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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.)
Another solution to 9 | Comment 53 of 62 |
Just to give some idea of the complexity here
Solution to 7 - 0 seconds
Solution to 8 - 59 seconds
Solution to 9 - 16.7 hours
running on a 2.8GHz Pentium 4. With the current algorithm for 10, I expect things will take months :(
Oh well, here is the solution anyway in case you want to compare with Rajal's or look for a pattern

Problem size: 9

Sizeof Pairing: 32

Arc list size: 4320

Size of a Seating: 32

Elements in search space: 20160

Size of search space: 645120

Solution found!!!

A B C D E F G H I

HI EF GI EH BD BG CF AD AC

GI EI FG FH BH CD AC DE AB

GH CF BH EI DG BI AE AC DF

FI CG BD CI FH AE BH EG AD

FH CD BI BF GH AD EI AE CG

FG DH EI BG CH AI AD BE CF

EI FH EG FG AC BD CD BI AH

EH CI BF EG AD CG DF AI BH

EG DG FH BI AF CE AB CI DH

EF EH FI GI AB AC DH BG CD

DI GH EF AG CI CH BD BF AE

DH CH BG AF GI DI CE AB EF

DG DF HI AB FI BE AH CG CE

DF FI GH AE DH AB CI CE BG

DE FG DH AC AI BH BI CF EG

CI DE AG BH BF EI CH DG AF

CH GI AE FI CG DH BE AF BD

CG DI AD BC HI GH AF EF BE

CF EG AH HI BI AG BF CD DE

CE HI AF GH AG CI DE BD BF

CD CE AB AH BG GI EF DI FH

BI AH EH EF CD DG FI BC AG

BH AI DI CF FG DE EH AG BC

BG AE DE CH BC HI AI DF FG

BF AG DG CE DI AH BC FI EH

BE AF DF CG AH BC DI EI GH

BD AC BE AI CF EH HI FG DG

BC AD AI BE DF EG FH GI CH

Solve completed after 60326 seconds


  Posted by Glorat on 2004-09-21 03:33:43
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