Start with a square as shown, whose perimeter is
800 inches. Penelope folds this in half along the
horizontal dotted line. She then folds the result in
half along the vertical dotted line shown, and so on,
for some number of similar alternating folds (horizontal then vertical). How many
folding-in-half steps does Penelope need to do in order to get the perimeter of the
resulting quadrilateral to be 100 inches?