  A one-dimensional (1D) $q$-state Potts model with $N$ sites, $m$-site
interaction $K$ in a field $H$ is studied for arbitrary values of $m$. Exact
results for the partition function and the two-point correlation function are
obtained at $H=0$. The system in a field is shown to be self-dual. Using a
change of Potts variables, it is mapped onto a standard 2D Potts model, with
first-neighbour interactions $K$ and $H$, on a cylinder with helical boundary
conditions (BC). The 2D system has a length $N/m$ and a transverse size $m$.
Thus the Potts chain with multi-site interactions is expected to develop a 2D
critical singularity along the self-duality line, $(e^{qK}-1)(e^{qH}-1)=q$,
when $N/m\to\infty$ and $m\to\infty$.
