In chess, a rook at position hr, ci can move in a straight line either horizontally or vertically (to hr x, ci or hr, c xi, for any integer x). (See Figure 5.11.) A rooks 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 rooks tour for any n-by-n chessboard for any n 1.

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