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 The Conversing Club 3 (Posted on 2004-03-28)
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)

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 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  GABCDEFG  GB AC BD CE DF EG FAABEDGCF  FB AE GF EG BD CA DCABGDCFE  EB AG DF GC FA CE BDABFEGCD  DB AF GD CA FG BE ECABDEGFC  CB AD FA BE DG GC EFACDFEBG  GC EG AD CF FB DE BAACBEGDF  FC CE AB GF BG DA EDACGFDBE  EC DE AG FB BA GD CFACEBFGD  DC EF AE GA CB BG FDADBFCEG  GD DF FE AB CG BC EAADECGBF  FD GF EG AE DC BA CBADFCBGE  ED CG FB AF GA DC BEAEDFBCG  GE FC BG EF AD DB CAAECDBGF  FE DG ED CB AC GA BFAFECBDG  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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