Mondrian Art Puzzles

Author(s):
You’re Mondrian’s mathematical boss. Instead of allowing Mondrian to randomly draw rectangles and colors -you lay out requirements: 1) Mondrian must cover an N by N canvas entirely with rectangles. 2) Every rectangle in the painting must have different dimensions. 3) Mondrian must use as few colors as possible, and rectangles with the same color cannot touch one another. Under these rules, Mondrian must try to minimize his score. A painting’s score is the area of its largest rectangle minus the area of its smallest rectangle.