Math CentralQuandaries & Queries


Question from Joshua:

Thank in advance for this great service

Golf - new - 3 teams of 20 - to create 20 unique groups of 3

For example use 3 teams of 3

1a 2a 3a
1b 2b 3b
1c 2c 3c

So groups are
1a 1b 1c
2a 2b 2c
3a 3b 3c

Groups can only have one a, one and one c - and that combo should be unique


How many weeks?

I think you can do:
1a, 1b, 1c; 2a, 2b, 2c, ..., 20a, 20b, 20c
1a, 2b, 3c; 2a, 3b, 4c, ..., 20a, 1b, 2c (when you get to 20x, wrap around to 1x in the next threesome)
1a; 4b; 7c; 2a, 5b, 8c, ...
1a, 8b, 15c; 2a, 9b, 16c, ...
1a, 10b, 19c; 2a, 11b, 20c, ...
1a, 12b, 4c; 2a, 13b, 5c, ...
1a, 14b, 7c; 2a, 15b, 8c, ...
1a, 18b, 15c; 2a, 19b, 3c, ...
1a, 20b, 19c; 2a, 1b, 20c, ...

and not have any repeated pairs. That's 9 weeks. More weeks are probably possible, just not with this particular scheme.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS