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)

I wrote a program to exhaustivly search for solutions. I've got them for 8 and 9 but 10 is taking a long time. 12 seems impractical (years?). Having trouble with formating so here is 8 and if that works I'll put 9 in another posting.

1 A C D E F G H B | BC AH AD CE DF EG FH BG
2 A D C E F H G B | BD AG DE AC CF EH BH FG
3 A E C G D H F B | BE AF EG GH AC BH CD DF
4 A F C D G H E B | BF AE DF CG BH AC DH EG
5 A G C F E H D B | BG AD FG BH FH CE AC DE
6 A H D F E G C B | BH AC BG FH FG DE CE AD
7 A D B E G F H C | CD DE AH AB BG GH EF CF
8 A E D H B F G C | CE FH AG EH AD BG CF BD
9 A F D G E H B C | CF CH AB FG GH AD DE BE
10 A G B H F D E C | CG GH AE EF CD DH AB BF
11 A H E D B G F C | CH DG AF BE DH CG BF AE
12 A E H C F B G D | DE FG FH AG AH BC BD CE
13 A F E B G C H D | DF EG GH AH BF AE BC CD
14 A G H C E B F D | DG EF EH AF BC BD AH CG
15 A H F C B G E D | DH CG BF AE DG CH BE AF
16 A F B C D H G E | EF CF BD CH AG AB EH DG
17 A G F D C H B E | EG EH DH CF AB DG AF BC
18 A H G C D B F E | EH DF DG BC AF BE CH AG
19 A G D B C E H F | FG CD BE BG CH AH AD EF
20 A H C B E D G F | FH CE BH EG BD AG DF AC
21 A H B D F C E G | GH DH EF BF CG CD AE AB

Posted by Rajal on 2004-09-02 11:31:02