(noun) a particularly baffling problem that is said to have a correct solution
he loved to solve chessmate puzzles
that's a real puzzler
(noun) a game that tests your ingenuity
(verb) be a mystery or bewildering to
This beats me!
Got me--I don't know the answer!
a vexing problem
This question really stuck me
(verb) be uncertain about; think about without fully understanding or being able to decide
We puzzled over her sudden departure