Am I crazy or are my chickens playing tricks on me?

I have 7 hens, three laying boxes (kitty litter boxes filled with bedding).  The girls all seem to prefer the box on the right, although occasionally someone lays an egg in the center. Between them, they lay between 2 and 6 eggs a day.  You can see the set-up below in a photo of the coop before the walls were put on.

Yesterday I went out before I went to work as usual and found 1 egg in the right box.  I thought I'd move it to the center and see if anyone got the hint and maybe lay an egg next to it in the center box.  When I came home from work, I found two eggs in the right box--NO eggs in the center.  I quizzed all family members and no one brought in eggs or moved anything.  Puzzling...

This morning there was another egg (right side box of course).  Again I moved it to the center box.  When I came home, guess what... Six eggs--in the right side box.  NO eggs in the center box.  Can a chicken move an egg like that?  It was lifted at least 3-4 inches and across the gap between the boxes 1-2 inches wide. 

I wish I had a webcam!  Is it really possible that one of my chickens (or maybe more working as a team) are moving eggs like this?