Hi,
The number of ways of choosing 2 teams from 6 teams is 6-choose-2 which is 15.Thus you need 15 games if each team is to play each other team. On any one day you can have at most 3 games and hence you will need at least a 5 day schedule. Here is one way to construct a schedule.
Label the teams 1, 2, 3, 4, 5 and 6. On each day team 1 plays one of the other teams so we can start as follows.
Day1 | 1-2 | ||
Day2 | 1-3 | ||
Day3 | 1-4 | ||
Day4 | 1-5 | ||
Day5 | 1-6 |
Now consider team 2. On day 2, team 2 could play team 4, on day 3 team 5 and on day 4 team 6. The only team left for team 2 to play is team 3 so they can play on day 5.
Day1 | 1-2 | ||
Day2 | 1-3 | 2-4 | |
Day3 | 1-4 | 2-5 | |
Day4 | 1-5 | 2-6 | |
Day5 | 1-6 | 2-3 |
The remaining games on days 2, 3, 4 and 5 are determined at this point.
Day1 | 1-2 | ||
Day2 | 1-3 | 2-4 | 5-6 |
Day3 | 1-4 | 2-5 | 3-6 |
Day4 | 1-5 | 2-6 | 3-4 |
Day5 | 1-6 | 2-3 | 4-5 |
If you look at the list so far you will see that the matches that arre missing are 3-5 and 4-6 an thus the schedule is completed by having these games on day 1.
Day1 | 1-2 | 3-5 | 4-6 |
Day2 | 1-3 | 2-4 | 5-6 |
Day3 | 1-4 | 2-5 | 3-6 |
Day4 | 1-5 | 2-6 | 3-4 |
Day5 | 1-6 | 2-3 | 4-5 |
Penny