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| Math Central | Quandaries & Queries |
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Question from Daniel: I am organizing team activities for a summer camp. We have 14 teams and 7 rotations and 7 different games. every team will play a different game each rotation. Where I am having trouble is I would like each team to play a different team each rotation without a repeat. Is that possible? if so what is the formula? |
Hi Daniel,
If I understand properly then yes, it is possible. It is actually possible for 13 consecutive days. Here is a schedule. The 14 positions in each sequence are the 14 teams. The numbers indicate who plays who. The zeros play each other, the ones, etc. On Day 1 the games are 1v3, 2v4, 5v7, 6v8, 9v11, 10v13, 12v14.
Day 1 : (0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 6, 5, 6)
Day 2 : (0, 1, 1, 0, 2, 3, 3, 2, 4, 5, 5, 6, 6, 4)
Day 3 : (0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 4, 6, 5)
Day 4 : (0, 1, 2, 3, 1, 0, 3, 2, 4, 5, 6, 5, 4, 6)
Day 5 : (0, 1, 2, 3, 2, 4, 5, 6, 0, 1, 3, 4, 5, 6)
Day 6 : (0, 1, 2, 3, 3, 4, 5, 6, 1, 0, 2, 5, 6, 4)
Day 7 : (0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6)
Hope this makes sense.
—Victoria
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