Sometimes it takes a stranger to knock some sense into you.
Hello Richard,
My mother is into brigde matches, I am into math so that is how I got interested in your Round Robin solutions. And this is my discovery: for an odd number of players (couples, for bridge) you can just throw out all the complex algorithms.
It is as easy as dialing!
Here's the idea:
Setup the edge graph with the odd couple at the top. Draw connecting lines (=the games) horizontally. This is the universal graph that suffices to play all the rounds in the competition: just turn the dial and off you go !
My mother uses the dial in a cardboard version. The names of the couples are written on the blackboard, then the cardboard dial is affixed to the blackboard. They play the competition while turning the dial at random for every round.
It works for any odd number, and, frankly, I think that there's nothing that beats the alluring simplicity of turning the dial.
The idea can be extended to even numbers of couples, but there are complications and your algorithms make for a more efficient schedule.
Well, just thought to tell you. I was happily amazed at the simplicity of it all.
Happy X-mas season !
LEX Wedemeijer
the Netherlands
LEX:
Thanks for the interest.
If you were able to run the java application, I think you would have seen something like 'turn the dial'. The edge graphs, are from the complicated algorithm I worked up. I can't prove it, but I think the patterns in the edge graphs are somehow related to factorizations and symmetries of the number.
For all the complexity I endured, it took me ten years to find the wisdom of the simple way!
December 21, 2001
