consider magic squares: here, a 3x3 grid where all 3-place rows, columns, and diagonals add to the same number but with the added twist that all the values in the grid are squares of some other number, and all values are unique and real. (so no negatives, repeats or imaginary parts)
The conjecture is that there is some solution. The math minds have not proven it either way as of 2014.
http://www.mathpages.com/home/kmath417.htm
This is just the start of some tools for testing ideas.
needs: in addition to Python, you may need to:
sudo pip install numpy sudo pip install magic_squares