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)

After my last posting and Glorat's test revealed that there where errors in my solution, I corrected the errors in the program I use to test a solution.  It should now work fine.

When analysing the errors in my last solution, it was clear that they where all situated at the 10th, 11 and the 1st and 2nd column, around where I "seeded" the figure 12.  This 12 was in conflict with the beginning of each row.  So there is a second rule to make seating generating circles (SGS).  First rule was that no member of a SGS should be more then once be neighbour of each other.  Second rule is that no member should form more then once a pair with the member 5 or 6 positions further on the circle.
Starting with a first SGS of 01, 02, 03,..11.  The following ones are found by putting the numbers around a circle, start at 01 and continue to go 5 positions further.  This gives
01, 06, 11,...  For the third SGS, place number two around the circle and use the same technique.

Then for the final solution, the 55 seatings, use the technique described in my former posting (1 clockwise, two anti-clockwise,three clockwise,...) to generate 5 times 11 seatings.

Every time that wheel goes 'round,
You're bound to cover just a little more ground

01 02 11 03 10 04 09 05 08 06 07 12
02 03 01 04 11 05 10 06 09 07 08 12
03 04 02 05 01 06 11 07 10 08 09 12
04 05 03 06 02 07 01 08 11 09 10 12
05 06 04 07 03 08 02 09 01 10 11 12
06 07 05 08 04 09 03 10 02 11 01 12
07 08 06 09 05 10 04 11 03 01 02 12
08 09 07 10 06 11 05 01 04 02 03 12
09 10 08 11 07 01 06 02 05 03 04 12
10 11 09 01 08 02 07 03 06 04 05 12
11 01 10 02 09 03 08 04 07 05 06 12
01 06 07 11 02 05 08 10 03 04 09 12
06 11 01 05 07 10 02 04 08 09 03 12
11 05 06 10 01 04 07 09 02 03 08 12
05 10 11 04 06 09 01 03 07 08 02 12
10 04 05 09 11 03 06 08 01 02 07 12
04 09 10 03 05 08 11 02 06 07 01 12
09 03 04 08 10 02 05 07 11 01 06 12
03 08 09 02 04 07 10 01 05 06 11 12
08 02 03 07 09 01 04 06 10 11 05 12
02 07 08 01 03 06 09 11 04 05 10 12
07 01 02 06 08 11 03 05 09 10 04 12
01 04 09 07 06 10 03 02 11 05 08 12
04 07 01 10 09 02 06 05 03 08 11 12
07 10 04 02 01 05 09 08 06 11 03 12
10 02 07 05 04 08 01 11 09 03 06 12
02 05 10 08 07 11 04 03 01 06 09 12
05 08 02 11 10 03 07 06 04 09 01 12
08 11 05 03 02 06 10 09 07 01 04 12
11 03 08 06 05 09 02 01 10 04 07 12
03 06 11 09 08 01 05 04 02 07 10 12
06 09 03 01 11 04 08 07 05 10 02 12
09 01 06 04 03 07 11 10 08 02 05 12
01 05 08 09 04 02 11 06 07 10 03 12
05 09 01 02 08 06 04 10 11 03 07 12
09 02 05 06 01 10 08 03 04 07 11 12
02 06 09 10 05 03 01 07 08 11 04 12
06 10 02 03 09 07 05 11 01 04 08 12
10 03 06 07 02 11 09 04 05 08 01 12
03 07 10 11 06 04 02 08 09 01 05 12
07 11 03 04 10 08 06 01 02 05 09 12
11 04 07 08 03 01 10 05 06 09 02 12
04 08 11 01 07 05 03 09 10 02 06 12
08 01 04 05 11 09 07 02 03 06 10 12
01 10 03 08 05 06 07 04 09 02 11 12
10 08 01 06 03 04 05 02 07 11 09 12
08 06 10 04 01 02 03 11 05 09 07 12
06 04 08 02 10 11 01 09 03 07 05 12
04 02 06 11 08 09 10 07 01 05 03 12
02 11 04 09 06 07 08 05 10 03 01 12
11 09 02 07 04 05 06 03 08 01 10 12
09 07 11 05 02 03 04 01 06 10 08 12
07 05 09 03 11 01 02 10 04 08 06 12
05 03 07 01 09 10 11 08 02 06 04 12
03 01 05 10 07 08 09 06 11 04 02 12
           

 

Posted by Hugo on 2004-10-14 14:28:47