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)

(In reply to re: No solutions for the 7 person case? - YES THERE IS! by GOM)

I let the search for 8 run for 24 hours and still nothing came up. The thing is that I don't know if it was still searching or if it was stuck in a loop. Back when I was trying to solve 7, I used the same program that solved 6 but it didn't work. I tried running it in debug mode (which runs about 100 times slower) and saw that it was looping on row 12. Same program that worked for 6 didn't work for 7. It encountered a situation that didn't show up in the search for 6 that it got stuck on. So just because I got my program to work for 7 doesn't mean that it's just a matter of time before it solves 8. It could still be in a loop. Or could it just be that it will take a few days for it to solve 8? I wasn't expecting that. It only took 4 minutes to solve 7. I'll have to keep digging.

Posted by Danny on 2004-08-16 17:12:03