Check the air cells on the 3 eggs you found. With the summer heat, those air cells would have certainly grown in a weeks time, if they were the original 3.
Look for hidden nest. Look for possibility of a snake eating the eggs, or a rat. Rats have been known to roll an egg out of the nest and to their tunnel. A snake will eat eggs without a trace.
IMO, it's not possible for hens to eat a week's worth of eggs without leaving some yolk or shell debris behind. Check UNDER the bedding in the nest. If they've been eating eggs, while there may not be any discernible goo at the top, the bottom of the bedding might have accumulated yolk/albumen which would have dried and glued the bedding to the bottom of the nest.