amaze (v)
baffle (v)
beat (v)
bewilder (v)
dumbfound (v)
flummox (v)
get (v)
gravel (v)
mystify (v)
nonplus (v)
perplex (v)
pose (v)
puzzle (v)
stick (v)
stupefy (v)
vex (v)

Definition: be a mystery or bewildering to
Example: This beats me!. Got me--I don't know the answer!. a vexing problem. This question really stuck me.

puzzle (n)

Definition: a game that tests your ingenuity

puzzle (v)

Definition: be uncertain about
Example: We puzzled over her sudden departure.

mystifier (n)
puzzle (n)
puzzler (n)
teaser (n)

Definition: a particularly baffling problem that is said to have a correct solution
Example: he loved to solve chessmate puzzles. that's a real puzzler.