puzzle

a particularly baffling problem that is said to have a correct solution; "he loved to solve chessmate puzzles"; "that's a real puzzler"

a game that tests your ingenuity

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"

be uncertain about; think about without fully understanding or being able to decide; "We puzzled over her sudden departure"