Quandaries
and Queries 

Question: I am running a golf tournament with twelve golfers. We will be playing four rounds of golf. I don't want to schedule the same two players together more than twice (if possible). How would I make a schedule that each player would play at least once with every other player? I would appreciate any help that you can give me. Thank you. 

Hi, In short the answer is no, it's not possible. Twelve golfers determine 66 pairs ( ^{1211}/_{2}=66). A 4some determines 6 pairs ( ^{43}/_{2}=6) so three 4somes determine 18 pairs. However we must have a repetition in each 4some after the first round giving at most 15 new pairs each round for a total of at most 18+15+15+15 = 63 < 66.
Denis 

