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)
Curse you Gamer for coming up with this puzzle.
Curse you Penny for saying there is no solution.
Curse SK for saying that there definitely is a solution....it's in the method.
My plan last week was to replace the suspension on my Jeep. I barely finished it because I wasted so much time on this puzzle. I've been searching for a pattern of changing seats that will allow for all 55 days, but I can't find it. Looking at it like the 12 hour positions on a clock, I've tried moving every 3rd person clockwise; Trading seats with the person directly across from each other; and a combination of both. The best I got so far is 18 days. I'm currently working on movements from 5 points on a star. Like the person at 12 moves to 7 and the person at seven moves to 2 and 2 moves to 10 and 10 moves to 5 who then moves to 12. It hasn't panned out yet.
I get the feeling that because there are 55 days, there should be either 11 permutations with 5 unique sub permutations or 5 permutations with 11 unique sub permutations. If the computers can't find the solution, there must be a pattern that coincidentally will. I haven't given up yet, but I have to stop thinking about it for a little while.
Don't you dare post the solution yet. I haven't completely mind my lost yet.
Edited on September 19, 2004, 7:53 am