Knight’s Tour

Chess and Math: A Closer Look at the Knight’s Tour

Alright, we are going to talk about the Knight’s Tour, “getting the Knight to visit all 64 squares only once.” In this article I found written by Patrick JMT for the US Chess Federation, he mentions that Euler has found a way to create his own open and closed Knight’s Tour. To clarify for those who don’t know much about chess, such as myself, a closed tour is when the Knight is able to end on the space it started and continue to follow the same sequences to recreate a new tour again and again. For an open tour, it’s when the Knight has visited all spaces but wasn’t able to end where it started. Relating this to graph theory, this would be paths and circuits.

On the topic of graph theory, Patrick mentions how the squares can be vertices and the moves made would be edges, creating a complex map of how the Knight would move. That type of graph was shown to us in 3D printed form in class.

Also in the article there is a graph called a Bipartite graph that would represent 32 black/white tiles  and  since the “Knight always alternates the colors of the squares it visits: if the Knight stands on a black square, it can only travel to a white square and vice versa.” This makes the Bipartite graph connect to spaces of which the Knight can move from one white square to multiple black squares, in other words plots, where you can move from one space to another.