problem vs mystifier

problem and mystifier both are nouns.

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

As nouns, mystifier is a hyponym of problem; that is, mystifier is a word with a more specific, narrower meaning than problem:

problem: a question raised for consideration or solution
mystifier: a particularly baffling problem that is said to have a correct solution

problem (noun)	mystifier (noun)
a source of difficulty	a particularly baffling problem that is said to have a correct solution
a question raised for consideration or solution
a state of difficulty that needs to be resolved