For the hole punching, I can see how to get E, in fact that is what I put for the answer. Not because I got it but because you can reason it out. However this is a horrible problem. You actually cant even fold it in real life, you just have to visualize it.
Heres how I reasoned it, hope it helps:
Step 1) You know for a fact there must be a hole on the top left, since that has never been moved. However this doesnt eliminate anything, but its just to point out that its there.
Step 2) Also note that when we do the first fold we are folding from the bottom up. After this you can say all of the paper int he top left quarter of the page are remaining where they are.
This means that when we unfold we will have a hole in the top left, and the bottom left. This eliminates A,B,C and leaves D and E.
Step 3) Next step, is to look at D. In order to make D, you would need a hole to the right of where the hole we orginally have is. So when we unfold and do the flip from left to right, we have that hole. However we dont have that. So we are only left with E.
Also I just looked at it again. The fold has to go from the top left to bottom right. Even though you cant realistically make this fold. Imagine it in a term of layers in the top left corner.
In step 1 you fold in half going up. Now you have 2 layers in the top left corner. After that you fold from right to left. This means you have 2x2 = 4 layers in the top left corner. Now out of those 4 layers you are taking 1 (why 1? because thats the only amout that works.) layer and you are folding that to the bottom left. This means that when you look at the quarter page piece, you have two triangles (like in step 3). However, the top left half has only 3 layers where hte bottom right has 5 layers. Now we put our hole punch in the top left. After that we unfold it so that we have 4 layers on each half (step 3 triangles) of the 1/4 page square. Also you have to imagine that the hole is temporarily covered since we just covered ti when we unfolded. Right now you should look exactly like Step 2, however you should know in the back of your mind you still have that hole in the top left corner. Now we unfold to form step 1. When we unfold, the part that covered the square is now in the top right. However there was no hole there. And we still have our hole in the top left (where there are now 2 layers) and we have 1 hole in the top right (where there is also 2 layers, 1 with the hole, and then one without the hole under it that we cannot see). Now we fold from step 1 into a whole page. We get one in the top left, one in the bottom left (unfolded the 2 layers), and then we get one in the bottom right (unfolded the two layers again).
Holy ****