Let $n$ be a positive integer. Show that the number of partitions of $n$, having one part more than $\frac n2$, is equal to the number of partitions of $n$ having more than $\frac n2$ parts.
The difficulty is in the fact that, a partition is not only finding the number of solutions to $x_1+\cdots+x_k=n, x_i\ge1~\forall i$, but that it has to be unordered. I am stuck there.