Try to paint the whole field in the same color.
You begin with only 1 field in the upper left corner and paint your way from there.
There are only 2 rules to obey, if you want to maximize the size your active field:
1. The field you want to add must have the same color as your active field!
2. The field you want to add must lie apposed to your active field (meaning that at least 1 side must lie directly next to your active field!).
Easy, isn´t it?
Well then, go ahead and paint your way through all the fields!