amaze

sense 1: affect with wonder; "Your ability to speak six languages amazes me!"
amaze astonish astound

sense 2: be a mystery or bewildering to; "This beats me!"; "Got me--I don't know the answer!"; "a vexing problem"
perplex vex get puzzle mystify baffle beat pose bewilder flummox stupefy nonplus gravel amaze dumbfound