Volleyball Cauldron schedules

[hodgesk]

Found things that are close, but not quite this one...

I'm looking to schedule some volleyball round robins.  13 players, 3 v 3 on 2 courts, so one player has a bye each round.  13 rounds, so each person has 1 bye round.  Each player plays with each other player twice, against each other player three times.  Can you help?

[Ian Wakeling]

I have found the following cyclic solution for your volleyball tournament which has the with and against balance that you are looking for.  I suspect other schedules may exists for 6n+1 players, i.e. 19, 25, 31 players etc.

        Court 1               Court 2           Bye
 ( 2 11  4 v 13  5 10) ( 6  7  8 v 12  3  9)   ( 1)
 ( 3 12  5 v  1  6 11) ( 7  8  9 v 13  4 10)   ( 2)
 ( 4 13  6 v  2  7 12) ( 8  9 10 v  1  5 11)   ( 3)
 ( 5  1  7 v  3  8 13) ( 9 10 11 v  2  6 12)   ( 4)
 ( 6  2  8 v  4  9  1) (10 11 12 v  3  7 13)   ( 5)
 ( 7  3  9 v  5 10  2) (11 12 13 v  4  8  1)   ( 6)
 ( 8  4 10 v  6 11  3) (12 13  1 v  5  9  2)   ( 7)
 ( 9  5 11 v  7 12  4) (13  1  2 v  6 10  3)   ( 8)
 (10  6 12 v  8 13  5) ( 1  2  3 v  7 11  4)   ( 9)
 (11  7 13 v  9  1  6) ( 2  3  4 v  8 12  5)   (10)
 (12  8  1 v 10  2  7) ( 3  4  5 v  9 13  6)   (11)
 (13  9  2 v 11  3  8) ( 4  5  6 v 10  1  7)   (12)
 ( 1 10  3 v 12  4  9) ( 5  6  7 v 11  2  8)   (13)

For the benefit of others, I think the 'close' schedule you refer to is the one for 12 players found here in reply #7.