An Alien integer program

The ‘Alien Tiles’ game is taken from Clifford Pickover's website (http://www.pickover.com/). It consists of a 7×7 grid of colored cells, initially all red. Each time a cell is clicked then that cell and all cells in the same row and column cycle from red to green to blue to purple and back to red. The objective is to change the color of the entire grid to green, blue or purple. This paper discusses formulations of the problem using mathematical programming.