Dan asked ... > Hmm, what about other rectangles also with area pi^2/6 ? > For example the pi/sqrt(6) x pi/sqrt(6) square. and I replied ... No, you need one edge of the rectangle to be at least 1.5, if the squares are placed othogonally. It looks even worse if they're rotated 45 degrees. But pi/2 x pi/3 looks like a possibility. This was too optimistic: With orthogonal placement, any packable rectangle must have a larger dimension >= 1 + 1/3 +1/4 = 1.58333... or smaller dimension >= 1/2 + 1/3 + 1/4 = 1.08333... But pi/2 x pi/3 is 1.5707... x 1.047..., which fails both criteria. It doesn't look like rotating any of the squares helps, but I haven't done the arithmetic to check this. Perhaps things go the other way: Maybe only the 1 x pi^2/6 rectangle works. Rich