  A set $U$ of unit vectors is selectively balancing if one can find two
disjoint subsets $U^+$ and $U^-$, not both empty, such that the Euclidean
distance between the sum of $U^+$ and the sum of $U^-$ is smaller than $1$. We
prove that the minimum number of unit vectors that guarantee a selectively
balancing set in $\mathbb{R}^n$ is asymptotically $\frac{1}{2} n \log n$.
