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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