The checker is standing on the corner field of a n x n chess-board. Each of two players moves it in turn to the neighbour (i.e. that has the common side) field. It is forbidden to move to the field, the checker has already visited. That who cannot make a move losts.
a) Prove that for even n the first can always win, and if n is odd, than the second can always win.
b) Who wins if the checker stands initially on the neighbour to the corner field?
