I don't know why but this game even on the lowest quality I'm finding it very difficult to enter the first door. I can't imagine how hard it will be if I'm able to get out of the first room...
I like the badge idea and have only needed to guess a few times, in which I found out how to do it later on. I really like the badge system and button controls. At first I mixed up the buttons and got a few errors from that, but I haven't done that in a while.
For the golden tree and pixelo duck, I know it takes time while with the badge equiped but A) does it reset if you take it off, and B) does it take time during puzzles or on main screen, or idle?