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| Math Central | Quandaries & Queries |
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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 So groups are Groups can only have one a, one and one c - and that combo should be unique |
Joshua,
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.
--Victoria
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