vex vs puzzle

vex is not a noun while puzzle is a noun.

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

As verbs, vex and puzzle are synonyms defined as:

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

vex (verb)	puzzle (verb)
be a mystery or bewildering to	be a mystery or bewildering to
subject to prolonged examination, discussion, or deliberation	be uncertain about; think about without fully understanding or being able to decide
change the arrangement or position of
cause annoyance in; disturb, especially by minor irritations
disturb the peace of mind of; afflict with mental agitation or distress