A puzzle...
I'm running a 6-team round-robin tournament. Here is a sample schedule, with the columns representing fields and the rows representing game numbers, but you don't have to use it as long as the constraints are satisfied (i.e. every team plays every other within the 5 rounds).
1 v 5 2 v 4 3 v 6
1 v 2 3 v 5 4 v 6
1 v 6 2 v 5 3 v 4
1 v 3 2 v 6 4 v 5
1 v 4 2 v 3 5 v 6
Now the problem with this is that team number one never has to change fields whereas team 3 is moving around every game. How do I optimize it for the least number of moves per team _and_ make it fair? What is that number? What does the schedule look like?
And, to make this a math/CS question, what's the generalized solution for n teams?
Right now I just need a solution for 6 teams, preferably by tomorrow morning! :)
1 v 5 2 v 4 3 v 6
1 v 2 3 v 5 4 v 6
1 v 6 2 v 5 3 v 4
1 v 3 2 v 6 4 v 5
1 v 4 2 v 3 5 v 6
Now the problem with this is that team number one never has to change fields whereas team 3 is moving around every game. How do I optimize it for the least number of moves per team _and_ make it fair? What is that number? What does the schedule look like?
And, to make this a math/CS question, what's the generalized solution for n teams?
Right now I just need a solution for 6 teams, preferably by tomorrow morning! :)