A rook is a chess piece that may, on a single turn, move any number of squares

Chapter 51, Problem 51.7

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A rook is a chess piece that may, on a single turn, move any number of squares horizonNote: A standard chess board is an 8 8 grid of squares. tally or any number of squares vertically on the board. That is, if squares A and B are in the same row [or same column] then we are permitted to move the rook from A to B. But if A and B are in neither the same row nor the same column, a move between these squares is illegal. Thus in every row and every column there are 8 2 pairs of squares between which the rook may move. This gives a total of 16 8 2 D 448 such pairs. Suppose a rook is placed on an empty chess board. Can we repeatedly move the rook so that it moves exactly once between each pair of squares in the same row and once between each pair of squares in the same column? Note: When the rook travels between squares A and B, it should traverse either from A to B or from B to A, but not both.