  We define the weak intermediate boundary conditions for the triharmonic
operator $- \Delta^3$. We analyse the sensitivity of this type of boundary
conditions upon domain perturbations. We construct a perturbation
$(\Omega_\epsilon)_{\epsilon > 0}$ of a smooth domain $\Omega$ of
$\mathbb{R}^N$ for which the weak intermediate boundary conditions on $\partial
\Omega_\epsilon$ are not preserved in the limit on $\partial \Omega$,
analogously to the Babu\v{s}ka paradox for the hinged plate. Four different
boundary conditions can be produced in the limit, depending on the convergence
of $\partial \Omega_\epsilon$ to $\partial \Omega$. In one particular case, we
obtain a ``strange'' boundary condition featuring a microscopic energy term
related to the shape of the approaching domains. Many aspects of our analysis
could be generalised to an arbitrary order elliptic differential operator of
order $2m$ and to more general domain perturbations.
