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Online education may have its uses, but the best education occurs in social settings where a number of people get together to teach and learn.

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Getting people together for educational purposes is a much harder problem than it looks.  People cannot be guaranteed to get along with some arbitrary collection of others.  Ideally there would be enough people that they could be divided into smaller groups of compatible individuals.  This can be a horrendous problem.

Suppose that there are 100 students, who are to be divided into 4 classes of 25.

Is this a simple problem or not?  Well, the answer is given by a binomial coefficient.  There are in fact 242,519,269,720,337,121,015,504 different ways of dividing 100 students into 4 classes of 25.

There are various algorithms for doing this.  One could write the students names on cards, shuffle the deck, and deal out four piles of 25.   Or, the teachers could take turns selecting the most desirable students, one at a time, from a diminishing pool of candidates.  Or, most often, the teachers get together and discuss ways of tweaking last year’s assignments.

These are all simplistic lo-tech solutions to the problem.  They cannot possibly produce good solutions, no matter how clever the teachers are.  Some  true hi-tech methods based on sophisticated algorithms are available and should be used.  One purpose of this website is to discuss good solutions to this problem and others in which good educational environments can be created using social combinatorics, a branch of social technology.

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