The meta post on math question gives three characteristics of math puzzle:
First: "Clever or elegant solution, often an "aha" moment"
But: "That "aha" moment depends on the final answer. What if the answer is 1 or pi? That will be considered an "aha" moment as per this characteristic. Ramanujan gave some equations which helps us to find the value of pi. Those equations are also "aha" but they cannot be considered puzzles"
Second: "Unexpected problem statement"
But:"Does that mean if there is Prof. Halfbrain in the question then it is a puzzle? Of course not."