P91 - Knight’s tour.

Another famous problem is this one: How can a knight jump on an N×NN×N chessboard in such a way that it visits every square exactly once?

Hints: Represent the squares by pairs of their coordinates of the form (X,Y)(X,Y), where both XX and YY are integers between 1 and NN. (Alternately, define a Point class for the same purpose.) 

Write a function jumps(N,(X,Y))jumps(N,(X,Y)) to list the squares that a knight can jump to from (X,Y)(X,Y) on a N×NN×N chessboard.  And finally, represent the solution of our problem as a list of knight positions (the knight’s tour).

It might be nice to find more than one tour, but a computer will take a long time trying to find them all at once.  Can you make a lazy list that only calculates the tours as needed?

Can you find only “closed tours”, where the knight can jump from its final position back to its starting position?