



 
Hi Rain, I don't think you're going to be too lucky with the numbers if all groups need to have the same size. For 40 people there are 780 (= 40 x 39 / 2) different pairings of people. The small numbers that are divisors of 40 are 4, 5, and 10. In each group of size 4 there are 6 pairs of people, in each group of 5 there are 10 pairs,and in each group of 10 there are 45 pairs. Eight groups of 5 account for 80 pairs, and since 80 is not a divisor of 780 there is no solution using only groups if size 5. Groups of size 10 can be ruled out in the same way. Ten groups of size 4 account for 60 pairs, so if it is possible to do this using groups of size 4 then you will need 13 rounds. That's a lot of activities! I don't know if the required combinatorial design exists though. (They usually don't.) There is a better chance of success if the groups can be of different sizes. Is that possible? Victoria  


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