Kirkman schoolgirls problem

One of the classical combinatorial problems.

In 1850 the Revd T.P. Kirkman published in The Lady's and Gentleman's Diary for 1850 the problem Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that not two shall walk twice abreast. He published his solution in the 1851 edition.

In modern terms this asks for a resolvable Steiner triple system, otherwise known as a Kirkman triple system, on 15 points.

References

• Robin Wilson, "Combinatorics: A Very Short Introduction", Oxford University Press (2016) ISBN 0-19-872349-0