Round Robin Tournament Scheduling

Schedules - You must register to Post and Download => Requests => Topic started by: Michael Kapoor(Guest) on February 10, 2014, 03:16:52 PM

Title: Round Robin within a Whist Tourney
Post by: Michael Kapoor(Guest) on February 10, 2014, 03:16:52 PM

I have 8 teams (A, B, C, D, E, F, G, H).  2 fields.  3 rounds each day.  

For each day, I want to pair up each team and have that grouping play a round robin so that each team is paired once with another team and opposes each team twice.  As an example for day 1:  Round 1 is A and B play C and D.  Round 2 is A and C play B and D.  Round 3 is A and D play B and C.  The other teams (E, F, G, H) will do something similar on the other field.  

Then comes the tricky part (for me):  I would like the above format to be repeated so that each team is paired with every other team and plays against all other pairings of teams through the course of the league.  

EX:
AB plays BC, BD, BE, BF, BG, BH, CD, CE, CF, CG, CH, DE, DF, DG, DH, EF, EG, EH, FG, FH, GH over the entire course of the league

How many days would be needed to do this?  What would the format/schedule look like?

I apologize if this question has already been asked.  I might have missed it as I am not great with some of the technical or math-oriented details.

Title: Re: Round Robin within a Whist Tourney
Post by: Ian Wakeling on February 11, 2014, 03:14:13 AM

It would take 35 days.  Essentially the problem boils down to finding all possible combinations of 4 things from 8, there are 70 of these, and then pairing the combinations up to make 35 days, with all teams competing exactly once per day.   I have put an example below, but it is still in a sorted order so you will need to randomize the order of the rows and then for each day,  randomly assign the two columns to the two fields.

1 2 3 4      5 6 7 8
1 2 3 5      4 6 7 8
1 2 3 6      4 5 7 8
1 2 3 7      4 5 6 8
1 2 3 8      4 5 6 7
1 2 4 5      3 6 7 8
1 2 4 6      3 5 7 8
1 2 4 7      3 5 6 8
1 2 4 8      3 5 6 7
1 2 5 6      3 4 7 8
1 2 5 7      3 4 6 8
1 2 5 8      3 4 6 7
1 2 6 7      3 4 5 8
1 2 6 8      3 4 5 7
1 2 7 8      3 4 5 6
1 3 4 5      2 6 7 8
1 3 4 6      2 5 7 8
1 3 4 7      2 5 6 8
1 3 4 8      2 5 6 7
1 3 5 6      2 4 7 8
1 3 5 7      2 4 6 8
1 3 5 8      2 4 6 7
1 3 6 7      2 4 5 8
1 3 6 8      2 4 5 7
1 3 7 8      2 4 5 6
1 4 5 6      2 3 7 8
1 4 5 7      2 3 6 8
1 4 5 8      2 3 6 7
1 4 6 7      2 3 5 8
1 4 6 8      2 3 5 7
1 4 7 8      2 3 5 6
1 5 6 7      2 3 4 8
1 5 6 8      2 3 4 7
1 5 7 8      2 3 4 6
1 6 7 8      2 3 4 5