A squared square <https://en.wikipedia.org/wiki/Squaring_the_square> is an NxN square that's tiled with smaller KxK squares, where no K occurs twice. I've long wondered about squared *tori*, (using the NxN square torus), which may be easier to find than squared squares. (If you don't require the K to be different, there is an amusing example of squared tori — where the tiles are all 1x1 squares — for any Pythagorean hypotenuse, i.e., any N such that N^2 = A^2 + B^2 for integers A, B.) Amusing because the sides of the tiles are not parallel to those of the NxN square. Can there be a smaller NxN squared torus than the smallest squared square? But how about the famous expression 1^2 + 2^2 + 3^2 + ... + L^2 = N^2 for L = 24 and N = 70, the unique nontrivial such equation. QUESTION: --------- Can a 70x70 square torus be tiled with one KxK square tile for each K in the range 1 ≤ K ≤ 24 ??? Possibly in a non-parallel fashion? —Dan