I was wondering if I could trouble you to assist me with the following: I am working on a schedule for 24 golfers. 6 groups of 4. I have 8 golf days (twice per week for a month).
Ideally, I would like to schedule all 24 golfers in 6 different groups of 4 on each day. Here is the catch.....no golfer in any group can be grouped togther more than once. Every group of 4 each day will have 4 new golfers that have never played together before. Is this possible?
Any assistance that you could provide will be greatly appreciated.
24 Golfers play in 6 foursomes per day for 8 days
To answer the original question -- for a tournament having n players playing each day in foursomes, each player grouped with each other exactly once -- there are two necesary conditions:
Put these conditions together you get that the number of golfers must be 12k + 4. The Handbook cited above says that these conditions can be satisfied for all k >= 0. Thus it is possible with n = 4, 16, 28, and so on. We provide below an example with n = 16 golfers.
16 golfers play in 4 foursomes per day for 5 days