Synonyms for Puzzle (same or very similar meaning)
WordNet sense 1 (a particularly baffling problem that is said to have a correct solution):
puzzler, teaser, mystifierWordNet sense 2 (be a mystery or bewildering to):
amaze, baffle, beat, bewilder, dumbfound, flummox, get, gravel, mystify, nonplus, perplex, pose, stick, stupefy, vexFrom the ODE community, based on WordNetadd/edit