This is a node about a vicar
that does not
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