Kirkman’s famous problem - 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. Kirkman’s solution is an example of a resolvable design. In this paper, the authors describe how one of them found such a design by looking in the algebraic number field. This is shown to be a particularly fertile field in which several other block design grow. The authors describe about spreads and packings in finite geometries and show how a particular packing in the geometry answers Kirkman’s question. The authors design is shown to be a solution to a certain problem in recreational mathematics called the Fifteen Hats Problem.
Kirkman’s simple arrangement question has led into many varied areas of mathematics.
The authors have posed certain questions at the end and have provided suitable references to help the reader to follow up.
It is an interesting paper. The Kirkman problem is simple to explain to school children but its solution has opened many new areas of interest to the mathematicians.