if u squint, you can see that the line of the blue and red triangles isnt really straight, and their angles are different. i guess that makes that hole?
If you use the grid and look at the partially blank squares and the hypotenuse and compare the two, you can see that the amount of blank space differs. (Sorry, it's bit difficult explain)
It dosn't matter that the lines aren't perfectly straight. They are straight enuf to were it dosn't matter. It all depends on the arangments! The yellow and green are streched because the long red one is on the top.
red and blue switch.. Easy.. But the green and orange. They were switched. One of them had 3 extending and other other had 2. When they switch the 3 and 2, the 2 was short.
Good problem that really makes you study the geometry *carefully*.
My only complaint is in regard to the hint, which says it's NOT an optical illusion. Well, uhm...it kind of IS. That's exactly what it is. The precise reason the problem is difficult is the simple fact that that second hypotenuse *appears* to be straight, but isn't quite. How does that not qualify as an optical illusion?
And what is to be made of a hint that tends to lead one *away* from the correct path to the answer? So, Joe Schmoe is eyeballing this problem, thinking to himself, "Gosh, I wonder if that hypotenuse is really straight or not? Hmmm, well, the all-knowing logic guru who designed the site says in the hint that it's NOT an optical illusion, so I guess it must be straight. Dang, where did I put that book on non-Euclidian geometry?"
Dont think its the gradient we need to look, may be i am naive. But i do have a logical explanation. Here it goes,
If we look at the Orange and green rectangle on the first diagram the area covered is 5 * 3 = 15 (Squares).
Re-arranging the rectangle on the bottom one has the area coverage of 8 * 2 = 16 (Squares). But there are only 15 squares available between the orange and and green shapes, therefore one square is left.
Still keeping the overall BIG triangle the same area and throw in the gradient some where in between. Where it fits i dont know?
My only complaint is in regard to the hint, which says it's NOT an optical illusion. Well, uhm...it kind of IS. That's exactly what it is. The precise reason the problem is difficult is the simple fact that that second hypotenuse *appears* to be straight, but isn't quite. How does that not qualify as an optical illusion?
And what is to be made of a hint that tends to lead one *away* from the correct path to the answer? So, Joe Schmoe is eyeballing this problem, thinking to himself, "Gosh, I wonder if that hypotenuse is really straight or not? Hmmm, well, the all-knowing logic guru who designed the site says in the hint that it's NOT an optical illusion, so I guess it must be straight. Dang, where did I put that book on non-Euclidian geometry?"
But I digress. Good problem anyway.
But that's the point...it is most definitely an optical illusion. A good one, too.
If we look at the Orange and green rectangle on the first diagram the area covered is 5 * 3 = 15 (Squares).
Re-arranging the rectangle on the bottom one has the area coverage of 8 * 2 = 16 (Squares). But there are only 15 squares available between the orange and and green shapes, therefore one square is left.
Still keeping the overall BIG triangle the same area and throw in the gradient some where in between. Where it fits i dont know?