Fitting

Figure 1: The layout problem: You are given a 16×16 square. You want to fill it with rectangles and triangles. Available rectangles: 2×2, 4×3, 7×5, 16×3. (8)×(32), (18)×(8), (288)×(32). All triangles are right isosceles triangles. For every rectangle with an irrational side, there is a triangle with a hypotenuse that matches that side. For every integral side of a rectangle, there is a triangle one of with a nonhypotenuse side that matches it. So, there may be multiple triangles of 2×2×(8), 4×4×(32), 3×3×s(18), 7×7×(98), 5×5×(50), 16×16×(512), and 12×12×(288).