Teacher2Teacher 
Q&A #4347 
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From: Carol To: Teacher2Teacher Public Discussion Date: 2000081812:17:18 Subject: Grouping students I spent all afternoon playing with this problem, first with the cylinders. Then I tried listing all possible combinations of 4, then 6, then 8, then 10 students by writing all possible ways students could be paired. Example for 4 studednts A, B, C, and D AA AB AC AD BA BB BC BD CA CB CC CD DA DB DC DD I eliminated the AA  DD diagonal along with the pairs above the diagonal. BA CA CB DA DB DC Then tried to find patterns with the remaining pairs. What I found was the following: Round 1 Round 2 Round 3 DA BA CA CB DC DB If you were to circle round 1 in one color, round 2 in a second color, and round three in a third color, you could see that they are in a symmetric pattern. When you do the same thing with 6 students A,B,C,D,E,F,G you can select pairs for each round by picking student pairs that are in a physical pattern, but not always exactly symmetric in itself, but symmetric with another round. If I could demonstrate this in color, it would be clearer. It is very hard to describe the patterns in words. As I tried to do this with 8 students it was more difficult to find the patterns, but I was able to do it. But 10 students was nearly impossibleor maybe I was getting tired. I think you are correct about looking for a computer program to do this. There should be a way to write a computer or graphing calculator program that could do this for any even number of students. I still want to think about it some more. Carol  Carol
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