Math CentralQuandaries & Queries


Question from Sommer, a parent:

I need a schedule for my kids basketball league. There are 4 teams.
We will play every Saturday for 4 weeks with 4 games per Saturday.
Week 5 will be the playoffs where 1st will play 4th and 2nd will play 3rd.
Week 6 will be winners of week 5. Please help!!


With 4 teams there are only 3 possible pairings of 2 games:

(i) AvB and CvD
(ii) AvC and BvD
(iii) AvD and BvC.

Each team has 3 possible opponents, so a balanced schedule -- one where every two teams play each other the same number of times -- requires a number of games that is a multiple of three. With 4 games per Saturday over 4 Saturdays, it seems that the teams in this league each play 8 games, so a balanced schedule isn't possible.

Creating a schedule is easy, just use (i), (ii) and (iii) above in some order, so that one of them is used twice and the other three times. For example: (i) and (ii) on Week 1, (iii) and (i) on week 2, (ii) and (iii) on week 3, and then add two pairings that make sense on the last week.

If home and away matter, one team can be home the first time the teams play, and the other can be home the second time they play. For teams that play each other three times, a choice needs to be made.

You've already said how to schedule the playoffs.

Good luck!

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