Ok, about the triangle puzzle with the hole formed when you rearrange. The one guy was right about the two smaller triangles not being the same angle, therefore the large shape is not a triangle, but a quadrilateral. Here is maybe a more understandable answer...One triangle has an angle of 20.556 and the other 21.801, according to Steve on that site (I'll assume he did his math right). Now, if the large shape was a triangle, it would have an area of 1/2(b*h) = 1/2(13*5) = 32.5. If we take the total areas of the four smaller shapes we get 1/2(5*2) = 5, 1/2(3*8) = 12, one figure with 8, and one with 7. 32.5 - 5 - 12 - 8 - 7 = 0.5 which is half of 1.0. Well, this is only half a square, where does the other half come from you ask? Well, when the green triangle is on top (this triangle has the larger angle of the two) it creates a "concave" hypotenuse, if you will. When you switch the two triangles, it creates a "convex" hypotenuse. If you drew a line from the lower left corner of the big triangle to its upper right corner, and superimposed both shapes in the drawing onto it, you would see that one has a hypotenuse above that line, and one below. The area of that space between the line you drew and either of the hypotenuses is the difference we calculated above (.5). Since there is .5 above and .5 below, we have a total of 1 extra square. That's a long explanation that would have been easier with a picture, but hopefully it's understandable.