Date: Wed, 23 Jun 1999 10:46:18 -0600 (CST)
Suppose that the groups are called A, B, C, D, E and F. Imagine them arranged around a wheel with A in the center as in the diagram. The lines indicate that in the first month A will meet with F, B with E and C with D. These three meetings are designated AF, BE and CD.
Continue to rotate the groups around the wheel for the third, fourth and fifth months to produce five months of three meetings each. These meetings can be arranged at three places as follows.
In scheduling the five months of meetings at the three places an attempt has been made to minimize the number of times each group is in any one place.
Your question asked for twelve months with each group meeting each other group at least twice a year, four times in each place. To do this duplicate the first ten months from the fifteen month schedule above. In this ten month period groups A, E and F are in place I four times, groups B and D are in place I three times and group C is in place I only twice. Thus in the remaining two months meetings BC and CD need to be scheduled at I. Simularly in the remaining two months AF and DF need to be scheduled at II and AE and BE need to be scheduled at III. Thus the following schedule will meet your requirements.
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