A person is standing at a corner of $4\times4$ square, he would like to travel each block exactly once before exiting from the opposite corner. Is there a way?
Colour each cell black or white like a checker board and suppose the starting point is black. Then the ending point is black. S means starting point and E means ending point.
That person has to walk $4^2-1$ times, so that person must end at a white cell. Not a black cell.