3v3 for various numbers...

[cvvcdad]

Hi!  I am going to be a HS volleyball coach for the first time this season, and I could really use your help!  I want to play a lot of 3v3 short games, constantly mixing up the teams both in terms of who any given player plays with and also who they are playing against.  This will allow me to quantify a couple major intangibles -- first and foremost, those that consistently lead to winning irregardless of teammates/opponents.

Anyway -- I also coach club ball, and run a camp.  So what I'm looking for is a round-robin-type matrix for n players playing 3v3, with each player playing x times with every other player and y times against every other player.  Ideally, this would be an automated solution where the input variable would be n (the total # of players), but I'll gladly take any and all solutions available.  If there's a website where I can find the answer, just point me to it.

Regarding "n" -- I would love to be able to generate/have solutions for any number of players; at camp we could have as many as 30-40 players.  But if such flexibility is not possible, I REALLY need solutions for n = 10, 11, 14, 16, 17, 19, 20, 22, 23, & 24 (I came up with manual solutions for other n's).  That way I can combine the varsity & JV players into one "tournament".

Btw, I'm far from a mathematician, so I'm afraid I need solutions handed to me.  I've been browsing the internet a bit, and I bow to everyone who understands the complicated stuff I'm seeing in search of my solution.

THANK YOU SO MUCH, IN ADVANCE, FOR YOUR HELP!  I have browsed the first couple pages of this Requests board, and am extremely impressed with both your abilities and willingness to help mathphobes like myself...  

[Ian Wakeling]

Hi,

There are already some schedules here that may be of use to you.  For example see the following links:

8 & 9 players

10 & 11 players

12 players

13 players

Notice that for n=12 & n=13 the schedules are perfect in the sense of the 'x' and 'y' balance that you are looking for.  No such balance will be possible for other values of n.

Below are a few more schedules along the same lines:

14 players, 14 rounds (2 byes per round):

(8 1 12 v 13 11 7) (9 14 6 v 4 3 2) (5 10)
(9 2 13 v 14 12 8) (10 1 7 v 5 4 3) (6 11)
(10 3 14 v 1 13 9) (11 2 8 v 6 5 4) (7 12)
(11 4 1 v 2 14 10) (12 3 9 v 7 6 5) (8 13)
(12 5 2 v 3 1 11) (13 4 10 v 8 7 6) (9 14)
(13 6 3 v 4 2 12) (14 5 11 v 9 8 7) (10 1)
(14 7 4 v 5 3 13) (1 6 12 v 10 9 8) (11 2)
(1 8 5 v 6 4 14) (2 7 13 v 11 10 9) (12 3)
(2 9 6 v 7 5 1) (3 8 14 v 12 11 10) (13 4)
(3 10 7 v 8 6 2) (4 9 1 v 13 12 11) (14 5)
(4 11 8 v 9 7 3) (5 10 2 v 14 13 12) (1 6)
(5 12 9 v 10 8 4) (6 11 3 v 1 14 13) (2 7)
(6 13 10 v 11 9 5) (7 12 4 v 2 1 14) (3 8)
(7 14 11 v 12 10 6) (8 13 5 v 3 2 1) (4 9)

16 players, 16 rounds (4 byes per round):
(15 5 11 v 7 12 14) (4 2 3 v 8 16 13) (10 1 9 6)
(16 6 12 v 8 13 15) (5 3 4 v 9 1 14) (11 2 10 7)
(1 7 13 v 9 14 16) (6 4 5 v 10 2 15) (12 3 11 8)
(2 8 14 v 10 15 1) (7 5 6 v 11 3 16) (13 4 12 9)
(3 9 15 v 11 16 2) (8 6 7 v 12 4 1) (14 5 13 10)
(4 10 16 v 12 1 3) (9 7 8 v 13 5 2) (15 6 14 11)
(5 11 1 v 13 2 4) (10 8 9 v 14 6 3) (16 7 15 12)
(6 12 2 v 14 3 5) (11 9 10 v 15 7 4) (1 8 16 13)
(7 13 3 v 15 4 6) (12 10 11 v 16 8 5) (2 9 1 14)
(8 14 4 v 16 5 7) (13 11 12 v 1 9 6) (3 10 2 15)
(9 15 5 v 1 6 8) (14 12 13 v 2 10 7) (4 11 3 16)
(10 16 6 v 2 7 9) (15 13 14 v 3 11 8) (5 12 4 1)
(11 1 7 v 3 8 10) (16 14 15 v 4 12 9) (6 13 5 2)
(12 2 8 v 4 9 11) (1 15 16 v 5 13 10) (7 14 6 3)
(13 3 9 v 5 10 12) (2 16 1 v 6 14 11) (8 15 7 4)
(14 4 10 v 6 11 13) (3 1 2 v 7 15 12) (9 16 8 5)

17 players, 17 rounds (5 byes per round)
(9 12 11 v 7 1 8) (4 17 13 v 5 10 2) (6 14 16 3 15)
(10 13 12 v 8 2 9) (5 1 14 v 6 11 3) (7 15 17 4 16)
(11 14 13 v 9 3 10) (6 2 15 v 7 12 4) (8 16 1 5 17)
(12 15 14 v 10 4 11) (7 3 16 v 8 13 5) (9 17 2 6 1)
(13 16 15 v 11 5 12) (8 4 17 v 9 14 6) (10 1 3 7 2)
(14 17 16 v 12 6 13) (9 5 1 v 10 15 7) (11 2 4 8 3)
(15 1 17 v 13 7 14) (10 6 2 v 11 16 8) (12 3 5 9 4)
(16 2 1 v 14 8 15) (11 7 3 v 12 17 9) (13 4 6 10 5)
(17 3 2 v 15 9 16) (12 8 4 v 13 1 10) (14 5 7 11 6)
(1 4 3 v 16 10 17) (13 9 5 v 14 2 11) (15 6 8 12 7)
(2 5 4 v 17 11 1) (14 10 6 v 15 3 12) (16 7 9 13 8)
(3 6 5 v 1 12 2) (15 11 7 v 16 4 13) (17 8 10 14 9)
(4 7 6 v 2 13 3) (16 12 8 v 17 5 14) (1 9 11 15 10)
(5 8 7 v 3 14 4) (17 13 9 v 1 6 15) (2 10 12 16 11)
(6 9 8 v 4 15 5) (1 14 10 v 2 7 16) (3 11 13 17 12)
(7 10 9 v 5 16 6) (2 15 11 v 3 8 17) (4 12 14 1 13)
(8 11 10 v 6 17 7) (3 16 12 v 4 9 1) (5 13 15 2 14)

19 players, 19 rounds (1 bye per round):
(12 14 1 v 15 11 8) (5 4 18 v 13 10 3) (9 19 17 v 7 2 6) (16)
(13 15 2 v 16 12 9) (6 5 19 v 14 11 4) (10 1 18 v 8 3 7) (17)
(14 16 3 v 17 13 10) (7 6 1 v 15 12 5) (11 2 19 v 9 4 8) (18)
(15 17 4 v 18 14 11) (8 7 2 v 16 13 6) (12 3 1 v 10 5 9) (19)
(16 18 5 v 19 15 12) (9 8 3 v 17 14 7) (13 4 2 v 11 6 10) (1)
(17 19 6 v 1 16 13) (10 9 4 v 18 15 8) (14 5 3 v 12 7 11) (2)
(18 1 7 v 2 17 14) (11 10 5 v 19 16 9) (15 6 4 v 13 8 12) (3)
(19 2 8 v 3 18 15) (12 11 6 v 1 17 10) (16 7 5 v 14 9 13) (4)
(1 3 9 v 4 19 16) (13 12 7 v 2 18 11) (17 8 6 v 15 10 14) (5)
(2 4 10 v 5 1 17) (14 13 8 v 3 19 12) (18 9 7 v 16 11 15) (6)
(3 5 11 v 6 2 18) (15 14 9 v 4 1 13) (19 10 8 v 17 12 16) (7)
(4 6 12 v 7 3 19) (16 15 10 v 5 2 14) (1 11 9 v 18 13 17) (8)
(5 7 13 v 8 4 1) (17 16 11 v 6 3 15) (2 12 10 v 19 14 18) (9)
(6 8 14 v 9 5 2) (18 17 12 v 7 4 16) (3 13 11 v 1 15 19) (10)
(7 9 15 v 10 6 3) (19 18 13 v 8 5 17) (4 14 12 v 2 16 1) (11)
(8 10 16 v 11 7 4) (1 19 14 v 9 6 18) (5 15 13 v 3 17 2) (12)
(9 11 17 v 12 8 5) (2 1 15 v 10 7 19) (6 16 14 v 4 18 3) (13)
(10 12 18 v 13 9 6) (3 2 16 v 11 8 1) (7 17 15 v 5 19 4) (14)
(11 13 19 v 14 10 7) (4 3 17 v 12 9 2) (8 18 16 v 6 1 5) (15)

Is it useful to carry on with more schedule for higher n, or is the number of rounds becoming too high?

Ian.

[cvvcdad]

Hi Ian --

This is perfect!  I can't tell you how much I appreciate your help!  This is really going to be a huge help -- to the benefit of both myself & the girls -- moving forward.  Pls don't take the time to do more schedules for higher numbers.  If I find out next summer that I need other schedules due to higher camp numbers, I'll re-post then for your help.

This really is a Godsend for me, Ian.  Thanks so much!