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 re: get started.....a hint by Charlie)

I found a sloution with 6 people. I tried to group it together so that some sorta pattern can be noticed. I kept A on the left because since this is on a round table it doestn't really matter where you start it. The columns on the right show the neighbors for each letter. I found that once I started keeping track of them the answer came a lot easier. I'll study this pattern more and see if I can find a solution with more people.

        A  B  C  D  E  F
ABEFDC BC AE AD FC BF DE
ABFECD BD AF ED AC CF BE
ABDCFE BE AD FD BC AF CE
ABCDEF BF AC BD EC DF AE
ACFBED CD EF AF AE BD BC
ACBFDE CE CF AB FE AD BD
ACEDBF CF DF AE BE CD BA
ADFCBE DE CE BF AF AB CD
ADBECF DF ED EF AB CF CA
AECBDF EF CD BE BF AC DA

Edited on June 23, 2004, 5:18 pm

Posted by Danny on 2004-06-23 17:16:24