  We show that the minimum number of orientations of the edges of the n-vertex
complete graph having the property that every triangle is made cyclic in at
least one of them is $\lceil\log_2(n-1)\rceil$. More generally, we also
determine the minimum number of orientations of $K_n$ such that at least one of
them orients some specific $k$-cycles cyclically on every $k$-element subset of
the vertex set. The questions answered by these results were motivated by an
analogous problem of Vera T. S\'os concerning triangles and $3$-edge-colorings.
Some variants of the problem are also considered.
