Sad to say, but you did. Golfers 1, 5, and 9 never play each other, for example.
Hrmph.
1. a, b, c
2. a, c, b
3. b, c, a
4. b, a, c
5. c, a, b
6. c, b, a
7. a, b, c
8. a, c, b
9. b, c, a
10. b, a, c
11. c, a, b
12. c, b, a
YEEEHAWWWWW!! Got it.