Question 13
A rook starts moving on an infinite chessboard, alternating horizontal and vertical moves. The length of the first move is one square, of the second – two squares, of the third – three squares and so on.
a) Is it possible for the rook to arrive at its starting point after exactly $2013$ moves?
b) Find all $n$ for which it possible for the rook to come back to its starting point after exactly $n$ moves.
a) Is it possible for the rook to arrive at its starting point after exactly $2013$ moves?
b) Find all $n$ for which it possible for the rook to come back to its starting point after exactly $n$ moves.