 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
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
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.