Stray Cat Doors is a cute casual game I played on my iPad. It is free, and had no advertisements. There are 6 Stages and the whole game took me about 2 hours. It is a puzzle game, where you work your way through a scene to pick up enough puzzle pieces to exit a door. It has some typical puzzle elements - finding clues to codes, 1 slider, inventory to use. It is just challenging enough to have you think about how to use the clues. The levels got more challenging as you moved on.
You can find it wherever you get your apps.
There is a full walkthrough here
Stray Cat Doors WT