Quandaries and Queries


I have a schedule I need to make of 6 teams. They must play each other once however no team can be the away team twice in a row. There must be 3 home games and 3 away games for each team.


Hi Greg,

The reason you are having trouble with this schedule is that it is impossible. First if there are 6 teams then each team plays 5 games not 6, it only has 5 opponents. But even with 5 games per team you can't do what you want.

Suppose that each team plays each weekend, so each weekend there are 3 games. The first weekend there are 3 home teams, call them a, b and c, and 3 away teams, call them d, e and f. The second weekend d, e and f must be home teams so a, b, and c must be away teams. The third weekend a, b and c must be home teams and hence d, e, and f must be away teams. And so on for weekends 4 and 5.

What I see here is that teams a and b are always both home teams or both away teams. This is clearly not the case when they play each other.



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