Math CentralQuandaries & Queries


Question from Terry:

We have a team league at our local golf course.
We have 22 teams, we would like it so that each team plays the other team only once.
I have tried the scenario.
1,21;2,20;3,19;4,18;5,17;6,16;7,15;8,14;9,13;10,11;12,X X+1=1 scenario
2, 1;3,21;4,20,5,19,6,18;7,17;8,16;9,15;10,14;11,13;1,X
using formula from other post in your forums.

I can get all the possible playing arrangements. The big quandary is setting up the schedule
so that each week, each team would start on a different hole.

I can get the first 11 weeks scheduled very easily, it is just trying to get the last 11 weeks scheduled?

Any help would be greatly appreciated.


It will take 21 weeks, as each team has 21 opponents. Number the teams 0, 1, ..., 20, and infinity.

Week 1: 1v19, 2v18, 3v17, ..., 10v11, 20 v infinity
Week 2: 2v20, 3v19, 4v18, ..., 11v12, 0 v infinity
Week 3: 3 v 0, 4v 20, ..., 12v13, 1 v infinity

To get each subsequent week, add one to each team number (infinity + 1 = infinity), and wrap around to 0 (like an odometer) after 20 (so 20+1 = 0).

A 22nd week, if desired, can be arranged randomly.

Hope this helps.

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