Question from Mike, a teacher:
Dear Math Central:
I have a combination problem where I need to identify 1 EXACT combination out of the possible thousands that will occur. So here's my problem:
I need to schedule 18 high school teams to play each other in a "Jeopardy!"-like academic competition. Teams compete against each other 6 at a time (simultaneously) in 3 different rooms. What will the minimum amount of matches (I believe 6 ?) we would have to play to ensure that each team plays every other team exactly twice?
And more importantly: what would that schedule look like?
The best I've come up with is having most teams playing twice, but with 2 pairs of teams having to play either only once or sometimes 3 times.
Thanks in advance for any help you can give! :-)