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\author{Sherwood Hachtman}
\title{Math 300 Day 1: Sets of Ages}

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\begin{theorem} Suppose 10 people, each of whom has age between 0 and 100, are in a room.  Show there are two disjoint subsets of these with the sums of ages equal.
\end{theorem}

\begin{proof}
There are at most a thousand sums of ages, but there are more than this many subsets of the people.  So there must be two of these with the same total age.
\end{proof}
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