there is a soccer league with k participating teams, where k is a positive even integer. suppose that the organizer of the league decides that there will be a total of k 2matches this season, where no pair of teams plays more than once against each other (ie. if team a and team b plays a match against each other, they never play against one another again for the rest of the season). prove that if every team has to play at least one match this season, then there is no team that plays two or more game