See problem in Webster's New World College Dictionary
noun
a question proposed for solution or consideration
a question, matter, situation, or person that is perplexing or difficult
Math. a proposition requiring solution by mathematical operations, constructions, etc.
adjective
presenting a problem of human conduct or social relationships: a problem novel
very difficult to deal with; esp., very difficult to train or discipline: a problem child
See problem in American Heritage Dictionary 4
(prŏbˈləm)
noun
A question to be considered, solved, or answered: math problems; the problem of how to arrange transportation.
A situation, matter, or person that presents perplexity or difficulty: was having problems breathing; considered the main problem to be his boss. See Usage Note at dilemma.
A misgiving, objection, or complaint: I have a problem with his cynicism.
adjective
Difficult to deal with or control: a problem child.
Dealing with a moral or social problem: a problem play.