Puzzles can be solved; they have answers.
But a mystery offers no such comfort. It poses a question that has no definitive answer because the answer is contingent; it depends on a future interaction of many factors, known and unknown. A mystery cannot be answered; it can only be framed, by identifying the critical factors and applying some sense of how they have interacted in the past and might interact in the future. A mystery is an attempt to define ambiguities.
Puzzles may be more satisfying, but the world increasingly offers us mysteries. Treating them as puzzles is like trying to solve the unsolvable—an impossible challenge. But approaching them as mysteries may make us more comfortable with the uncertainties of our age.
So Paul took his stand in the open space at the Areopagus and laid it out for them: "I'm here to introduce you to this God.... He doesn't play hide-and-seek with us. He's not remote; he's near. We live and move in him, can't get away from him!" ~Acts 17