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Grouping Students Problem  Combinatorics?
Posted:
Apr 14, 2016 10:28 AM


I am a high school science teacher and I am looking to somehow figure out how to have my 24 students have set groups of two, three, and four.
For Example (in the first marking period):
Duo Groups AB CD EF GH IJ KL
Trio Groups ACE BDF GIK HJL
Quartet Groups ???? ???? ????
CONDITIONS 1. There should be no two students that are in multiple groups with each other.
ex) AB, ABC, BCDE (A and B are together in the Duo and Trio. B and C are together in the Trio and Quartet.)
2. Every student must be in a duo, trio, or quartet.
ex) AB, ACE, AFGL (Student A is in a Duo, Trio, and Quartet.)
3. By the end of the school year (four marking periods) each student will have interacted with every other student  as few repeats as possible. (This means that in one marking period one student will have interacted with six others. If there are four marking periods and this student interacts with six each marking period they should be able to interact with everyone in the 24 student class and have just one repeat.)
HELP!!!!!!
I know this has something to do with combinations, but there are so many conditions that I feed overwhelmed. I don't have much programming experience outside of Excel/Google Docs and I know this can't be done by hand. Any advice would be appreciated.



