Chickens and eggs

For weeks now, each day we find one egg broken and eaten. Clearly, this will not do.  There are 22 chickens, including one rooster, in the flock, various breeds, and I started separating them 2 at a time to see if I could discover the culprit, essentially dividing the flock into two areas.  Rather a pain, since now I have to have two feeders and two heated waterers.

Now, the odds are that I will not have to go through the entire flock to find the guilty party, right?  But that's exactly what happened.  Each day I'd remove two hens and the next day there'd be a broken egg in the original coop.  Each night I'd band the two I'd removed the day before so I could identify them if they were out together.  Finally I was down to two hens, having already ruled out the rooster.  I removed one and the one that was left laid and ate her egg the next day.  Hallelujuah!  I'd found the culprit.  I removed her, asked my brother, who is not at all squeamish, to take care of the problem, and put the rest together.  He never came, and the next thing i knew, that %*!@# hen was back in with the rest of them.  AAARRRGGH!

No problem, I thought.  I've banded all except the one.  I just have to find the one without the leg band.  Sneaky chickens that they are, two others had shed their bands. Okay, three is better than 22.  I removed one of the three.  Not guilty.  Two to go.  This morning, I walked into the coop and caught the egg-eating hen red handed--or yolk-beaked, if you will, egg dripping from her beak as she pecked away at her egg.  I was infuriated!  I grabbed her, and wrung her neck on the spot.  I heard the bones crunch.  Then I stomped to the house, tossed her on the ground, and to my amazement, she slowly got up, shook herself, and sat there looking around.  An hour later she was pecking at this and that in the yard, and a while after that, she was in the barn again.

Now I've heard of cats having nine lives, but chickens?  For now, I'm going to let her have the run of the barn.  Who knows?  Maybe her head is screwed on straight, now.