Applications of Student Activity Problems for Some Kirkman Type Problems

Vites Longani, Decha Samana, Sasisophit Buada

Abstract

In this paper we apply the ideas from recent works on Student Activity Problems in proposing a theorem on some Kirkman type problems. That is, we find that for any prime number $p\geq 3$ it is possible for a school teacher to take $p^2$ school girls on a walk each day of the $p+1$ days, walking with $p$ rows of $p$ girls each, in such a way that each pair of girls walk together in the same row on exactly one day.