five teams in four groups

[Raylonlarsson]

Hello

I can not find any solution to my problem in the forum.
We run an annual double round robin golf tournament with five teams in four groups. Each group winner progressing to the semi and then final each year.

We want to change the composition of each group, each year, to avoid teams playing the same teams.
We realise 5 into 4 will not go but there must be a method where the minimum duplication will happen.


Any help would be highly appreciated?

[Ian Wakeling]

For the 2nd year, it's possible to have a minimum of 4 pairs of teams duplicated.  For example

Code: [Select]

Year Group T1 T2 T3 T4 T5
  1    1    2  7 17 18  1
  1    2   14 12  9 15 16
  1    3    4  8  6 11 20
  1    4    3 10 19 13  5
  2    1   11 13 16 19  2
  2    2   14  4  8  1 10
  2    3    5 12 15 20  7
  2    4    3  9 18 17  6
Here the duplicated pairs are (4 8 ) (12 15) (17 18) & (13 19).

The duplication gets worse and worse the more years that are added. 12 pairs for 3 years, and 24 pairs for 4 years.

[Raylonlarsson]

Hi Ian

As far as I understand there is no clear mathematically solution, isn't it?  

Anyway, thank you for your time and pointing me out.

[Ian Wakeling]

While the number of groups is less than the number of teams per group, then there can be no nice solutions - the schedule above is the best possible.   So 25 teams in 5 groups of 5 has a solution without replication that can be descibed mathematically, see here for an example.

Ian