  An exponent $\beta$ which characterises non-equilibrium coarsening processes
is calculated in a deterministic solvable model of coarsening for a 1D q-state
Potts system. We study how the fraction of sites P which have never changed
their state, scale with the characteristic domain length $<\ell>$. $\beta$ is
defined by P \sim $<\ell>^{\beta -1}$. We propose a new model of coarsening
that prevents correlations from developing between domains thereby ensuring
tractability and an exact result for any q.
