Round Robin Tournament Scheduling

Schedules - You must register to Post and Download => Requests => Topic started by: arnaud on October 25, 2011, 11:43:42 AM

Title: 16 players - threesomes or foursomes
Post by: arnaud on October 25, 2011, 11:43:42 AM

Hi,

I have found on this forum a really great schedule for 14 golfers with some foursomes and threesomes rounds which is exactly what I need..

the Schedule is here

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

Except that I need the same (foursomes and threesomes) but for 16 or 18 players (and I really really don't know how to do that)..

So if someone could help me that will be really fantastic..

thanks,

arnaud

Title: Re: 16 players - threesomes or foursomes
Post by: Ian Wakeling on October 26, 2011, 08:31:36 AM

Surely the best option for 16 players is to have four foursomes which is covered here and elsewhere as the social square.  Or are you considering 4 threesomes + 1 foursome?

With 18 players I think you may need as many as 8 rounds (of 3 foursomes + 2 threesomes) before it is possible to have a schedule where everyone plays at least once with everyone else, there will be many pairs that play twice. Can you manage that many rounds?  But if you wanted 5 rounds then see Ed Pegg's page where he discusses How long can 20 golfers play in foursomes? (https://web.archive.org/web/20120503232317/http://www.maa.org/editorial/mathgames/mathgames_08_14_07.html), simply delete a pair of players such as A & G, who never occur together, to derive an 18 player schedule. Note that as the 20 player, 6 round foursome schedule is known not to exist, then it will mean that there are no nice solutions to the 18 players 6 round problem.

Let me know the number of rounds you would like to have with 18 players and I will make a schedule for you.

Ian.

Title: Re: 16 players - threesomes or foursomes
Post by: arnaud on October 26, 2011, 09:27:03 AM

Hi Ian,

First I would like to thank you very much for your help..

Ok for the 18 players, I will try to deal with the existing table..

But for the 16 players, I think it will be perfect to have 1 foursomes and 3 threesomes as you suggest..

thanks

arnaud