\font\largerbold = cmbx10 scaled \magstep1
\font\largerrm =cmr12 scaled \magstep2
\def\map{{\tt Maple}}
\font\largertt = cmtt10 scaled \magstep2
\def\H{\char `\^}
\def\R{{\sevenbf RET}}
\def\Q{\hskip 1in}
\def\QQ{"}
\nopagenumbers
\overfullrule=0pt
\font\sc=cmcsc10.tfm
\magnification=\magstep1
\def\ts{\textstyle}
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\def\q{$\,$\raise-.13in\hbox{\vrule height .35in width.8pt}$\,$}
\rightline{\sevenrm  January 31, 2000}

\medskip

\centerline{\largerbold Math 103 contest and homework problem}

\smallskip

Each of you will get a part of a shared secret. At least \raise -1.2pt
\hbox{\largerrm\thinspace three\thinspace} people will need to share
their information to obtain the secret.  I created a quadratic
polynomial, $y=B+\{?\}x+\{??\}x^2$. Each student in the class will get
a (non-zero) value of $x$ and the value $y$ corresponding to that
value of $x$. The secret is a word specified by the number $B$, using
the rather simple method described below.  Every student must
participate in some group and send me ``the secret'' (the word) before
the next class meeting. Also identify all of the participants in the
group. The group which sends me the secret first (as determined by
time-stamp on their e-mail) will win a \raise -1.2pt
\hbox{\largerrm\thinspace real prize\thinspace} (bought by me, with my
own money [!]). Hints are available by e-mail or in person.

\smallskip

\noindent{\bf Further rules}
\smallskip
\item{1.} Each group may have 3, 4, or 5 members. 

\item{2.} No more than 2 members of a group should be math or computer
science majors. Majors are determined by what's listed on the student
web page. 

\smallskip

\noindent {\bf Numbers to letters (easy version)} 

\smallskip 

The alphabet has 26 letters. Suppose we associate each letter with a
two-digit number in the simplest way: ${\tt A} \to 01$, ${\tt B} \to
02$, $\ldots\;$, ${\tt Z}\to 26$. Thus the word {\tt WIGGLE} would be
associated to the number 230907071205 ({\tt W} is the $23^{\rm rd}$
letter of the alphabet, {\tt I} is the $9^{\rm th}$ letter of the
alphabet, etc.).

\smallskip

\noindent {\bf Some more useful information about \map}

\smallskip

\map\ can remember numbers and formulas. The instruction

\Q {\it  A:=17324099;}

\noindent will cause \map\ to remember that you'd like the variable
$A$ to equal the number 17324099 (until you tell the program otherwise
or exit the session). Please note that you must type {\it colon} ({\it
:}) followed by {\it equal sign} ({\it =}) so \map\ will attach the
value 17324099 to the name, $A$. You can call variables by lots of
names. Their names must begin with a capital or a small letter. Upper
and lower case do matter, so that $A$ and $a$ are different variables
to \map. {\it Frog}\/ is an allowable variable name. This name is
\underbar{not} the same as {\it frog}\/ or {\it FROG}. I sometimes use
long variable names so that I won't get confused. You can also do
arithmetic with the variables. If {\it A}\/ is the number above, \map\
will compute {\it 3*A-26}\/ if you type {\it 3*A-26;}\/ and it will
square {\it A}\/ if you type {\it A\H 2;}. 
Suppose you wanted to solve the equations
\noindent$\eqalign{ 21x+73y&=46\cr
51x+31y&=17\cr}$\thinspace . 
You could tell \map\ {\it Firstx:=21;}\/ and {\it Firsty:=73;}\/ and
{\it Firstconst:=46;}, followed by {\it Secondx:=51;}\/ and {\it
Secondy:=31;}\/ and {\it Secondconst:=17;} and then:
%\vskip -.2in

\centerline{$\eqalign{ 21x+73y&=46\cr
51x+31y&=17\cr} \Rightarrow 
\eqalign{ 1x+{\ts{{73}\over {21}}}y&={\ts{{46}\over {21}}}\cr
51x+31y&=17\cr} \Rightarrow
\eqalign{ 1x+{\ts{{73}\over {21}}}y&={\ts{{46}\over {21}}}\cr
(51-51)x+\left(31-51\left({\ts{{73}\over{21}}}\right)\right)y&=
17-51\left({\ts{{46}\over{21}}}\right)\cr}$}

\noindent So $y= {{17-51\left({\ts{{46}\over{21}}}\right)}\over
{\left(31-51\left({\ts{{73}\over{21}}}\right)\right)}}= {{663}\over
{1024}}$.  I had \map\ do all this work and keep track of it with
various variable names. All I did was copy things from the screen. I
did \underbar{no} arithmetic!

\vfil\eject\end
