Shortly after we adopted the girls, they figured out that if they pushed on my bedroom door, it would pop opened. This was never a real problem until we got the puppy. Indeed, even after the puppy, it was almost a year before this ever became a problem. She stays pretty much in place all night and during the day when we were out, she was confined in a small area downstairs. 
This summer, however, we started giving her half the downstairs and up the stairs. We would close the bedroom doors to keep her from a steady diet of Bionicle and Lego pieces, but there was no way to close her from our room. The cats would just pop it opened and let her in. Eventually, being a smart dog, she figured out that her nose was just as powerful as that of a cat and she could pop the door opened herself. I can't tell you the number of balls of yarn she would wrap herself up in or how many shoes she ate.
Finally, this weekend, DH fixed the door so that no one can pop it opened again. He did this while I was helping out at cub camp. I was exhausted and in pain from standing on concrete all day. So after a glass of red wine, to help the foot pain, I headed off to bed. Not thinking too clearly, I let the door close and latch. This was never a problem before. The cats would simply open it if it was latched.
As I relaxed in bed, or rather fell into a wine/pain induced coma, I began to hear the door rattle. Gently at first, and then more of a crescendo, the door would rattle as the cats tried ever harder to push it opened. They were not happy, but I was so exhausted and the thought of putting any weight on my feet did not sound good. So I tried to ignore it. I reasoned that if I opened the door, they would learn that all they had to do was to rattle the door and I would open it.
After a very brief silence, I heard the jingling of the bell on a cats collar from down the hall. It approached ever closer and then I heard Crash! Obviously, one of the cats had taken a running start from down the hall and thrown her body against the door.
That got me out of bed. I limped to the door and opened it. Both cats were lurking in the doorway of Firstborn's room. Nadia was standing looking at my room expectantly and a little guiltily. Georgia was sitting with her back to me acting like nothing at all was happening.
I know the culprit. While she is far more shy around people and far more jumpy around strange noises, new experiences, and movements, Nadia is an insistent cat. She knows what she wants and she will not take no for an answer. Georgia would try the door once and then patiently wait. Nadia would give me hell.
The two cats calmly strutted into the room as I stood there assessing the situation.
I left them there until DH went to bed. As he finished up in the bathroom, I heard the door latch. Great, I thought. I'm going to be hearing it again. Sure enough, the rattling started right after he went to bed. It continued and again, I was too tired to get up. I reasoned with my tired brain that I had to just live with it and let them rattle tonight so that I would have hundreds of sleep-filled, quiet nights in the future. Eventually the noise stopped.
I awoke the next morning with two cats in bet with me and the door opened. Did they figure out how to use the doorknob? No, DH had been awakened by the door rattling and let them in. Inconsistent rewards. They are trained now. So much for ever sleeping with the door latched again.
