KöMaL 2010 A504

Prove that for arbitrary integers 0<$r$<$k$<$t$ there exists a positive integer $N$($r$,$k$,$t$) which satisfies the following property: whenever $G$ is an $r$-uniform hypergraph with at least $N$($r$,$k$,$t$) vertices such that there is at least one hyperedge on any $k$ vertices, then $G$contains a complete subgraph with $t$ vertices. (A hypergraph is a graph whose edges are arbitrary subsets of the vertices. The graph is called r-uniform if all edges contain exactly $r$ vertices. An $r$-uniform hypergraph is complete if any $r$ of its vertices form an edge.)