We count the number of Coxeter's friezes over a finite field. Our method uses
geometric realizations of the spaces of friezes in a certain completion of the
classical moduli space M0,n allowing repeated points in the
configurations. Counting points in the completed moduli space over a finite
field is related to the enumeration problem of counting partitions of
cyclically ordered set of points into subsets containing no consecutive points.
In Appendix we provide an elementary solution for this enumeration problem