permutate pairings

Question

NON ACADEMIC QUESTION: Over the years I have struggled with a (social) math problem involving organising golfers in a travelling group so as to maximise playing combinations whilst minimising duplication. So, 9 players, 4 rounds/days, 3 tee times each day. First day easy; A plays with B and C, DEF, GHI. Second day ADG, BEH, CFI. So far so good but by the third day, say, AEI, BDF, CGH we already have duplications and by the fourth day more duplications and also some players never playing with their travelling companions at all!

 

As I say, this is purely a fun question but if any aspiring geniuses out there can find an algebraic solution to find permutations for any number of players with any number of games, it would be greatly appreciated.

 

Thanks in anticipation.

 

Michael

Answer 1

Try this as an example:

 

DAY 1  EHI, GFA, BDC
DAY 2  IGD, AEB, FCH 
DAY 3  BIF, ECG, DAH 
DAY 4  CIA, HBG, FDE

 

I think with this arrangement, everyone plays with everyone else one time.  Does this suit your needs?

Fairways and greens !!