CZ-SK-MO 2016 Problem 6

We put a figure of a king on some $6 \times 6$ chessboard. It can in one thrust jump either vertically or horizontally. The length of this jump is alternately one and two squares, whereby a jump of one (i.e. to the adjacent square) of the piece begins. Decide whether you can choose the starting position of the pieces so that after a suitable sequence $35$ jumps visited each box of the chessboard just once.