The Mondrian art puzzle

Start with a square grid having n rows and n columns. Split the grid up into at least two squares and rectangles, as long as you don’t repeat the same sized square or the same sized rectangle twice. Once you are done, compute your score M(n), that is the difference between the piece of largest area and the piece of lowest area. What is the best score you can achieve for a fixed value of n? Is there an n such that M(n) = 0?

We will show some recent computational results that give a lower bound on n.

This is joint work in progress with Natalia Garcia Colin and Erika Roldan.