Given an nxn chessboard size, a king is placed in a box
arbitrary coordinate ( x , y) . The problem is to determine the n ^ 2-1
Figure movements so that all board squares are visited once, if there is such a sequence of movements .

The solution to the problem can be expressed as a matrix of dimension nxn representing the chessboard. Each element ( x , y) of this matrix solution
k contain a natural number indicating the order number that has been
accessed box coordinates ( x , y) .

The algorithm works in stages at each stage k deciding where to
moves .

As there are eight possible moves in each step , this will be the
maximum number of children that will be generated by each node .
As for explicit restrictions , the way in which we defined
structure representing the solution ( in this case a two dimensional array of
natural) numbers , we know that its components can be numbers
between zero (indicating that a cell has not been visited yet) n ^ 2 , which is the order of the last possible move . Initially the board is filled with zeros and there is a 1 only in the original box ( x0 , y0 ) .

Implied restrictions in this case will limit the number of children who
generated from a square by checking the movement does not take the king off the board or on a box previously visited .
Having defined the structure that represents the solution and the restrictions
I will use to implement the algorithm that solves the problem just use the general scheme , obtaining :


The mov_x and mov_y variables contain the legal moves of a King
(according to the rules of chess), and are initialized at the beginning of the main program by MovimientosPosibles case:

I have implemented well in Mathematica