noun (n)

• a state of difficulty that needs to be resolved(noun.state)

  Example:
  She and her husband are having problems.
  Urban problems such as traffic congestion and smog.
  

  Synonym:
  job
  

  source: wordnet30
• a question raised for consideration or solution(noun.communication)

  Example:
  Our homework consisted of ten problems to solve.
  

  source: wordnet30
• a source of difficulty(noun.cognition)

  Example:
  What's the problem?.
  

  Synonym:
  trouble
  

  source: wordnet30
• A question proposed for solution; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt.(noun)

  source: webster1913