Nouns

(n)puzzle, puzzler, mystifier, teasera particularly baffling problem that is said to have a correct solution“he loved to solve chessmate puzzles”, “that's a real puzzler”
(n)puzzlea game that tests your ingenuity

Verbs

(v)perplex, vex, stick, get, puzzle, mystify, baffle, beat, pose, bewilder, flummox, stupefy, nonplus, gravel, amaze, dumbfoundbe a mystery or bewildering to“This beats me!”, “Got me — I don't know the answer!”, “a vexing problem”, “This question really stuck me”
(v)puzzlebe uncertain about; think about without fully understanding or being able to decide“We puzzled over her sudden departure”