TITLE: Optimal scheduling dilemma (A textbook math problem IRL)?
QUESTION [5 upvotes]: I am trying to solve a scheduling problem for a boys camp.
I have 12 teams(A through L), 6 sports for them to play, and 6 periods for them to play in(P1 through P6).
                 P1-P2-P3-P4-P5-P6
Soccer          |AB|KJ|IF|GB|EJ|CF|
Football        |CD|AL|KH|ID|GL|EH|
Kick-ball       |EF|CB|AJ|KF|IB|GJ|
Volley Ball     |GH|ED|CL|AH|KD|IL|
Hockey          |IJ|GF|EB|CJ|AF|KB|
Water Polo      |KL|IH|GD|EL|CH|AD|

Here is how schedules are ranked:
1: Teams can only play one game per period.
2: Two points are awarded for every different sport a team plays 
3: One point is subtracted every time a team match-up is repeated(e.g., Team C plays team F twice)
Given this system, a perfect schedule(one where every team played every sport and never competed against the same team twice) would have a score of 144.

REPLY [2 votes]: P1-P2-P3-P4-P5-P6
Soccer          |AG|BH|CI|DL|EK|FJ|
Football        |BC|JG|DE|HI|FA|LK|
Kick-ball       |KJ|CD|GH|EF|IL|AB|
Volley Ball     |EL|FK|AJ|BG|CH|DI|
Hockey          |FI|AL|BK|CJ|DG|EH|
Water Polo      |DH|EI|FL|AK|BJ|CG|

@Vince Kroon is incorrect. Here, I have reformatted your schedule using the information from this answer mentioned by @Kevin Costello.
@Vince Kroon was correct in saying that this problem is unsolvable for $n = 2$, but it is, however, solvable for any n where $n>2$.