Given $N=mn$ real numbers $a_i$, we seek to partition them into $n$ subsets $S_j$ ($1\le j\le n$), each containing $m$ numbers, so as to maximize $\prod_{j=1}^n \sum_{a_i\in S_j} a_i$. Can we transform this problem to the problem of maximizing $\min_{1\le j\le n} \sum_{a_i\in S_j} a_i$?