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The Conversing Club 3 (Posted on 2004-03-28) Difficulty: 5 of 5
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)

No Solution Yet Submitted by Gamer    
Rating: 4.5714 (14 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts another 7 | Comment 44 of 62 |
(In reply to re: No solutions for the 7 person case? - YES THERE IS! by GOM)

While playing around with my search mechanism to make it easier to solve 8, I happened upon another solution for 7...

          A  B  C  D  E  F  G
ABCDEFG  GB AC BD CE DF EG FA
ABEDGCF  FB AE GF EG BD CA DC
ABGDCFE  EB AG DF GC FA CE BD
ABFEGCD  DB AF GD CA FG BE EC
ABDEGFC  CB AD FA BE DG GC EF
ACDFEBG  GC EG AD CF FB DE BA
ACBEGDF  FC CE AB GF BG DA ED
ACGFDBE  EC DE AG FB BA GD CF
ACEBFGD  DC EF AE GA CB BG FD
ADBFCEG  GD DF FE AB CG BC EA
ADECGBF  FD GF EG AE DC BA CB
ADFCBGE  ED CG FB AF GA DC BE
AEDFBCG  GE FC BG EF AD DB CA
AECDBGF  FE DG ED CB AC GA BF
AFECBDG  GF CD EB BG FC AE DA

This one matches my previous solution only in lines 1 & 9. Not that it matters much, but.... I left the program running over the weekend... 60 hours.... to solve 8 and it came up with nothing. There has to be another way to solve these without going through all the combinations alphabetically. I think it's time to start thinking creatively. I'll come up with something eventually.......


  Posted by Danny on 2004-08-23 17:40:52
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