  We consider the problem of distinguishing convex subsets of $n$-cyclotomic
model sets $\varLambda$ by (discrete parallel) X-rays in prescribed
$\varLambda$-directions. In this context, a `magic number' $m_{\varLambda}$ has
the property that any two convex subsets of $\varLambda$ can be distinguished
by their X-rays in any set of $m_{\varLambda}$ prescribed
$\varLambda$-directions. Recent calculations suggest that (with one exception
in the case $n=4$) the least possible magic number for $n$-cyclotomic model
sets might just be $N+1$, where $N=\operatorname{lcm}(n,2)$.
