  Heffter arrays are partially filled arrays that have been introduced in [1]
as a tool to construct regular embeddings of graphs on surfaces. These
constructions can be achieved from the solution of a tour problem on the filled
cells of the array, introduced in [3] and called Crazy Knight's Tour Problem.
In particular, the knight's move is seen as the composition of an horizontal
move and a vertical one, where the directions (leftward or rightward, upward or
downward respectively) are prescribed in advance for each row and each column
of the array and each filled cell is mapped to the first filled cell
encountered along that direction. Then, a solution to the Crazy Knight's Tour
Problem is a set of directions such that the resulting move function is a tour
over the array. Here, we consider a particular class of square arrays, and we
construct solutions to the tour problem in some infinite families of these
arrays.
