Each square of the three by three grid is painted so that the whole picture has at least the two lines of symmetry indicated. Each grid square is painted one solid color. What is the maximum number of colors that could have been used?
Let the grid be numbered
123
456
789
Based on the symmetry lines the groups that must be the same color are
{5}
{1,3,7,9}
{2,4,6,8}
Thus 3 colors are the maximum that can be used.
+1207 
