Math CentralQuandaries & Queries


Question from John, a parent:

How can I set up a schedule for 2 teams of 10 on a team to play each individually against each other over a 10 day span at 10 different course with 10 different start times each day. I was looking to not repeat any competition. As an example, Team A would consist of players 1-10, Team B would consist of players 11-20. I would want to have 10 start times a day for 10 days where a member of team A plays a member of team B each day without repeating any matches and any of the same courses and not repeating any of the same start times. Any help in this would be GREATLY appreciated!!!!


You can schedule the matches this way. Let’s also number the players in team B from 1 to 10. Now list the players in Team B twice like this: 1, 2, …, 10, 1, 2, …, 10.

For n = 1, 2, …, 10, on Day n, player number x from team A plays against the player listed in position n + x -1 above. For example, on Day 5, player 2 from team A plays against against the player listed in position 5 + 2 - 1 (player B 6), and player 8 from team A plays against the player listed in position 5 + 8 - 1 (player B 2). Each player from team A will play each player from team B once.

Now, to schedule the courses, first make a 10 x 10 array that starts like this:
1 2 3 4 5 6 7 8 9 10
10 1 2 3 4 5 6 7 8 9
9 10 1 2 3 4 5 6 7 8
and where each subsequent row is obtained from the one above by shifting each entry right and wrapping it around. (The diagonal entries are all equal to 1.) The way to read the array is that when player i from team A meets player j from team B, they use the course whose number is in row i and column j of the array. Every player will use every course exactly once.

Hope this helps.


About Math Central
* Registered trade mark of Imperial Oil Limited. Used under license.


Math Central is supported by the University of Regina and the Imperial Oil Foundation.
Quandaries & Queries page Home page University of Regina Imperial Oil Foundation