Kirkman's tetrahedron and the fifteen schoolgirl problem

Giovanni Falcone, Marco Pavone, Giovanni Falcone

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)887-900
Number of pages14
JournalTHE AMERICAN MATHEMATICAL MONTHLY
Volume118
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • General Mathematics

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