This is a node about a vicar and schoolgirls that does not involve the News of The World.

In 1850 the Reverend Thomas Penyngton Kirkman proposed the following problem in combinatorics in the Lady's and Gentleman's Diary

Fifteen young ladies of a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk abreast more than once.

It is possible (and not too hard) to find an arrangement of the schoolgirls that satisfies Kirkman's requirement. There are seven essentially different solutions. Here is one of them. If you can't do it, try the same problem for nine schoolgirls and four days which is a bit easier. In general if n is a positive integer which is congruent to 3 modulo 6 then it is possible to arrange n schoolgirls into triples for (n-1)/2 days in such a way that no two schoolgirls are in the same triple twice. This result was proved by Ray-Chaudhuri and Wilson in the seventies.

In mathematical terms this is a question about Steiner triple systems.

Some historical information was sourced from http://www-groups.dcs.st-and.ac.uk/~history/

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