
\problem

%{\bf (Binomial coefficients)}

Give a combinatorial argument to show that
\[C(2n,2) = 2 C(n,2) + n^2.\]

\problem
% (Andrew)  {\bf (Birds)}

Let $A$ be a set of $n$ integers, for some $n>1$.  Show there exists
two subsets $B,C$ such that $B$ is a proper subset of $C$ and the sum
of the elements in $B$ is congruent (mod $n$) to the sum of the
elements in $C$.

