clearly I have to enter that second sequence of code within the
first 2 minutes. That ought to be easy: I’ve practiced over and
over on a keyboard that’s not plugged in, and I’ve got it to the point
where I can do it in 9 seconds flat. However there’s one more
twist
(I swear, Eve watched too much Batman when she was a kid)! If the
sensor detects a bounce while I’m in the process of entering that
sequence of code, It triggers the poison gas, and Will dies.
This means I’ve got to figure out if there’s any 9-second window (or
even a little longer?) with no bounces at all. Maybe I could
enter the code while the first shoe is falling? Or while it’s
bouncing the first time? I know that once these shoes start
bouncing, they keep bouncing faster and faster, and they do this for a
long time -- am I right that there’s no time between the two shoes to
enter the code?
I know that Will trusts you. Is there any way that you could help
us out again? I hate to bother you, but on the other hand the
fate of the entire world depends on this!
I think I’ve found my sole mate.
Yours sincerely,
Iowa Jones
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