Many members of the club disliked the lack of variety and togetherness at the club. Although the club still had 12 members, some members were threatening to quit because each schedule was so short and there were so few people around each table.

To satisfy their request, the club decided to seat themselves around a big table and create a longer schedule. The twelve members of the club seated themselves in a schedule such that during each block of 55 days, no person was between the same pair of people. How was the schedule constructed?

(Based on The Round Table)

(In reply to A more systematic approach...but still too big for the computer by Charlie)

Maybe you can set your program to find solutions for fewer people and see if there's patterns in each solution as you add more people. IOW, if your computer is able to find solutions for 8 & 10 people but 12 is too difficult for it, then studying the patterns in the solutions for 8 & 10 might help you refine your program to make it easier for it to solve for 12.  just a suggestion.

oh, if you could, could you please post the solutions for 8 & 10 people, I'd like to study the patterns myself. I found that odds follow different patterns than evens so since our ultimate goal is to solve for 12, I'd forget about 9 & 11.

Posted by Danny on 2004-06-24 09:49:26