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 I give up !! :-( by Penny)

I've been trying to get past the 46-day barrier too, my algorithm comes back with only 46 unique combinations (but managed to get it down to a minute for calculation).  We know that 55 is the upper bound for the number of seating plans but I haven't yet figured out a way to prove the lower bound.. Will keep trying when I have time...

Rush

Posted by Rush on 2004-07-28 11:21:29