  In this paper we study the number of special directions of sets of
cardinality divisible by $p$ on a finite plane of characteristic $p$, where $p$
is a prime. We show that there is no such a set with exactly two special
directions. We characterise sets with exactly 3 special directions which
answers a question of Ghidelli in negative. Further we introduce methods to
construct sets of minimal cardinality that has exactly 4 special directions for
small values of $p$.

Combinatorics