Question 6
Let $m \ge 2$ be an integer, $A$ a finite set of integers (not necessarily positive) and $B_1$, $B_2$, …, $B_m$ subsets of $A$. Suppose that, for every $k=1,2,\dots,m$, the sum of the elements of $B_k$ is $m^k$. Prove that $A$ contains at least $\frac{m}{2}$ elements.