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Question from Angie, a parent:

I have 6-teams that can only play 3 days a week. Each team must get 18 games in for the season. I have to split them being the home team and the away team sometimes.

Hi Angie,

The number of ways of choosing two teams from six teams is 15 so you could arrange a schedule of 15 games where each team plays each other team exactly once. You want 3 more game so some matchups are going to appear more than once.

Number the teams from 1 to 6. H designated the home team and A the away team. Here is a schedule that will work.

  H A H A H A
Week 1 1 2 4 3 6 5
Week 2 1 3 5 2 4 6
Week 3 1 4 2 3 5 6
Week 4 5 1 6 2 3 4
Week 5 2 1 3 6 4 5
Week 6 6 1 2 4 3 5

Penny

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