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 Remember "The Perfect Shuffle" ? by Penny)

Well, I'm not giving up on this one! Even if it takes me (or my computer) from now until the end of eternity! Besides, what I gave up on was trying to find a pattern in the solutions for various numbers of cards. The original problem had already been solved. It's hard to find patterns from one solution to another when each one keeps getting bigger. For ex, for each of the solutions, the first row may consist of all the letters in order, and the first column may all be A's and there may be patterns in the second and last columns, but as the schedule gets bigger there's more randomness in there. But, the more patterns you can predict before you even start searching, the easier it would be on your computer. I'll have the solution soon.

Posted by Danny on 2004-08-14 12:53:38