Question 136
Manni and Miku play the following game with rooks on an $8 \times 8$ chessboard. At the beginning of the game, Miku places 8 rooks to the squares of the board according to his will. Then both players make moves alternately, Manni starts. On any move, each player shifts exactly one rook along a rank or file (i.e. row or column) by one or more squares in one direction. If a rook moves to a square that contains another rook, the latter is removed from the board; it is not allowed to move a rook over another. A player who is the first to remove a rook from the board wins; however, neither moving nor removing a rook that was moved by the opponent on his last move is allowed. Does either of the players have a winning strategy and if yes then which of them?