Of course you take a lateral approach and say that the "worm-eaten paper" is the missing part and therefore the sumof the zeros would of course be zero?
But if you do that, you have to consider that the zeros on the page may form a pattern that looks like a number. Now you have to go over the many possible dimentions of the page and check them all! Thankfully, you have a head start, since you can use this OCR code; all you have to account for now is rotation.