Monkey and banana problem

The monkey and banana problem is a famous toy problem in artificial intelligence, especially logic programming.

Formulation of the problem

A monkey is in a room. Suspended from the ceiling is a bunch of bananas, beyond the monkey's reach. In the corner of the room is a box. How can the monkey get the bananas?

The solution is of course that the monkey must push the box under the bananas, then stand on the box and grab the bananas. However, figuring this out requires a planning algorithm.

In other variants of the problem, the bananas are in a chest and the monkey first has to open chest using a key.