puzzle

(noun) a particularly baffling problem that is said to have a correct solution. Synonyms: puzzler, mystifier, teaser. Examples: "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. Synonyms: perplex, vex, stick, get, mystify, baffle, beat, pose, bewilder, flummox, stupefy, nonplus, gravel, amaze, dumbfound. Examples: "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. Examples: "We puzzled over her sudden departure."