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)

It's late at night, and I'm not thinking right... like coming here instead of doing homework... so forgive me for repetition/mistakes/garbage.

It seems like you could divide this group into 2 groups of 6.  Then, you would have them alternate each seat in a circle.  Every day, you would rotate one group and keep the other the same.  For example:

AGBHCIDJEKFL
ALBGCHDIEJFK
AKBLCGDHEIFJ

And so forth.  When possibilities here are exhausted, switch the orders of the two groups, and do it over.  The way I see it, you could get 15 days out of this... which isn't much now that I think about it.  But that's not the end.  You can change the groups around to get the rest of the days.

Posted by Tristan on 2004-03-30 01:50:42