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Schedules - You must register to Post and Download => Requests => Topic started by: Sera on June 07, 2013, 01:02:19 PM

Title: Complex Camp Games
Post by: Sera on June 07, 2013, 01:02:19 PM

Trying to organize some camp games stations, and initially thought I could use a solution found on these forums, but the group numbers have increased!

I'm not even sure if this is possible without clashes but here goes.

30 teams, 10 games stations, 10 rounds
So each round 3 teams compete against each other at 1 station.
Is it possible for every team to play all 10 types of games (a different one at each station) PLUS not play the same teams more than once?

Have been trying to do this manually and it's been very complex!

Any help would be greatly appreciated.

Title: Re: Complex Camp Games
Post by: Ian Wakeling on June 08, 2013, 03:33:25 AM

I have found the solution below which I think meets all the requirements.

        S1         S2         S3         S4         S5         S6         S7         S8         S9         S10
R1  ( 1  6 24) (23 15 17) (22 19 10) (27 18  2) (14 29 25) (13  5  7) ( 3 16 12) (11  9 30) (20 26  8) (21  4 28)
R2  ( 2  7 25) (24 11 18) (23 20  6) (28 19  3) (15 30 21) (14  1  8) ( 4 17 13) (12 10 26) (16 27  9) (22  5 29)
R3  ( 3  8 21) (25 12 19) (24 16  7) (29 20  4) (11 26 22) (15  2  9) ( 5 18 14) (13  6 27) (17 28 10) (23  1 30)
R4  ( 4  9 22) (21 13 20) (25 17  8) (30 16  5) (12 27 23) (11  3 10) ( 1 19 15) (14  7 28) (18 29  6) (24  2 26)
R5  ( 5 10 23) (22 14 16) (21 18  9) (26 17  1) (13 28 24) (12  4  6) ( 2 20 11) (15  8 29) (19 30  7) (25  3 27)
R6  (19 29 13) ( 2 30 10) (15 27  5) (25  6 11) ( 4  8 18) (20 28 22) (23  7 26) (21 16  1) (24 14  3) ( 9 17 12)
R7  (20 30 14) ( 3 26  6) (11 28  1) (21  7 12) ( 5  9 19) (16 29 23) (24  8 27) (22 17  2) (25 15  4) (10 18 13)
R8  (16 26 15) ( 4 27  7) (12 29  2) (22  8 13) ( 1 10 20) (17 30 24) (25  9 28) (23 18  3) (21 11  5) ( 6 19 14)
R9  (17 27 11) ( 5 28  8) (13 30  3) (23  9 14) ( 2  6 16) (18 26 25) (21 10 29) (24 19  4) (22 12  1) ( 7 20 15)
R10 (18 28 12) ( 1 29  9) (14 26  4) (24 10 15) ( 3  7 17) (19 27 21) (22  6 30) (25 20  5) (23 13  2) ( 8 16 11)

It also has a interesting property that you might be able to make use of.  If the 30 teams are divided into 6 divisions, 1-5 in division 1, 6-10 in division 2,..., 26-30 in division 6, then all of the competition is interdivisional. Hope that helps.