Is it permissible to answer questions in a diverse cultural competition (history, science, art) in order to obtain a financial prize, and is it permissible to inform a friend of the answer in order to share the amount?

The aforementioned answer is not permissible, neither directly nor by assisting, because it involves aiding in evil and elevating its status. It is not befitting for someone who shows signs of uprightness to speak in a way that suggests their knowledge of various forms of wickedness.