A co-worker came to me one day, several years ago, and said,
"I'm in this baseball league and we need to make a schedule so that
each team plays every other team once." "I was thinking of writing a
computer program to make the job easier and maybe selling it, but
I don't know any systematic way to make the schedule myself." "If you
can figure it out I'll buy you dinner."
I like puzzles, so I started thinking and soon found a solution.
When I told my friend the next day he was disappointed. It was too
simple. You don't need a computer program. He never did buy me dinner
either.
So here's my solution. I hope someone can get some use out of it.
Represent each team by a different letter. Arrange them in a box, 2
letters high and as wide as you need. You will see eleven such boxes below.
The box represents all the team match ups for a given day. The teams that
are above and below eachother play eachother on that day. In the first
box below team A plays B, L plays C, K plays D, etc.
To get the next set of game match ups, draw a new box. Copy the team
in the lower left corner of the 1st box into the same position in the new box.
That's team A in the example below. I've colored it differently since only
it stays in the same position all the time.
Then rotate the remaining letters counter clockwise (anti-clockwise) one
position. You'll see that below in the second box, where team A plays C.
Use the same process to go from box 2 to box 3, and so forth until you
have one fewer box than you have teams. At that point each team will have
played every other team once. Simple, no?
The following example shows the situation for 12 teams.