  In this paper, we introduce the n-th discrete topological complexity and
study its properties such as its relation with simplicial
Lusternik-Schnirelmann category and how the higher dimensions of discrete
topological complexity relate with each other. Moreover, we find a lower bound
of $n-$discrete topological complexity which is given by the n-th usual
topological complexity of the geometric realisation of that complex.
Furthermore, we give an example for the strict case of that lower bound.
