A closed knight’s tour of a board consists of a sequence of knight moves, where each square is visited exactly once and the sequence begins and ends with the same square. For boards of size where and are odd, a tour is impossible because there are unequal numbers of white and black squares. By deleting a square, we can fix this disparity, and we determine which square to remove to allow for a closed knight’s tour.
"Knight's tours on boards with odd dimensions." Involve 8 (4) 615 - 627, 2015. https://doi.org/10.2140/involve.2015.8.615