Here's an idea for a problem in a mystery with a monkey. The monkey
has witnessed the crime, and at some point, or at several points, or
if you lure him into the Scene Of The Crime Room with a Banana, he
mimics some important action from the crime sequence that gives you
an important clue as to what happened.

It seems as though a monkey would be an interesting "character" in a
game with or without this problem.