KöMaL 2009 K212

Four football teams organize a championship. Every team plays every other team once. The winning teams scores 3 points, the losing team scores 0 points and each team scores 1 point if there is a draw. The Albatrosses did not lose any game and won the tournament. The Black Sheep came out second. They did not have any draws. The third place went to the Cheerful Devils who did not win any game. The Dragonflies were in the fourth place. (In the case of equal scores, the order of teams is determined by the game played against each other. If it is a draw, a tie is declared.) Show that under the given conditions the scores of the four teams were different. List who was the winner in which game and which games ended with a draw. Justify your answers.