This question asks you to examine ways in which this gnomon can be cut into pieces that can then be reassembled to form squares. The several cuts are to be of length 1 perpendicular to the sides of the gnomon. The pieces are to have integer side-lengths.

Two ways of assembling pieces to make squares are the same if the pieces forming one square can be paired off with the pieces forming the other and paired pieces can be superimposed on one another.

Find all ways of answering this question.

So far I have found out that the gnomon is 33 squared.
I have tried to solve this problem in many ways but I am yrt to exceed. I will keep trying to solve this problem.

Obviously you can't make a single square (since the side would have to be sqrt(33). But there are many ways you can make many squares.

Cut the gnomon into 1x1 pieces and there are lots of possibilities: a 4x4, a 3x3 and two 2x2s for instance or a 5x5 and 2 4x4s - or 33 1x1s for that matter.

If you bar 1x1 cuts, then cutting 8 2x1 pieces and 3 3x1 pieces gives you 1 3x3 square and 6 2x2s (or a 3x3, a 4x4, and 2 2x2s).

And so on.