In the game of chess, a knight in row R and column C may move to row 1 ≤ R' ≤ B and column 1 ≤ C' ≤ B (where B is the size of the board) provided that either
|R - R'| = 2 and |C - C'| = 1
or
|R - R'| =1 and |C - C'| = 2
A knight's tour is a sequence of moves that visits all squares exactly once before returning to the starting point.
a. If B is odd, show that a knight's tour cannot exist.
b. Give a backtracking algorithm to find a knight's tour.