Math CentralQuandaries & Queries


Question from James, a teacher:


I would like to put together a season schedule for 9 teams with each team playing three or 4 games leading to a 1 to 9 ranking.


If every team plays every other team, then it is guaranteed that such a ranking exists. The trouble is that there can be more than one possibility. If there are teams that don't play each other, then there is no guarantee that such a ranking exists. Imagine, for example, two teams that played exactly the same opponents and beat them by identical scores,but did not play each other. Which of those would come first?


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