  In this short note we consider an unconventional overdetermined problem for
the torsion function: let $n\geq 2$ and $\Omega$ be a bounded open set in
$\mathbb{R}^n$ whose torsion function $u$ (i.e. the solution to $\Delta u=-1$
in $\Omega$, vanishing on $\partial\Omega$) satisfies the following property:
$\sqrt{M-u(x)}$ is convex, where $M=\max\{u(x)\,:\,x\in\overline\Omega\}$. Then
$\Omega$ is an ellipsoid.
