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 am determined to solve this diabolical puzzle ! by Penny)

one more idea. If you're planning to find the solution by finding one day at a time, then if you run into a dead-end, back track by rearranging the last day that you figured out, that may not be the best way to do it. IOW, if you got up to 40 days then ran into a dead end, then by rearranging the 40th day to try and get farther might not be the best thing to do. If days 2-40 are all part of the same solution but day 1 is part of a different solution then by rearranging the 1st day to try and find a combination that fits into the others you would be better off than wiping out all of the days you already figured out. Of course, it's not easy to figure out which days are good and which are not. All you can know is that if you run into a dead end then there is a mistake somewhere in the days you already chose. Of course if there was a way to know which ones to change that would make it a whole lot easier. Maybe there is a way?

Edited on June 29, 2004, 7:00 pm

Posted by Danny on 2004-06-29 18:59:03