# The Kirkman Schoolgirls Problem

## by Dana Ernst

Published November 13, 2015 in Science

In 1850, the Reverend Thomas Kirkman, posed an innocent-looking puzzle in the Lady’s and Gentleman’s Diary, a recreational mathematics journal:

“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 “abreast” means “in a group,” so the girls are walking out in groups of three, and each pair of girls should only be in the same group once. It turns out that this problem is harder than it looks. Is it even possible? We will begin by tinkering with a simpler problem and then spend some time playing with Kirkman's original problem. Time permitting, we will also discuss generalizations of the problem that form the backbone of a branch of mathematics called combinatorial design theory.

This talk was given at the Northern Arizona University Friday Afternoon Mathematics Undergraduate Seminar (FAMUS) on Friday, November 13, 2015.