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\begin{document}

\noindent
{\large\bf Honors Calculus Challenge Problem \#1}

\bigskip

A hare challenges a tortoise to a 100-meter footrace.
Doubtful about his chances, the tortoise asks 
the hare to give him a small headstart.
The hare cheerfully agrees to give the tortoise a headstart ---
of 1 centimeter!

On the day of the race the hare and tortoise are joined
by many of their supporters. The starting pistol is fired, 
the athletes start running, and the following events take place:

\begin{enumerate}
\item[(i)] At each moment of the race the tortoise 
is being watched by at least one of his supporters.
\item[(ii)] Each supporter of the tortoise watches 
him for exactly one minute, during which the tortoise
travels exactly one meter.
\item[(iii)] At each moment of the race the hare
is being watched by at least one of his supporters.
\item[(iv)] Each supporter of the hare watches 
him for exactly one minute, during which the hare
travels exactly four meters.
\end{enumerate}

\bigskip

\noindent
{BUT THE TORTOISE WINS!!}

\bigskip

Explain how this could be! Tell why the tortoise
cannot win without a headstart, but has a chance
to win if given any headstart of positive length.
\end{document}

