Bridge Club Scheduling

[kulawinski]

Bridge Club - 12 couples - play 6 times a year with 4 couples at 3 different homes playing each other - need a schedule whereby no one couple plays any other couple more than two times in any one year. A solution would make a very senior club very happy.  Thank you. [smiley=dankk2.gif]  

[Ian Wakeling]

I don't believe that it is possible to have a schedule with the properties that you have described.  There will always be a few pairs of couples who meet together three times.  The schedule at the bottom of this topic is about the best that you can do.

[Ian Wakeling]

Just had another thought as I was re-reading the old messages.  It is possible to keep within the 'no pair more than twice' rule, but only if you are prepared to have a few pairs who never meet.  The best solution I have is:

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

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

which has 3 missing pairs: (1 12), (2 10) and (3 11).  I guess you could use this to your advantage, if perhaps it is better that some couples should be kept away from others!

Ian.