Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Combinatorial Problems Arising from English Country Dance

Robert A. Messer

A popular form of folk dance is English country dance.
In one simple English country dance, four couples dance as two groups of two couples.
As the dance progresses, each couple moves to a new position and dances with another couple.
Can you have such a dance where each couple dances in each of the four positions
with each of the other three couples?
What are other mathematical restrictions on such dances?