See the original puzzle
This is one of those puzzles where the solution is very simple and easy to find, but only if you're looking at it the right way.
So here's what you do:
1. Fold the rectangle in half along a vertical line. Unfold it.
2. Fold the rectangle along a diagonal. Unfold it.
3. There's one last fold, shown in this diagram. (The diagram shows a square, but this works for a rectangle of any dimensions.) Unfold it again.
4. The diagram shows the intersection of two creases (made by steps 2 and 3). Fold the bottom edge of the paper up to this intersection. This is the one third fold.