Encyclopaedia of DesignTheory: A Kirkman triple system

A Kirkman triple system is a resolvable Steiner triple system. Kirkman had asked, in the Lady's and Gentleman's Diary in 1850,

Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast.
Here is a solution. The girls are called X, A, B, C, D, E, F, G, a, b, c, d, e, f, g.

Day 1 X, A, a E, G, f C, D, g B, F, d b, c, e
Day 2 X, B, b F, A, g D, E, a C, G, e c, d, f
Day 3 X, C, c G, B, a E, F, b D, A, f d, e, g
Day 4 X, D, d A, C, b F, G, c E, B, g e, f, a
Day 5 X, E, e B, D, c G, A, d F, C, a f, g, b
Day 6 X, F, f C, E, d A, B, e G, D, b g, a, c
Day 7 X, G, g D, F, e B, C, f A, E, c a, b, d

Note that {a,b,c,d,e,f,g} is a subsystem of the Steiner triple system.

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Peter J. Cameron
6 August 2002