12 guys, 3 rounds of golf

[jclark]

We have 12 guys who play in a 3 round annual golf tournament.  We want a mixer schedule with the highest number of unique players in a foursome, with the least number of duplicates in the foursome. In other words, as a golfer, I don't want to play in a foursome with the same guy twice.

[Richard A. DeVenezias]

Here is one schedule that has some people repeating pairups within the foursomes. The (1,2) pair repeats twice (they are in same foursome over all three rounds).  #7 is in three different repeating pairs.


 1  2  3  4       5  6  7  8       9 10 11 12
 1  2  5  9       3  6  7 10       4  8 11 12
 1  2  6 11       3  5  7 12       4  8  9 10

repeats
1 with 2 in 2,3
3 with 7 in 3
4 with 8 in 3
5 with 7 in 3
6 with 7 in 2
9 with 10 in 3
11 with 12 in 2

I speculate there does not exist a schedule which can reduce the repetition further, nor eliminate the multiple repeats.

[jclark]

Thank you Richard.

[Richard A. DeVenezias]

You're welcome.

Here is another schedule suggested by Ian Wakeling.  It has nine distinct pairs of repeats.

 1  2  3  4       5  6  7  8       9 10 11 12
 1  5  9 11       3  7  8 12       2  4  6 10
 1  4  7 11       3  8  9 10       2  5  6 12

The repeats are
(1,4) (1,11) (2,4) (2,6) (3,8) (5,6) (7,8) (9,10) (9,11)

Here is a better visual for the repeat pairs (maybe call them repairs or pairpeats  :))