Suppose 2n teams play in a round-robin tournament. Over a period of 2n 1 days, every team plays every other team exactly once. There are no ties. Show that for each day we can select a winning team, without selecting the same team twice. (Hint: Consider a bipartite graph with a set of team vertices and a set of day vertices. Take any set of days W and assume not all teams won in some day in W. Let tw be a team that did not win in any day in W. Consider the implication on the number of teams that won at least once in some day in W. Invoke Halls Theorem.)