puzzler vs mystifier

puzzler and mystifier both are nouns.

Word	Noun	Adjective	Verb	Adverb
puzzler	Yes	No	No	No
mystifier	Yes	No	No	No

As nouns, puzzler and mystifier are synonyms defined as:

puzzler and mystifier: a particularly baffling problem that is said to have a correct solution

Other synonyms of puzzler include puzzle, teaser.

puzzler (noun)	mystifier (noun)
a particularly baffling problem that is said to have a correct solution	a particularly baffling problem that is said to have a correct solution