Your goal is to make two squares of the same size from a set of rectangles. Each of the rectangles has an aspect ratio of 1:2.

Select two sets of rectangles from the list:

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 16, 17, 18, 21, 23, 31

Some of the rectangles will be in both squares, no rectangle will be repeated in one square. No gaps or overlaps, one tiling is unique and the other has a sub-rectangle that can be flipped. Only the short side of each rectangle is listed.

This time I think it's only fair to allow computers. However good hand solvers will probably still be able to hand solve this.