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)

The algorithms posted so far are flawless in theory, but tend to break down when you have a significant number of days' schedules produced. It becomes more and more difficult to add new days.  Also, if you have, say, 36 days' schedules already, they may constitute a dead-end. They may represent such a combination of schedules that it is mathematically impossible to proceed. My plan is to have my program initialize a large number of 55-day virtual tables (millions if necessary) with one day's schedule each, randomly generated, each different, and then to begin to randomly generate additional days. Each day will be added to each table it is consistent with. If I run this program all night for successive nights, and code it to save its results to a dataset, then after a week or two it might hit on the correct schedule.

But even this may be underestimating the huge number of possible combinations, only one of which is the answer to this diabolical puzzle.

Posted by Penny on 2004-06-26 09:58:18