IMAC 2007 Problem 3

The $m \times n$ chessboard is colored by black and white. In one step, two neighbouring squares are selected (squares with a common side) and their color changes according to the follwing way:

• white becomes black,
• black become red,
• Red becomes white. For which $m$ and $n$ , these steps can change the colors of all the initial squares from white to black and from black to white?