The COG Theorem
If you have 17 teams, every has 16 games to play, or four games each weekend.
For example, here is a matrix for 17 teams for one weekend, every team gets four games.
|
Team |
Plays |
|
|
|
|
1 |
2 |
3 |
4 |
5 |
|
2 |
1 |
6 |
7 |
8 |
|
3 |
1 |
9 |
10 |
11 |
|
4 |
1 |
12 |
13 |
14 |
|
5 |
1 |
15 |
16 |
17 |
|
6 |
2 |
7 |
8 |
9 |
|
7 |
2 |
6 |
10 |
11 |
|
8 |
2 |
6 |
12 |
13 |
|
9 |
3 |
6 |
14 |
15 |
|
10 |
3 |
7 |
16 |
17 |
|
11 |
3 |
7 |
12 |
13 |
|
12 |
4 |
8 |
11 |
14 |
|
13 |
4 |
8 |
11 |
14 |
|
14 |
4 |
9 |
12 |
13 |
|
15 |
5 |
9 |
16 |
17 |
|
16 |
5 |
10 |
15 |
17 |
|
17 |
5 |
10 |
15 |
16 |
You simply rotate the matrix each weekend so every team plays each other team once. With 16 teams, you only have 15 games to play, so you end up with three weekends of four games, and one weekend of three games.
The hard part of course is scheduling this so each team has a reasonable time span between their morning and afternoon games.
-- Crazyoldgoalie 17 Sep 08 --