Projective Space Walk for Kirkman's Schoolgirls

Abstract

In 1847 T. P. Kirkman proposed his now classic fifteen schoolgirls problem: “A school-mistress was in the habit of taking her girls for a daily walk. The girls were fifteen in number, and were arranged in five rows of three each, so that each girl might have two companions. The problem is to dispose them so that for seven consecutive days no girl will walk with any of her school-fellows in any triplet more than once” (Ball and Coxeter 1960).