First off, I have to warn, I’m not much of a maths wizz, so if I’ve messed up any terms, I apologise (except for ‘maths’, which is the correct Australian way of saying ‘math’ ;))

I was once chatting with someone who was doing a Phd in Mathematics, and he mentioned that he’d solved a problem that a friend of his (who was a teacher) was having, using the branch of mathematics he was expert in (which I think was something like set theory).

The problem is as follows:

There are twenty students in a class. Students are to be paired up for a week, and then rotated, so the following week everyone is working with a different partner. No two students are to be paired together more than once for the nineteen weeks the class is together.

For example, if there were four students:

week 1:

student 1 and 2 work together; student 3 and 4 work together

week 2:

student 1 and 3 work together; student 2 and 4 work together

week 3:

student 1 and 4 work together; student 2 and 3 work together

I can work it out for ten students by hand, but there’s supposedly a mathematical way of doing it, which can be extended to very large numbers of students. Do any of the wise folk here have any suggestions?