Ah, egg eating- the #1 trick in a chickens arsenal of Worthless Chicken Tricks. I have had a few egg eaters so I know the frustration you are going through. You can try the golf ball method to see if you can break the egg eaters habit. Place a golf ball in the nests. They can't break it so they give up and evetually stop trying to eat the eggs-sometimes. Or can also blow out an egg then fill the empyt egg with super hot-hot sauce. I've used this method and it worked on the normal birds. Although I did have two young cockerels who liked the hot sauce and wanted some tortilla chips and beer to go along with the hot sauced eggs.
If you can, seperate them all, each with their own nests, to see if you can figure out who the egg eater is. Then get the fry pan out. Now, just as an FYI once a egg eater-always an egg eater. It is a pretty bad habit and ultimately an egg eater has to be debeaked. The egg eater also has a terrific ability of teaching the other chickens to eat eggs, or while the egg eater is commiting his or her crime, the other chickens discover the yummy goodness of eating eggs. It's really a bad habit and hard to break.
It helps to pick the eggs up as soon as possible to prevent the little miscreant from getting to the goods. As far as why they start, sometimes it's typically a calcium deficency, or if they are broody, they will pick at an egg to see if the shell is strong enough for them to bother setting on to brood. Oddly once the broody breaks an egg, they are no longer broody.
Well, I hope this helps you find your culprit. Good luck!