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 No solutions for the 7 person case?
No one has noticed this before, but there is a certain similarity between this puzzle, and another highly rated puzzle, SilverKnight's "Perfect Shuffle." In that thread, Charlie noted "In the specific deck sizes asked for: 52 cards require 8 shuffles; 64 require 6; 10 cards require 6 also." But the unanswered question was: why? In this puzzle, "The Conversing Club 3", as you noted, it is impossible to arrange 15 days for 7 people, but very easy to find 48 days for 12 people. This defies common sense, which is what makes it a good perplexus entry, like "Perfect Shuffle".
As Danny stated in "Perfect Shuffle", "BLLAH!!!! it's too complicated, forget it, i give up!"
Edited on August 13, 2004, 9:27 am
Posted by Penny
on 2004-08-13 09:19:42