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| Math Central | Quandaries & Queries |
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Question from Paul, a parent: I'm trying to set up a game matrix for my kids that will have 4 games in 4 time slots with 8 teams. And every team is playing a different game in a different time slot. I provided the initial matrix and I am trying to ensure that no 2 teams play each other more than once. That's my problem. Please help, I've been at it for hours. |
Paul,
I think this will work: http://mathcentral.uregina.ca/QQ/database/QQ.09.15/h/joel1.html
Each station corresponds to a game.
—Victoria
What you need is a "Greco-Latin Square" design
https://en.wikipedia.org/wiki/Graeco-Latin_square
Adapted to your problem:
| 8 | 9 | 10 | 11 | |
|---|---|---|---|---|
| C | 1,2 | 3,6 | 5,8 | 7,4 |
| T | 3,4 | 1,8 | 7,6 | 5,2 |
| D | 5,6 | 7,2 | 1,4 | 3,8 |
| P | 7,8 | 5,4 | 3,2 | 1,6 |
Good Hunting!
RD
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