  Warnsdorffs rule for a knights tour is a heuristic, i.e., it is a rule that
does not produce the desired result all the time. It is a classic example of a
greedy method in that it is based on a series of locally optimal choices. This
note describes an analysis that determines how good the heuristic is on an 8 X
8 chessboard. The order of appearance in a permutation of the eight possible
moves a knight can make determines the path the knight takes. A computer
analysis is done of the 8! permutations of the order of a knights moves in
Warnsdorffs rule on an 8 X 8 chessboard for tours starting on each of the 64
squares. Whenever a tie occurs for moves to vertices that have the lowest
degree, the first of these vertices encountered in the programming loop is
chosen. The number of permutations of the 8! total that yield non-Hamiltonian
paths is tallied. This will be the same value if we consistently choose the
last of these vertices encountered.
