  The goal of this paper is to solve Problem 481 from the list of research
problems in the special issue of Discrete Mathematics dedicated to the Banff
International Research Station workshop on "Generalizations of de Bruijn Cycles
and Gray Codes" in 2004. Overlap cycles are generalizations of de Bruijn cycles
and Gray codes that were introduced originally in 2010 by Godbole et al. In
this paper we prove that s-overlap cycles for k-permutations of [n] exist for
all k<n.
