Exercise: A local athletics league is creating a schedule. There are 11 teams in the league, and they would like to meet in 3-way competitions so that each team faces all of the others, in as few competitions and with as little duplication as possible. How should the schedule be laid out?
Thoughts so far: From the perspective of one team, there are 10 opponents. Meeting two at a time, it seems like a 5-competition schedule should be possible. Which would allow each team to face each other exactly once.
Full disclosure: I'm not actually a student. I'm a high school track coach, working with our league commissioner to solve this exact problem for the 2015 spring season. I've read "Designs, Geometry, and a Golfer's Dilemma", but otherwise haven't dealt with vector spaces or other abstract mathematics in at least a decade. I've tried adapting the schedule provided in that paper (for 16-teams in 4-way competition), but haven't had much luck yet. I figure a mathematician could either help me find a solution or at least tell me if one doesn't exist, which would save me from the pain of further Brute Force.
Thanks,
Coach Tim
Thoughts so far: From the perspective of one team, there are 10 opponents. Meeting two at a time, it seems like a 5-competition schedule should be possible. Which would allow each team to face each other exactly once.
Full disclosure: I'm not actually a student. I'm a high school track coach, working with our league commissioner to solve this exact problem for the 2015 spring season. I've read "Designs, Geometry, and a Golfer's Dilemma", but otherwise haven't dealt with vector spaces or other abstract mathematics in at least a decade. I've tried adapting the schedule provided in that paper (for 16-teams in 4-way competition), but haven't had much luck yet. I figure a mathematician could either help me find a solution or at least tell me if one doesn't exist, which would save me from the pain of further Brute Force.
Thanks,
Coach Tim