### Abstract

We give a visual construction of two solutions to Kirkman's fifteen schoolgirl problem by combining the fifteen simplicial elements of a tetrahedron. Furthermore, we show that the two solutions are nonisomorphic by introducing a new combinatorial algorithm.It turns out that the two solutions are precisely the two nonisomorphic arrangements of the 35 projective lines of PG(3,2) into seven classes of five mutually skew lines. Finally, we show that the two solutions are interchanged by the canonical duality of the projective space.

Lingua originale | English |
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pagine (da-a) | 887-900 |

Numero di pagine | 14 |

Rivista | THE AMERICAN MATHEMATICAL MONTHLY |

Volume | 118 |

Stato di pubblicazione | Published - 2011 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cita questo

Falcone, G., Pavone, M., & Falcone, G. (2011). Kirkman's tetrahedron and the fifteen schoolgirl problem.

*THE AMERICAN MATHEMATICAL MONTHLY*,*118*, 887-900.