12 teams, 8 rounds (3x4 + 4x4)

[whitecollar91]

Hello everyone,

I need to create a schedule for a tournament and its quite complex - at least for me

There are 12 teams playing together in 8 rounds. 

Odd rounds are played: 3 games, 4 teams per game
Even rounds are played: 4 games, 3 teams per game

For example:

1st round

(ABCD) (EFGH) (IJKL)

2nd round

(AEI) (BFJ) (CGK) (DHL)


Satisfying solution is where teams play at least once with each other and max twice.

Thanks in advance for any help with that! 

[Ian Wakeling]

I think the following will work - you just need to alternate the two types of round to get the final schedule.

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

Each team should have 2 teams who they play once, and 9 teams who they play twice.

[whitecollar91]

Works fine, thanks a lot!

[Ian Wakeling]

I was looking again at this and spotted a repeated block in the schedule above, specifically teams 1,3 and 5 make up 2 of the blocks of 3.  So I offer the following alternative schedule:

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