We are a group of 8 golfers (2 foursomes) and want to golf 3 games together. How can we arrange it so that we all get to golf with each other at least once?
At another venue, we have 18 golfers (3 foursomes, 2 threesomes) and want to golf 6 games together. Same question, how can we arrange it so that we all get to golf with each other at least once?
Just another golfer with a ???
Kindest Regards,
Sally
Hi Sally,
For the 8 golfers an arrangement is:
Game 1: {P1 P2 P3 P4} - {P5 P6 P7 P8}
Game 2: {P1 P2 P5 P6} - { P3 P4 P7 P8}
Game 3: {P1 P2 P7 P8} - { P3 P4 P5 P6}
In the second venue, what you want is impossible.
In all, you have {18 choose 2} = 18X17/2 = 153 pairs of people that want to play with each other. Each match will allow 24 pairs of people to play together:
each foursome brings 6 pairs together and each threesome brings 3 pairs together. So with 6 games there are at most 24X6 = 144 pairs that play together.
Claude