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| Math Central | Quandaries & Queries |
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Qduestion from Joseph, a teacher: We have a 15 team tournament. Each team plays all other teams. We need a schedule were each game has a work team. Thus at each fields we have two teams playing and one working. All teams need to play each other and also be a work team. Any help would be appreciated!! |
Joseph,
I think you can use a Kirkman Triple System. See
https://en.wikipedia.org/wiki/Kirkman's_schoolgirl_problem. On each day, one of the triples of teams is assigned to a field.
This triple system has the property that each pair of teams is in the same triple exactly once.
To get your schedule, run through the system three times (a total of 21 match days; this is the best possible). The first time teams A, B, C are on the same field, the work team is A. The second time it is B, and the third time it is C.
Hope this works for you.
—Victoria
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