  Non-Hermitian quantum systems with explicit time dependence are of
ever-increasing importance. There are only a handful of models that have been
analytically studied in this context. Here, a PT-symmetric non-Hermitian
$N$-level Landau-Zener type problem with two exceptional points of $N$th order
is introduced. The system is Hermitian for asymptotically large times, far away
from the exceptional points, and has purely imaginary eigenvalues between the
exceptional points. The full Landau-Zener transition probabilities are derived,
and found to show a characteristic binomial behaviour. In the adiabatic limit
the final populations are given by the ratios of binomial coefficients. It is
demonstrated how this behaviour can be understood on the basis of adiabatic
analysis, despite the breakdown of adiabaticity that is often associated with
non-Hermitian systems.
