  For a finite set of points $X$ on the unit hypersphere in $\mathbb{R}^d$ we
consider the iteration $u_{i+1}=u_i+\chi_i$, where $\chi_i$ is the point of $X$
farthest from $u_i$. Restricting to the case where the origin is contained in
the convex hull of $X$ we study the maximal length of $u_i$. We give sharp
upper bounds for the length of $u_i$ independently of $X$. Precisely, this
upper bound is infinity for $d\ge 3$ and $\sqrt2$ for $d=2$.
