Mind games.  Well, perhaps not what that means between people …

We are speaking here of the simple enchantment of using your mental skills to solve a problem, whether it is practical or not.

Someone raises a question that causes us to think.  It is the thinking, the mental exercise, that becomes addictive … much as some are addicted to physical exercise.  It is the challenge to swim that river or climb that mountain or to jump that gap.

Mathematically, there is great satisfaction in ‘cracking a hard nut.’  The Danish mathematician, Piet Hein, observed that “Problems worthy of attack prove their worth by fighting back.”

Solving a (difficult) problem is especially satisfying if we gained a new insight and learned to think in a new way.