You have a square piece of paper and you do not know its length or width.
What is the minimum number of folds required in order for the paper to only show 1/16 of its original size, 2/16 of it's original size, 3/16 of its original size........15/16 of its original size.
Note: You do not know where halfway marks or quarter marks lie on this piece of paper therefore you must use folds to mark these areas. You are allowed to use folds as guides to make other folds.
other combinations will require selective folding of the triangles achieved by several 4 straight folds(resulting in progressively smaller rectangles) and one cross fold (creating a triangle). I'm not sure if all 16 can be achieved simply through manipulation, but what you could do (cheat) is rip the paper along one or two of the folds which will greatly increase the possibilities.
cheating
