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 Here is your hint, sir
I know all that.I only beg to differ on "No reasonable person would try to solve this problem manually. It calls for a program....".
I tried to find an algorithm to create an "n+1" th seating out of a given "n"th seating and to ensure that all the distinct configurations are exausted. Delegating the work "by force" to machine does not appeal challenging to me.
Hint: try with 6 people and 10 days.