5.13 In chess, a rook at position r, c can move in a straight line either horizontally or vertically (to r x, c or ct x, for any integer x). (See Figure 5.11.) A rook's tour is a sequence of legal moves, starting from a square of your choice, that visits every square of the board once and only once. Prove by induction that there exists a rook's tour for any n-by-n chessboard for any n 21 2 Figure 5.11: A rook can move to any of the positions marked with a circle