Here's one, an old classic:
You are stuck in a room with nothing in it, no windows and only one reinforced steel door which is locked. In the centre of the room is a pipe solidly wedged into the floor which, as far as you can tell, goes about 3 feet into the floor and is protruding by about 1 foot. It is too narrow for you to fit your arm in. A voice from the other side of the door tells you that there is a small ball resting in the bottom of the pipe which contains the key to the door, and if you can get it out, you are free to go. If you don't you will surely starve in here.
How do you get the ball out?