SOLUTION: I have a group of 8 people who play bridge every month. There are 4 people per table so 2 tables per month I need to develop a list of who plays with each other. I want to arrang

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Question 654404: I have a group of 8 people who play bridge every month. There are 4 people per table so 2 tables per month
I need to develop a list of who plays with each other. I want to arrange it so that everybody gets to play with each other as equal as possible over the course of a year
I feel that there has to be a simple mathmatical way of doing this instead of just trying to be random.
Thanks for your help!
Ann
AnnMarion123@hotmail.com
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

Re TY, Set UP should not result in any duplicate pairs.  See below:

"arrange it so that everybody gets to play with each other as equal as possible over the course of a year"

first: number people 1-8 and Make a List of Your  Possible Pairings:

1 with 2-8  7 pairings

2 with 3-8  6 pairings

3 with 4-8  5 pairings

4 with 5-8  4 pairings

5 with 6-8  3 pairings

6 with 7&8  2 pairings

7 with 8    1 pairings

              28 Possible pairings  (Statisticallly, that would be 8C2)

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

2-3	2-4	2-5	2-6		2-8     2-7	

3-4	3-5	3-6	3-7	3-8		

4-5	4-6	4-7	4-8			

5-6	5-7	5-8				

6-7	6-8					

7-8						

As random drawing may result in 2 "1s", as You pointed out, rather than redrawing...

might be simpler to just go down the columns and choose the pairings, for ex: (1-2, 3-4) (2-3,4-5) etc

Might then recommend drawing 4 pairings(out of a box originally containing the 28)each month

(do not replace them in that box) and assign them to one of the two tables.

After 7 months, All of the 28 pairings could go back in a box for another round of drawings. 



  

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