problem vs brain-teaser

problem and brain-teaser both are nouns.

Word	Noun	Adjective	Verb	Adverb
problem	Yes	No	No	No
brain-teaser	Yes	No	No	No

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

problem (noun)	brain-teaser (noun)
a source of difficulty	a difficult problem
a question raised for consideration or solution
a state of difficulty that needs to be resolved