A round-robin tournament of n contestants is a tournament in which each of the contestants...

A round-robin tournament of n contestants is a tournament in which each of the contestants play each other exactly once, with the outcome of any play being that one of the contestants wins and the other loses. For a fixed integer k,k, a question of interest is whether it is possible that the tournament outcome is such that for every set of kplayers, there is a player who beat each member of that set. Show that if

then such an outcome is possible.