Round Robin Tournament Scheduling

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1
Requests / Re: Round robin Mixer Balanced
« Last post by Ian Wakeling on July 02, 2022, 10:50:09 AM »
Sorry there are too many variants here to consider them all.  It is actually impossible to meet your criteria if the number of players is 21 or more.  For example with 21 players there are 7 who will have only 6 games (the ones with a bye), and those 7 players can only play on court with a maximum of 18 others, so there must be at least two players who they never meet.  For me this makes 20 players the most interesting scenario, and it turns out that it is possible to meet your criteria (all different partners, and on court with each other person at least once). Here is a possible schedule:

 (2  7 v 12 17) ( 4  3 v  1  5) (10  8 v  9  6) (11 13 v 14 15) (20 18 v 19 16)
 (5 10 v 15 20) ( 1  2 v  6  7) (11 12 v 16 17) ( 3  8 v 13 18) ( 4  9 v 14 19)
 (1  7 v 13 19) ( 2  8 v 14 20) ( 3  9 v 15 16) ( 4 10 v 11 17) ( 5  6 v 12 18)
 (3 10 v 12 19) ( 4  6 v 13 20) ( 5  7 v 14 16) ( 1  8 v 15 17) ( 2  9 v 11 18)
 (3  6 v 14 17) ( 4  7 v 15 18) ( 5  8 v 11 19) ( 1  9 v 12 20) ( 2 10 v 13 16)
 (1 10 v 14 18) ( 2  6 v 15 19) ( 3  7 v 11 20) ( 4  8 v 12 16) ( 5  9 v 13 17)
 (1  6 v 11 16) ( 2  3 v  4  5) ( 7  8 v  9 10) (15 13 v 14 12) (17 18 v 19 20)

The schedule has 4 repeated opponent pairs (3 5), (8 9), (13 14), (18 19) which all occur in the 1st & 7th rounds. Finally note that the partnerships are all formed from within two groups, players 1-10, and players 11-20.

[comment added later: 20 players is doubly interesting since it is not possible to meet the "on court with each other at least once" criterion with 19 players.  For 19 players there must be at least two players who have only 5 games (2 byes), and who must have at least three other players who they never meet.]
2
You will need 15 weeks to play all the other teams twice.  For example:

(A B) (D F)
(C E) (A D)
(B D) (A F)
(D E) (C F)
(A C) (B E)
(E F) (C D)
(B F) (A E)
(D E) (B C)
(A E) (C F)
(B F) (A D)
(B C) (E F)
(C D) (A B)
(D F) (C E)
(A C) (B D)
(A F) (B E)
3
6 Team Tennis League schedule for  10 weeks so that each team plays all the others twice.
Schedule 4 teams at a time with 2 byes each week.  
This seem easy but I cant seem to get the spreadsheet to solve this.
HepBil
4
Requests / Round robin Mixer Balanced
« Last post by LindaG on June 29, 2022, 12:30:53 AM »
Looking for RR doubles mixers. We will have 12-26 players show each week for 7 rounds. A player’s partner will be a different person each game and play on court with each person at least once. And byes equal as can be. 
 
12-15 players 3 courts 
16-19 players 4 courts 
20-23 players 5 courts 
24-27 players 6 courts 
5
Requests / Re: Please help!
« Last post by Ian Wakeling on June 28, 2022, 04:02:35 AM »
Here is a schedule with similar properties to the one above for 33 players , 6 courts and 30 rounds.  For these numbers the byes can't be balanced and so players 10,11,12,22,23,24 have only 21 games, while the other players have 22 games.

        Court 1        Court 2        Court 3        Court 4        Court 5        Court 6                  BYES
  (11  4 v  9 22) (32  7 v 15 26) (33 14 v  5 21) (27 25 v 16  6) (28 30 v 31 17) ( 1 29 v 18 20)  (12 19  8 13 23 10  2 24  3)
  (12  5 v  7 23) (33  8 v 13 27) (31 15 v  6 19) (25 26 v 17  4) (29 28 v 32 18) ( 2 30 v 16 21)  (10 20  9 14 24 11  3 22  1)
  (10  6 v  8 24) (31  9 v 14 25) (32 13 v  4 20) (26 27 v 18  5) (30 29 v 33 16) ( 3 28 v 17 19)  (11 21  7 15 22 12  1 23  2)
  (25  7 v 16 11) (15 24 v 21  3) (22 12 v 32 30) (13  5 v 17  6) (19 33 v 29  4) ( 1  2 v 28  8)  (26 27 31 23 14  9 10 20 18)
  (26  8 v 17 12) (13 22 v 19  1) (23 10 v 33 28) (14  6 v 18  4) (20 31 v 30  5) ( 2  3 v 29  9)  (27 25 32 24 15  7 11 21 16)
  (27  9 v 18 10) (14 23 v 20  2) (24 11 v 31 29) (15  4 v 16  5) (21 32 v 28  6) ( 3  1 v 30  7)  (25 26 33 22 13  8 12 19 17)
  (11 12 v 15 18) (32 22 v 33  2) (24 29 v  5 14) ( 1 31 v  8 27) (21 25 v  7 19) ( 6 13 v  9  3)  (26 23 28 10  4 17 30 20 16)
  (12 10 v 13 16) (33 23 v 31  3) (22 30 v  6 15) ( 2 32 v  9 25) (19 26 v  8 20) ( 4 14 v  7  1)  (27 24 29 11  5 18 28 21 17)
  (10 11 v 14 17) (31 24 v 32  1) (23 28 v  4 13) ( 3 33 v  7 26) (20 27 v  9 21) ( 5 15 v  8  2)  (25 22 30 12  6 16 29 19 18)
  (30 26 v  4 24) ( 8 23 v 11 21) (27  3 v 28 25) (22 15 v  2 13) (19 14 v 18 33) (31  5 v  7  6)  (12  9 10 17  1 20 32 29 16)
  (28 27 v  5 22) ( 9 24 v 12 19) (25  1 v 29 26) (23 13 v  3 14) (20 15 v 16 31) (32  6 v  8  4)  (10  7 11 18  2 21 33 30 17)
  (29 25 v  6 23) ( 7 22 v 10 20) (26  2 v 30 27) (24 14 v  1 15) (21 13 v 17 32) (33  4 v  9  5)  (11  8 12 16  3 19 31 28 18)
  (18 23 v 25 20) (10 17 v 12 29) ( 5  6 v 22 21) (14  2 v 28 26) ( 1 33 v 11 32) ( 7 24 v  9 30)  (16 13  3  4 31 15  8 27 19)
  (16 24 v 26 21) (11 18 v 10 30) ( 6  4 v 23 19) (15  3 v 29 27) ( 2 31 v 12 33) ( 8 22 v  7 28)  (17 14  1  5 32 13  9 25 20)
  (17 22 v 27 19) (12 16 v 11 28) ( 4  5 v 24 20) (13  1 v 30 25) ( 3 32 v 10 31) ( 9 23 v  8 29)  (18 15  2  6 33 14  7 26 21)
  (29 21 v 26 22) (33 15 v 18 25) (19 10 v  8 30) ( 7 27 v  4 16) (17  2 v 23  1) (12  6 v 14 20)  ( 9  3 24  5 32 11 31 13 28)
  (30 19 v 27 23) (31 13 v 16 26) (20 11 v  9 28) ( 8 25 v  5 17) (18  3 v 24  2) (10  4 v 15 21)  ( 7  1 22  6 33 12 32 14 29)
  (28 20 v 25 24) (32 14 v 17 27) (21 12 v  7 29) ( 9 26 v  6 18) (16  1 v 22  3) (11  5 v 13 19)  ( 8  2 23  4 31 10 33 15 30)
  (30  4 v 29  2) (13 26 v  9  8) ( 7 20 v 33 17) (11  1 v 32 27) (14 18 v 16 22) ( 3 12 v 21 19)  (10 31  5 24 15 25 28 23  6)
  (28  5 v 30  3) (14 27 v  7  9) ( 8 21 v 31 18) (12  2 v 33 25) (15 16 v 17 23) ( 1 10 v 19 20)  (11 32  6 22 13 26 29 24  4)
  (29  6 v 28  1) (15 25 v  8  7) ( 9 19 v 32 16) (10  3 v 31 26) (13 17 v 18 24) ( 2 11 v 20 21)  (12 33  4 23 14 27 30 22  5)
  (24 32 v 23 16) (33 30 v 14  8) (12  1 v 26  6) (31 19 v  7  2) (11 29 v 15 27) (18 28 v 21  4)  (10  9  5 13  3 17 22 20 25)
  (22 33 v 24 17) (31 28 v 15  9) (10  2 v 27  4) (32 20 v  8  3) (12 30 v 13 25) (16 29 v 19  5)  (11  7  6 14  1 18 23 21 26)
  (23 31 v 22 18) (32 29 v 13  7) (11  3 v 25  5) (33 21 v  9  1) (10 28 v 14 26) (17 30 v 20  6)  (12  8  4 15  2 16 24 19 27)
  (16  8 v 14 29) ( 1 21 v 10  5) (24 13 v 25  2) (19 32 v 30 18) (12  9 v 22 23) (11 17 v  4  3)  ( 6 26 28  7 33 31 15 20 27)
  (17  9 v 15 30) ( 2 19 v 11  6) (22 14 v 26  3) (20 33 v 28 16) (10  7 v 23 24) (12 18 v  5  1)  ( 4 27 29  8 31 32 13 21 25)
  (18  7 v 13 28) ( 3 20 v 12  4) (23 15 v 27  1) (21 31 v 29 17) (11  8 v 24 22) (10 16 v  6  2)  ( 5 25 30  9 32 33 14 19 26)
  (11 31 v 14 13) ( 8 12 v  4 28) ( 1 17 v 16  9) (22 10 v 32 25) (27  6 v 33 24) (15 19 v 26 20)  (29 18  3 23 21 30  7  5  2)
  (12 32 v 15 14) ( 9 10 v  5 29) ( 2 18 v 17  7) (23 11 v 33 26) (25  4 v 31 22) (13 20 v 27 21)  (30 16  1 24 19 28  8  6  3)
  (10 33 v 13 15) ( 7 11 v  6 30) ( 3 16 v 18  8) (24 12 v 31 27) (26  5 v 32 23) (14 21 v 25 19)  (28 17  2 22 20 29  9  4  1)
6
Requests / Re: Please help!
« Last post by Ian Wakeling on June 28, 2022, 03:32:48 AM »
Here is a doubles schedule for 31 players, 6 courts and 31 rounds, all the partnerships are different, players oppose each other once or twice (if you do play the last round it will be balanced in the sense that everyone has exactly 7 byes and the same number of games).  I don't know what you mean by 'Beijing' doubles, so hope that's not something important.

    Court 1        Court 2        Court 3          Court 4        Court 5        Court 6                BYES
 ( 1 19 v 30 23) (24  9 v 12 14) ( 6 11 v  5 27) ( 7 26 v  8  2) (18  4 v 21 10) (28 20 v 16 13)  (25 29 15 17  3 31 22)
 ( 2 20 v 31 24) (25 10 v 13 15) ( 7 12 v  6 28) ( 8 27 v  9  3) (19  5 v 22 11) (29 21 v 17 14)  (26 30 16 18  4  1 23)
 ( 3 21 v  1 25) (26 11 v 14 16) ( 8 13 v  7 29) ( 9 28 v 10  4) (20  6 v 23 12) (30 22 v 18 15)  (27 31 17 19  5  2 24)
 ( 4 22 v  2 26) (27 12 v 15 17) ( 9 14 v  8 30) (10 29 v 11  5) (21  7 v 24 13) (31 23 v 19 16)  (28  1 18 20  6  3 25)
 ( 5 23 v  3 27) (28 13 v 16 18) (10 15 v  9 31) (11 30 v 12  6) (22  8 v 25 14) ( 1 24 v 20 17)  (29  2 19 21  7  4 26)
 ( 6 24 v  4 28) (29 14 v 17 19) (11 16 v 10  1) (12 31 v 13  7) (23  9 v 26 15) ( 2 25 v 21 18)  (30  3 20 22  8  5 27)
 ( 7 25 v  5 29) (30 15 v 18 20) (12 17 v 11  2) (13  1 v 14  8) (24 10 v 27 16) ( 3 26 v 22 19)  (31  4 21 23  9  6 28)
 ( 8 26 v  6 30) (31 16 v 19 21) (13 18 v 12  3) (14  2 v 15  9) (25 11 v 28 17) ( 4 27 v 23 20)  ( 1  5 22 24 10  7 29)
 ( 9 27 v  7 31) ( 1 17 v 20 22) (14 19 v 13  4) (15  3 v 16 10) (26 12 v 29 18) ( 5 28 v 24 21)  ( 2  6 23 25 11  8 30)
 (10 28 v  8  1) ( 2 18 v 21 23) (15 20 v 14  5) (16  4 v 17 11) (27 13 v 30 19) ( 6 29 v 25 22)  ( 3  7 24 26 12  9 31)
 (11 29 v  9  2) ( 3 19 v 22 24) (16 21 v 15  6) (17  5 v 18 12) (28 14 v 31 20) ( 7 30 v 26 23)  ( 4  8 25 27 13 10  1)
 (12 30 v 10  3) ( 4 20 v 23 25) (17 22 v 16  7) (18  6 v 19 13) (29 15 v  1 21) ( 8 31 v 27 24)  ( 5  9 26 28 14 11  2)
 (13 31 v 11  4) ( 5 21 v 24 26) (18 23 v 17  8) (19  7 v 20 14) (30 16 v  2 22) ( 9  1 v 28 25)  ( 6 10 27 29 15 12  3)
 (14  1 v 12  5) ( 6 22 v 25 27) (19 24 v 18  9) (20  8 v 21 15) (31 17 v  3 23) (10  2 v 29 26)  ( 7 11 28 30 16 13  4)
 (15  2 v 13  6) ( 7 23 v 26 28) (20 25 v 19 10) (21  9 v 22 16) ( 1 18 v  4 24) (11  3 v 30 27)  ( 8 12 29 31 17 14  5)
 (16  3 v 14  7) ( 8 24 v 27 29) (21 26 v 20 11) (22 10 v 23 17) ( 2 19 v  5 25) (12  4 v 31 28)  ( 9 13 30  1 18 15  6)
 (17  4 v 15  8) ( 9 25 v 28 30) (22 27 v 21 12) (23 11 v 24 18) ( 3 20 v  6 26) (13  5 v  1 29)  (10 14 31  2 19 16  7)
 (18  5 v 16  9) (10 26 v 29 31) (23 28 v 22 13) (24 12 v 25 19) ( 4 21 v  7 27) (14  6 v  2 30)  (11 15  1  3 20 17  8)
 (19  6 v 17 10) (11 27 v 30  1) (24 29 v 23 14) (25 13 v 26 20) ( 5 22 v  8 28) (15  7 v  3 31)  (12 16  2  4 21 18  9)
 (20  7 v 18 11) (12 28 v 31  2) (25 30 v 24 15) (26 14 v 27 21) ( 6 23 v  9 29) (16  8 v  4  1)  (13 17  3  5 22 19 10)
 (21  8 v 19 12) (13 29 v  1  3) (26 31 v 25 16) (27 15 v 28 22) ( 7 24 v 10 30) (17  9 v  5  2)  (14 18  4  6 23 20 11)
 (22  9 v 20 13) (14 30 v  2  4) (27  1 v 26 17) (28 16 v 29 23) ( 8 25 v 11 31) (18 10 v  6  3)  (15 19  5  7 24 21 12)
 (23 10 v 21 14) (15 31 v  3  5) (28  2 v 27 18) (29 17 v 30 24) ( 9 26 v 12  1) (19 11 v  7  4)  (16 20  6  8 25 22 13)
 (24 11 v 22 15) (16  1 v  4  6) (29  3 v 28 19) (30 18 v 31 25) (10 27 v 13  2) (20 12 v  8  5)  (17 21  7  9 26 23 14)
 (25 12 v 23 16) (17  2 v  5  7) (30  4 v 29 20) (31 19 v  1 26) (11 28 v 14  3) (21 13 v  9  6)  (18 22  8 10 27 24 15)
 (26 13 v 24 17) (18  3 v  6  8) (31  5 v 30 21) ( 1 20 v  2 27) (12 29 v 15  4) (22 14 v 10  7)  (19 23  9 11 28 25 16)
 (27 14 v 25 18) (19  4 v  7  9) ( 1  6 v 31 22) ( 2 21 v  3 28) (13 30 v 16  5) (23 15 v 11  8)  (20 24 10 12 29 26 17)
 (28 15 v 26 19) (20  5 v  8 10) ( 2  7 v  1 23) ( 3 22 v  4 29) (14 31 v 17  6) (24 16 v 12  9)  (21 25 11 13 30 27 18)
 (29 16 v 27 20) (21  6 v  9 11) ( 3  8 v  2 24) ( 4 23 v  5 30) (15  1 v 18  7) (25 17 v 13 10)  (22 26 12 14 31 28 19)
 (30 17 v 28 21) (22  7 v 10 12) ( 4  9 v  3 25) ( 5 24 v  6 31) (16  2 v 19  8) (26 18 v 14 11)  (23 27 13 15  1 29 20)
 (31 18 v 29 22) (23  8 v 11 13) ( 5 10 v  4 26) ( 6 25 v  7  1) (17  3 v 20  9) (27 19 v 15 12)  (24 28 14 16  2 30 21)
7
Requests / Re: Please help!
« Last post by kjgrossman on June 27, 2022, 02:29:57 PM »
Okay, for my group of 64 I am just going to play 3's and I got that figured out.  So, what I need is a Beijing's doubles schedule for 31 players on 6 courts for 30 rounds and 
33  players Beijings doubles  on 6 courts for 30 rounds.  Is that do able?  THANK YOU SO MUCH!!
8
Requests / Re: Please help!
« Last post by Ian Wakeling on June 27, 2022, 09:54:59 AM »
Approximately how many rounds do you think you can play?  I need to have some idea.

Is the size of 64 player group absolutely fixed?  I ask as if you have 10 courts with 6 players per court, then a schedule for 60 players is obviously best.
9
Requests / Re: Please help!
« Last post by kjgrossman on June 27, 2022, 09:20:42 AM »
Ahhh...yes I did not do a very good job thinking this through in my description. 

I have 5 nets but because they are playing only on half the court I actually have 10 courts available for the group of 64 and 6 courts available for the group of 31 and 32.  After reading your reply you are probably correct and to prevent too many kids from sitting out in the group of 64 lets change that to groups of 3's playing on 10 courts.  Does that sound like a better idea?  

Thank you so much for your help!!
10
Requests / Re: Please help!
« Last post by Ian Wakeling on June 27, 2022, 04:01:22 AM »
To me it seems that you will have way too many players sitting around doing nothing.  Taking 32 players and 3 courts of doubles as an example, you could play 8 rounds as follows:

    Court 1      Court 2      Court 3
  (32 16 11 26) (30  6 23 22) (15  1 19  7)
  (25  9 12 27) (31  7 24 23) (16  2 20  8)
  (26 10 13 28) (32  8 17 24) ( 9  3 21  1)
  (27 11 14 29) (25  1 18 17) (10  4 22  2)
  (28 12 15 30) (26  2 19 18) (11  5 23  3)
  (29 13 16 31) (27  3 20 19) (12  6 24  4)
  (30 14  9 32) (28  4 21 20) (13  7 17  5)
  (31 15 10 25) (29  5 22 21) (14  8 18  6)

Here no two players appear on court together twice, so they are free to split into two-vs-two any way you like. There will be 20 players with a bye in each round, and any one player has 3 games and 5 byes.

Can you state how many rounds you will be able to play?  Are there more than 5 courts available?