DE-BUNDESWETTBEWERB 2008 Problem 4

In a planar coordinate system we got four pieces on positions with coordinates. You can make a move according to the following rule: You can move a piece to a new position if there is one of the other pieces in the middle of the old and new position. Initially the four pieces have positions $\{(0,0),(0,1),(1,0),(1,1)\}$ . Given a finite number of moves can you yield the configuration $\{(0,0), (1,1), (3,0), (2, - 1)\}$ ?