In a league of 5 football teams which play in a round robin tournament (i.e. two teams play each other once only with no ties/draws allowed) show that it is possible for all five teams to be league leaders.

In a league of 6 hockey teams which play in a round robin tournament (i.e. two teams play each other once only with no ties/draws allowed) show that it is impossible for all six teams to be league leaders.