12 teams 8 rounds

[mustardjohn]

I am starting a couples bridge group. We have 12 couples who will meet and play at three houses (4 couples at each house) each month for 8 months. I can not figure out how maximize the number of times each couple plays at the same house. I may just not have enough rounds, 8, but I keep getting some couples that play each other 3 times in the 8 months and some couples that play each other only once in 8 months.

This is site has some real smart folks on it. I looked around some but still can't solve my problem

I could sure use some help. Thanks

[Ian Wakeling]

It's possible to arrange that all pairs of couples meet together at the same house either two or three times each.

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

I think that may solve your problem.  If you had 11 months then it would be possible to do better and have all pairs of couples meet exactly three times each.

[mustardjohn]

Thank you so much! Yes, I had the 11 month solution from the Whisk tables on this site but I could not figure out the truncated 8 month schedule. Every time I tried to fix the one couple it put another couple to one time. So thanks again!!