puzzle vs mystify

puzzle is a noun but mystify is not a noun.

Word	Noun	Adjective	Verb	Adverb
puzzle	Yes	No	Yes	No
mystify	No	No	Yes	No

As verbs, puzzle and mystify are synonyms defined as:

Other synonyms of puzzle include amaze, baffle, beat, bewilder, dumbfound, flummox, get, gravel, nonplus, perplex, pose, stick, stupefy, vex.

puzzle (noun)	mystify (noun)
a game that tests your ingenuity
a particularly baffling problem that is said to have a correct solution

puzzle (verb)	mystify (verb)
be a mystery or bewildering to	make mysterious
be uncertain about; think about without fully understanding or being able to decide	be a mystery or bewildering to