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\begin{document}

\handout{teamprobs2}{Problems for Recitation 2}{September 18, 1998}

\begin{enumerate}

\item {\em Handshakes. } I recently went to a party with my spouse;
there were 11 other married couples there.  A lot of handshaking
happened (but of course no one shook hands with their spouse).  At the
end, it turned out that for every $k$ from $0$ to $22$, someone other
than me had shaken hands with exactly $k$ people.  How many people did
I shake hands with?  Prove your answer.

\item {\em Geometric mean vs Arithmetic mean. }  Show that for any
non-negative real numbers $x_1,x_2,\ldots,x_n$,
$$(x_1x_2\ldots x_n)^{\frac{1}{n}} \leq \left( x_1 + x_2 + \ldots + x_n \over n \right) $$ 
\end{enumerate}

\end{document}

